A group of 4 adults and 5 children is visiting an amusement park.
Admission is $15 per adult and $9 per child. Find the total cost of
admission for the group.
​

Answer:

x = 4

Step-by-step explanation:

Simplify the equation 5x + 4y = 8 to get y = 2 - [tex]\frac{5}{4}[/tex] x

then substitute the y into 2x - 3y = 17 to get the answer. sorry im not good at explaining but it should be right.

To find the x-value of the solution to the system of equations, we can use the method of substitution. Solve one equation for x, substitute it into the other equation, and solve for y. Finally, substitute the value of y back into the expression for x to find the x-value.

To find the value of x in the system of equations, we can use the method of substitution. Firstly, solve one of the equations for x or y. Let's solve the second equation for x:

2x - 3y = 17 → 2x = 17 + 3y → x = (17 + 3y)/2

Now substitute this value for x into the first equation and solve for y:

5((17 + 3y)/2) + 4y = 8 → 17 + 3y + 4y = 8 → 17 + 7y = 8 → 7y = -9 → y = -9/7

Finally, substitute the value of y back into the expression we found for x:

x = (17 + 3(-9/7))/2 → x = (17 - 27/7)/2 → x = (119/7 - 27/7)/2 → x = 92/7/2 → x = 92/14 → x = 46/7

Therefore, the x-value of the solution to the system of equations is 46/7.

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Answer:

9.2 gallons

Step-by-step explanation:

18.4/2 = 9.2 gallons

False. The answer is -4

Answer:

the measure of the obtuse base angle of the trepezoid is 111.

Step-by-step explanation:

An isosceles triangle has one vertex angle and two congruent base angles. Also, we know that the sum of all angles in a triangle must equal 180 degrees. So we can say that:

Vertex Angle + Base Angle + Base Angle = 180.

Vertex Angle + 2 x (Base Angle) = 180.

2 x (Base Angle) = 180 - Vertex Angle

2 x (Base Angle) = 180 - 42

2 x (Base Angle) = 138

Base Angle = 69

Also, we know that angles on one side of a straight line always add to 180 degrees.

So we can say that:

Base Angle + ? = 180

? = 180 - Base Angle

? = 180 - 69

? = 111

So, the measure of the obtuse base angle of the trepezoid is 111.

It is B

-2 =3(-1) + 1

Answer:

D

Step-by-step explanation:

This is called "implication". So if A (is true), then B MUST be true. If B is false, the implication is false. In all other cases, the implication is true. Suppose A is false, then it doesn't matter what B is, the implication is true, since we don't care what B is.

It's a bit confusing I suppose. Below is a truth table using P and Q in stead of A and B.

Final answer:

The correct answer is D: If A is true, then B must be true. This represents a logical conditional where the statement is true unless the antecedent A is true and the consequent B is false.

Explanation:

The statement "If A, then B" is a logical conditional, which can be represented as A
ightarrow B in logical notation. This statement best matches option D: If A is true, then B must be true. In logic, the only time a conditional statement is false is when the first part (the antecedent A) is true and the second part (the consequent B) is false. Otherwise, the statement is considered true, regardless of the individual truth values of A or B. This includes when A is false; the truth value of B does not affect the truth value of the conditional in this case. Therefore, if A is true, the conditional obliges B to also be true for the statement to remain true.

Answer:

(4,4), (2,8)  (4,8)  and all points in the shaded region as attached below

Step-by-step explanation:

This question is on solutions for inequalities equations

Give the equation as;

x+2y ≥ 10.......................................rewrite the equation for graphing purposes

x+ 2y = 10.............................................compose a table for values of x with corresponding values of y

x  -2    0   2  

y   6    5    4

Plot and shade the wanted region as show in the attached graph

For example point (4,4)  or point (2,6) will satisfy the  inequality  x+2y ≥ 10 as;

(4,4)........ x+2y ≥ 10------4+2(4)  ≥ 10

20 ≥ 10 ,,,,,,,,,,,,,,,,,,which is okay

15/2.0=7.5. The average velocity of the person is 7.5.

