The value of y varies inversely as the square of x, and y=4, when x=3.

Find the value of x when y=9

The number of adult tickets sold is 165 and number of students tickets sold were 35

Solution:

Let "a" be the number of adult tickets sold

Let "s" be the number of student tickets sold

Cost of 1 adult ticket = $ 50.00

Student tickets are 50% less than adult tickets

Cost of 1 student ticket = Cost of 1 adult ticket - 50 % of Cost of 1 adult ticket

[tex]\rightarrow 50.00 - 50 \% \text{ of } 50.00\\\\\rightarrow 50 - \frac{50}{100} \times 50\\\\\rightarrow 50 - 25 = 25[/tex]

Thus Cost of 1 student ticket = $ 25

Given that a concert venue can hold 200 people

So we get,

number of adult tickets sold + number of student tickets sold = 200

a + s = 200 ----- eqn 1

The venue was sold out and made a revenue of $9125 for one event

So we can frame a equation as:

number of adult tickets sold x Cost of 1 adult ticket + number of student tickets sold x Cost of 1 student ticket = $ 9125

[tex]a \times 50.00 + s \times 25 = 9125[/tex]

50a + 25s = 9125 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "s"

From eqn 1,

a = 200 - s --- eqn 3

Substitute eqn 3 in eqn 2

50(200 - s) + 25s = 9125

10000 - 50s + 25s = 9125

-25s = 9125 - 10000

-25s = -875

Substitute s = 35 in eqn 3

a = 200 - 35

Thus the number of adult tickets sold is 165 and number of students tickets sold were 35

Answer:

As addition property of equality clearly states that if we add the same number to both sides of an equation, the sides remain equal.

Step-by-step explanation:

[tex]2x + 2y = 14[/tex]

[tex]-x + y = 5[/tex]    Add x in both sides (Addition Property of Equality)

[tex]2x + 2y = 14[/tex]

[tex]y = x + 5[/tex]    Multiply both sides by 2

[tex]2x + 2y = 14[/tex]

[tex]2y = 2x + 10[/tex]    Subtract 2x in both sides

[tex]+\left \{ {{2x + 2y=14} \atop {-2x + 2y=10}} \right.[/tex]       ∵adding both equation

[tex]4y = 24[/tex] divide both sides by 4

[tex]y = 6[/tex]

Put the value of y = 6 to the equation [tex]-x + y = 5[/tex]

[tex]-x + 6 = 5[/tex]  Subtract 6 from both sides

[tex]-x = -1[/tex]    Change the sign

[tex]x = 1[/tex]     

Keywords: Addition property of equality, reason, proof

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Answer:

[tex]7[/tex]

Step-by-step explanation:

[tex]\frac{7^{-1}}{7^{-2}}[/tex]

[tex]7^{-1-(-2)}[/tex]

[tex]7^{-1+2}[/tex]

[tex]7^{1}[/tex]

[tex]7[/tex]

I used the following rules:

[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]

[tex]a^1=a[/tex]

[tex]a \neq 0[/tex]

Answer:

x = 1.5[tex]t^{2}[/tex]  , y = 3 + 2at.

Step-by-step explanation:

For the parabola [tex]Y^{2}[/tex] = 4aX ,

General form will be

(X = a[tex]t^{2}[/tex] , Y = 2at) ,

Thus , for the parabola [tex](y-3)^{2}[/tex] = 6(x +8)

Here , a = 1.5 and Y from the above equation should be substituted by y - 3 and X must be substituted by x + 8. After substitution of the same we can  use the general equation formula for this parabola also.

Thus , general equation comes out to be :-

x + 8 = 1.5[tex]t^{2}[/tex] , y - 3 = 2at

x = 1.5[tex]t^{2}[/tex]  , y = 3 + 2at.

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Substitute 1 in everywhere you see 'x'

2(1)^3 - 3(1)^2 - 18(1) + 8

Solve:

f(1) = -11

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Final answer:

To evaluate the function f [tex](x) = 2x^3 - 3x^2 - 18x + 8[/tex] at x=1, substitute 1 for every instance of x in the function and simplify to get f(1) = -11.

Explanation:

The question appears to be a math problem where the student is asked to evaluate a function at a specific input. Specifically, the function given is  [tex]f(x) = 2x^3 - 3x^2 - 18x + 8[/tex] and the student has been asked to evaluate this function when x is equal to 1. To find f(1), we replace every instance of x in the function with 1.

So, f(1) = [tex]2(1)^3 - 3(1)^2 - 18(1) + 8[/tex]= 2(1) - 3(1) - 18 + 8 = 2 - 3 - 18 + 8 = -11.

Thus, f(1) evaluates to -11.