For this case we must find the value of the variable "x" of the following equation:

[tex]12 = x + 3[/tex]

So, we follow the steps:

Subtracting 3 from both sides of the equation we have:

[tex]12-3=x+3-3[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]9 = x\\x = 9[/tex]

Thus, the value of x is 9.

Answer:

[tex]x = 9[/tex]

Answer:

see explanation

Step-by-step explanation:

Using the rules of exponents

• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

(a)

[tex]27^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{27}[/tex] = 3

(b)

[tex]25^{-\frac{1}{2} }[/tex]

= [tex]\frac{1}{25^{\frac{1}{2} } }[/tex] = [tex]\frac{1}{\sqrt{25} }[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

B

Step-by-step explanation:

formula   s =4*pi*r^2

s=4(3.14)(3^2)

s = 12.56(9)s= 113.04

Answer:

x=√2, x=-√2, x= 3 and x=-3

Step-by-step explanation:

We need to solve the equation x^4 - 11x^2+18=0

We can replace x^4 = u^2 and x^2 = u

So, the equation will become

u^2 -11u+18 = 0

Factorizing the above equation:

u^2 -9u-2u+18 =0

u(u-9)-2(u-9)=0

(u-2)(u-9)=0

u=2, u=9

As, u = x^2, Putting back the value:

x^2 =2 , x^2 =9

taking square roots:

√x^2 =√2 ,√x^2=√9

x=±√2 , x = ±3

so, x=√2, x=-√2, x= 3 and x=-3

Final answer:

The real zeros of the polynomial equation x^4 - 11x^2 + 18 = 0 are found by factoring the equation as a quadratic in x^2, which yields the real zeros x = 3, x = -3, x = √2, and x = -√2.

Explanation:

To find the real zeros of the polynomial equation x4 - 11x2 + 18 = 0, we can attempt to factor it. Notice that the equation resembles a quadratic in form, with x2 taking the place of x. If we let y = x2, our equation becomes y2 - 11y + 18 = 0, which is a quadratic equation.

Factoring the quadratic equation gives us (y - 9)(y - 2) = 0. Thus, the solutions for y are y = 9 and y = 2. Since y = x2, we now solve for x by finding the square roots of these solutions.

For y = 9, the values of x are x = 3 and x = -3. For y = 2, the values of x are x = √2 and x = -√2. Therefore, the real zeros of the original polynomial equation are x = 3, x = -3, x = √2, and x = -√2.

You can use this equation to find the axis of symmetry or the vertex of the quadratic equation as long as it is in standard form

X= (-b/2a)

The answer is x=2

Answer:

The answer will be x = 2.

Step-by-step explanation:

Answer:

[tex]\large\boxed{A=25\pi}[/tex]

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

We have the center A(-3, 3) and the point on the circle B(1, 6).

The radius is equal to the distance between the center and the any point on the circle.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute:

[tex]r=\sqrt{(1-(-3))^2+(6-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex]

[tex]A=\pi(5^2)=25\pi[/tex]

The area of the circle centered at A(-3, 3) and passing through B(1, 6) is 25π square units.

The subject of this problem is geometry, specifically about the area of a circle.To find the area of a circle, we need to know the radius. Since B is on the circle, AB is the radius. The area (A) of a circle is found using the formula A = πr², where r represents the radius of the circle. Here, the radius of the circle can be determined by finding the distance between the center A(-3, 3) and a point on the circle B(1, 6).

The formula for distance between two points in a plane is √[(x₂ - x₁)² + (y₂ - y₁)²]. Substituting values, we get r = √[(1 - -3)² + (6 - 3)²] = √[(4)² + (3)²] = √[16 + 9] = √25 = 5. Therefore, the radius is 5.

Substitute r = 5 in the area formula: A = π * (5)² = 25π square units.

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Answer:

[tex]\large\boxed{(3x-7)(3x-5)=9x^2-36x+35}[/tex]

Step-by-step explanation:

[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(3x-7)(3x-5)\\\\=(3x)(3x)+(3x)(-5)+(-7)(3x)+(-7)(-5)\\\\=9x^2-15x-21x+35\qquad\text{combine like terms}\\\\=9x^2+(-15x-21x)+35\\\\=9x^2-36x+35[/tex]

Answer:

C

Step-by-step explanation:

Given ΔLMN and ΔPQR are similar, then

∠L, ∠P and ∠M, ∠Q and ∠N, ∠R are congruent

Hence ∠L = ∠P = 80° → C

Answer:

The Answer is C, 80 degrees

Step-by-step explanation:

Answer:

y = 1

x = 4

{x,y} = {4,1}

Step-by-step explanation:

[2]

x - 3y = 1

 + 3y       +3y

x = 3y + 1

[1]

x + 3y = 7

(3y + 1) + 3y = 7

      - 1            - 1

(3y) + 3y = 6

6y = 6

6      6

y = 1

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

x = 3y + 1

y = 1

x = 3(1) + 1

x = 4

y = 1

x = 4

{x,y} = {4,1}

let's notice that the center of the circle is at the orgin, and that the distance from the center to an endpoint B is its radius.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ O(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]

[tex]\bf \stackrel{radius}{r}=\sqrt{(4-0)^2+(5-0)^2}\implies r=\sqrt{4^2+5^2} \\\\\\ r=\sqrt{16+25}\implies r=\sqrt{41} \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{0}{ k})\qquad \qquad radius=\stackrel{\sqrt{41}}{ r} \\\\\\ (x-0)^2+(y-0)^2=(\sqrt{41})^2\implies x^2+y^2=41[/tex]

Answer:

The correct answer is option B

Step-by-step explanation:

B.  x2 + y2 − 41 = 0

To solve the inequality, you need to isolate/get x by itself:

171 > -6x    Divide -6 on both sides [dividing/multiplying a negative number on

-28.5 < x      [dividing/multiplying a negative number in an inequality causes the sign (<, >, ≤, ≥) to flip]

-28.5 < x    [x is a number greater than -28.5]

So your graph should have an open circle at -28.5 (the first small line next to -28), and the arrow pointing to the right since x is greater than -28.5 (increasing)      The 1st option is your answer

[use the o---> and put it at -28.5]

Answer: im not even joking im trying to answer the same question rn because i have a math test tomorrow and havent done any of the unit yet

Step-by-step explanation:

To solve the equation (x - 3)(x + 9) = -27, we simplified and set the quadratic equation to zero, which leads to solutions x = 0 or x = -6. We need to cross-verify this with the original equation as the student suggested different solutions.

To find a solution to the equation (x - 3)(x + 9) = -27, we can start by simplifying the left side of the equation. We'll distribute the terms:

x² + 9x - 3x - 27 = -27

Then we combine like terms:

x² + 6x - 27 = -27

To make it easier to solve, we want to set the equation to zero:

x² + 6x - 27 + 27 = 0

x² + 6x = 0

We factor out an x:

x(x + 6) = 0

Now, we can use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero:

x = 0 or x + 6 = 0

Which gives us the solutions:

x = 0 or x = -6

But the student has mentioned that the solutions are x = 3 or x = -7. To double-check, we substitute these values back into the original equation:

(3 - 3)(3 + 9) and (-7 - 3)(-7 + 9)

Both expressions simplify to an identity. Thus, there may be a mistake in our initial simplification, and we should review it to ensure accuracy.

Step-by-step explanation:

i) An intersecting system of linear equations

A system of linear equations comprises of two or more linear equations. Linear equations are simply straight line equations with a given slope and a unique y-intercept .

Solutions to systems of linear equations can be determined using a number of techniques among them being;

Elimination method

Substitution method

Graphical method

The graphs of a system of linear equations will intersect at a unique single point if the lines are not parallel.

An example of intersecting system of linear equations;

y = 2x -5 and y =5x + 4

The two lines will intersect at a particular single point since the slopes are not identical. The attachment below demonstrates this aspect.

ii) A parallel system of linear equations

Two lines are said to be parallel if they have an identical slope but unique y-intercepts. Parallel lines never intersect at any given point since the perpendicular distance between them is always constant.