[tex]AB=BC=CD=AD = \sqrt{10}[/tex]

As all the sides have same length, ABCD is a square

Step-by-step explanation:

To prove ABCD a square we have to find the lengths of each side

So,

the distance formula will be used to find the lengths

The distance formula is:

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

Now,

[tex]AB = \sqrt{(2-1)^2+(0-3)^2}\\= \sqrt{(1)^2+(-3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]

[tex]BC = \sqrt{(5-2)^2+(1-0)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]

[tex]CD = \sqrt{(4-5)^2+(4-1)^2}\\= \sqrt{(-1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]

[tex]AD = \sqrt{(4-1)^2+(4-3)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]

we can see that

[tex]AB=BC=CD=AD = \sqrt{10}[/tex]

As all the sides have same length, ABCD is a square

Keywords: Distance formula, square

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Answer:

Step-by-step explanation:

Final answer:

To simplify the given expression involving fractions and variables, multiply, divide, and subtract accordingly to obtain the simplified form. Therefore, the simplified expression is   [tex](9/4)x^2 - (1/25)y^2.[/tex]

Explanation:

The given expression is:

[tex]81/36 * x^2 - y^2/25[/tex]

To simplify this expression:

Multiply 81/36 which equals 9/4.

Then, divide [tex]x^2[/tex] by 4, and subtract [tex]y^2[/tex] divided by 25.

Therefore, the simplified expression is  [tex](9/4)x^2 - (1/25)y^2.[/tex]

Answer:ioj;i;

Step-by-step explanation:

fkuyhjgyhkuyh

Answer:

Step-by-step explanation:

Let the base = x inches

So, h = 2x - 1

Area of triangle  = 60 square inches

(1/2) * base *height = 60

(1/2) * x * (2x-1) = 60

x *(2x-1) = 60*2

2x² - x = 120

2x² - x - 120 = 0

2x²  - 16x + 15x - 15*8 = 0

2x ( x - 8) + 15 (x -8) = 0

(x-8) (2x + 15 ) = 0

x- 8 = 0      {ignore 2x +1 as it will give negative value}

x = 8

Base = 8 inches

Height = 2*8 - 1 16 - 1 = 15 inches

Answer:

most likely isosceles

Step-by-step explanation:

due to the fact that two angles are congruent and the other angle is probably not it would make it all isosceles triangle

A triangle with two 45-degree angles is a special type of triangle known as an isosceles triangle.

In a triangle, if two angles are congruent, then the opposite sides of those angles are also congruent. In an isosceles triangle, two sides are equal in length, and the angles opposite those sides are congruent. Since two angles of the triangle are 45 degrees each, their opposite sides are also equal in length, making it an isosceles triangle.

Answer:

31

Step-by-step explanation:

[tex]\bf \displaystyle\sum\limits_{j=1}^{10}~2j+7\implies \displaystyle\sum\limits_{j=1}^{10}~2j+\displaystyle\sum\limits_{j=1}^{10}~7\implies 2\displaystyle\sum\limits_{j=1}^{10}~j+\displaystyle\sum\limits_{j=1}^{10}~7 \\\\\\ 2\cdot \cfrac{10(10+1)}{2}~~+~~(10)(7)\implies 2\cdot 55+70\implies 110+70\implies 180[/tex]

Here's how I'm assigning a different variable to the value of each digit:

10x + y, where x is the first digit, and y is the second digit (you can test if this equation works)

The sum of the digits is 1/5 the value of the number. Using the information, we can form the equation:

x + y = (1/5)(10x + y)

Simplify

x + y = 2x + (1/5)y

The tens digit is one less than the ones digit. Using this information, we can form the equation:

x = y - 1

Adding both sides by 1 gives

x + 1 = y

Substituting this into the y's the first equation gives:

x + x + 1 = 2x + (1/5)(x + 1)

Distribute and simplify

2x + 1 = 2x + (1/5)x + 1/5

Subtract both sides by 2x

1 = (1/5)x + 1/5

Subtract 1/5 from both sides

4/5 = (1/5)x

Multiply both sides by 5

4 = x

x = 4

Use this to solve for y

x + 1 = y

4 + 1 = y

y = 5

Thus, x = 4 and y = 5. The 2 digit number is XY, which is 45.

Let me know if you need any clarifications; this was a very interesting math problem to solve!

Answer:

b. No she will not have enough bracelets for all 32 classmates if she orders 5 more packages of bracelets

Step-by-step explanation:

write out the equation

p=the number of packages she needs to buy

32=5+4p

subtract five from both sides

32-5=5-5+4p

27=4p

dived both side by 4

27/4=4p/4

6.75=p round to 7

Check your answer:

4 x 7 = 28

add the number of bracelets she already has

28 + 5 = 33 bracelets

33>32

So 7 packages is the minimum number of packages she needs to buy

Answer: The required probability is 0.004.

Step-by-step explanation:

Since we have given that

Number of pieces = 50

Number of defective pieces = 5

So, we need to draw 2 defective pieces.

So, the probability of drawing 2 defective pieces one after the other on the first and second samples would be

[tex]\dfrac{5}{50}\times \dfrac{4}{49}\\\\=\dfrac{20}{2450}\\\\=0.004[/tex]

Hence, the required probability is 0.004.