Thus a parallel system of linear equations has no solution. An example of parallel system of linear equations;

y = 3x - 4 and y = 3x + 8

The attachment below demonstrates this aspect.

iii) A coincident system of linear equations

A system of linear equations is said to be coincident if the two straight lines are identical. That is the lines have an identical slope and y-intercept. Basically, we are just looking at the same line. Two parallel lines can also intersect if they are coincident, which means they are the same line and they intersect at every point.

Therefore, this system of linear equations will have an infinite number of solutions.

Answer:

8 - 6x

Step-by-step explanation:

just trust me the other guy's wrong

Answer:

2x^(10)y^(12)

Hope This Helps!   Have A Nice Day!!

Answer:

The correct answer is 2X¹⁰Y¹²

Step-by-step explanation:

Points to remember

identities

Xᵃ * Xᵇ = X⁽ᵃ⁺ᵇ⁾

Xᵃ/Xᵇ = X⁽ᵃ⁻ᵇ⁾

To find the equivalent to given expression

It is given that,

60X²⁰Y²⁴/30X¹⁰Y¹²

Using identities we can write,

60X²⁰Y²⁴/30X¹⁰Y¹² = (60/30) * (X²⁰/X¹⁰) * (Y²⁴/y¹²)

  = 2 * X⁽²⁰ ⁻ ¹⁰⁾ * Y⁽²⁴ ⁻ ¹²⁾

  = 2 * X¹⁰ * Y¹²

  = 2X¹⁰Y¹²

The correct answer is 2X¹⁰Y¹²

Area of a triangle= base • height/2;

A=17•4/2= 17•2=34 ft^2

The answer is:

The sixth option,

[-6,6]

To solve the problem, we need to find which of the given options match with the solution to the inequality. As we know, solving inequalities is almost the same that solving equalities, we need to isolate the variable and then, find where it satisfies the given condition (inequality)

So, solving the inequality we have:

[tex]-3x^{2} +1\leq -107\\-3x^{2}\leq -107-1\\-3x^{2} \leq -108\\3x^{2} \leq 108\\x^{2} \leq \frac{108}{3}\\\sqrt{x^{2} } \leq \sqrt{36}\\ x^{2\leq } +-36\\(x-6)(x+6)\leq 0[/tex]

Therefore, we have that the solutions to the inequality are:

First solution:

[tex]x-6\leq 0\\x\leq 6[/tex]

Second solution:

[tex]x+6\leq 0\\x\leq-6[/tex]

Hence, the correct option is the sixth option, the solution is described by the following solution set :

[-6,6]

Have a nice day!

Answer: Sqrt(36/16)

sqrt(36/16)=6/4=3/2 rational

Answer:I believe the answer is 12 because it takes 4, 1/4 unit cube to make 1 cubic unit so to make 3 cubic units you need 12, 1/4 unit cubes if that makes any sense. :) Please make Brainliest if this helped.

Answer:

28 grams

Step-by-step explanation:

1 cup is 8 grams of fiber, since a half a cup is 4 you times it by 2

then 8x3 because you're multiplying the fiber of one cup by 3. which equals 24, but you still have a half of cup of oats left. and since 4 grams equal a half a cup you just simply add 4 onto 24 which equals 28

Answer:

28 grams

Step-by-step explanation:

because i a mulpitplyed the numbers to get my answer

Answer:

-2p² − 11p − 35

Step-by-step explanation:

Simplifying:

-2(p + 4)² − 3 + 5p

-2(p² + 8p + 16) − 3 + 5p

-2p² − 16p − 32 − 3 + 5p

-2p² − 11p − 35

This is also the standard form.

Answer:

-2p^2 - 11 p - 35

Step-by-step explanation:

Please, use " ^ " to indicate exponentiation.  Thus:

–2(p + 4)^2 – 3 + 5p

Now perform the exponentiation first, obtaining:

-2(p^2 + 8p + 16) - 3 + 5p, or

-2p^2 - 16 p - 32  - 3 + 5p

Now rearrange these terms in descending order by powers of p:

-2p^2 - 11 p - 32  - 3, or

-2p^2 - 11 p - 35