Final answer:

Calculating the probability of drawing two defective pieces sequentially from a set of 50 pieces with 5 defectives.

Explanation:

The probability of drawing 2 defective pieces one after the other without replacement:

Find the probability of drawing the first defective piece: 5/50 = 1/10.

Since the pieces are drawn without replacement, the probability of drawing the second defective piece after the first is: 4/49.

Multiply the probabilities: (1/10) * (4/49) = 4/245.

Answer:

-85

Step-by-step explanation:

(-8.5)(-5)(-2)

Multiply

(42.5)(-2)

-85

Hope this helps :)

Answer:

[tex]m\angle BOC=30^o[/tex]

Step-by-step explanation:

step 1

Find the measure of angle COD

we know that

[tex]m\angle COF=m\angle COD+m\angle DOF[/tex] ---> by addition angle postulate

we have

[tex]m\angle COF=150^o[/tex] ----> given problem

[tex]m\angle DOF=90^o[/tex] ----> because AD is perpendicular to BF

substitute the given values

[tex]150^o=m\angle COD+90^o[/tex]

[tex]m\angle COD=150^o-90^o[/tex]

[tex]m\angle COD=60^o[/tex]

step 2

Find the measure of angle BOC

we know that

[tex]m\angle BOC+m\angle COD=90^o[/tex] ---> by complementary angles

we have

[tex]m\angle COD=60^o[/tex]

substitute

[tex]m\angle BOC+60^o=90^o[/tex]

[tex]m\angle BOC=90^o-60^o[/tex]

[tex]m\angle BOC=30^o[/tex]

short answer: 30 degrees :)

Answer:

≈ 12.5 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (10, - 11) and (x₂, y₂ ) = (- 1, - 5)

d = [tex]\sqrt{(-1-10)^2+(-5+11)^2}[/tex]

   = [tex]\sqrt{(-11)^2+6^2}[/tex]

   = [tex]\sqrt{121+36}[/tex]

   = [tex]\sqrt{157}[/tex] ≈ 12.5 ( to the nearest tenth )

Answer:

The quantity of gasoline used for 11 hours is 18.37 gallons .

Step-by-step explanation:

Given as :

The quantity of gasoline use by generator = 5.5 gallons

The generator use 5.5 gallons of gasoline for duration = 3 [tex]\dfrac{1}{3}[/tex] hours

I.e The generator use 5.5 gallons of gasoline for duration = [tex]\dfrac{10}{3}[/tex] hours

Let The quantity of gasoline use by generator for 11 hours = x gallons

Now, According to question

Applying unitary method

∵For [tex]\dfrac{10}{3}[/tex] hours of power generate ,The quantity of gasoline use = 5.5 gallons

So For 1 hour of power generate ,The quantity of gasoline use = [tex]\frac{5.5}{\frac{10}{3}}[/tex] gallons

∴  For 11 hours of power generate ,The quantity of gasoline use = [tex]\frac{5.5}{\frac{10}{3}}[/tex] × 11 gallons

i.e For 11 hours of power generate ,The quantity of gasoline use = 1.67 × 11

Or, For 11 hours of power generate ,The quantity of gasoline use = 18.37 gallons

Hence,The quantity of gasoline used for 11 hours is 18.37 gallons . Answer

Answer:

Step-by-step explanation:

Step-by-step explanation:

equation-

(x-3) (x-4) =

[tex] {x }^{2} - 3x - 4x + 12 = {x}^{2} - 7x + 12[/tex]

Given the roots 3 and 4 of a quadratic equation, and the leading coefficient 2, the quadratic equation can be derived as 2x^2 - 14x + 24.

To find a quadratic equation given its roots and leading coefficient, you use the factored form of a quadratic equation, x = (x - root1)(x - root2).  

Given that the roots are 3 and 4, the equation takes the form of x = (x - 3)(x - 4). When you multiply this out, you get x^2 - 7x + 12.

The problem also states that the leading coefficient is 2, so we multiply our obtained equation by 2 to get: 2x^2 - 14x + 24.

So, the requested quadratic equation is 2x^2 - 14x + 24.

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1 year = 12 months.

2 years = 12 x 2 = 24 months.

Multiply the number of times it sells out per month by the number of months:

7 x 24 months = 168 times.

Answer:

48000

Step-by-step explanation:

12000 students

4%

1 =annually

12×4×1= 48000

Answer:12,000

Step-by-step explanation:can’t give you one cuz I’m doing this in mathxl :p

Answer:

C. [tex]y^2=9[/tex]

Step-by-step explanation:

1. [tex]y^2 = 9[/tex]

2. [tex]y = \frac{+}{}\sqrt{9}[/tex]

3. Equation solutions:

[tex]y_{1} = 3\\y_{2} = -3[/tex]

Answer:

The rate of interest applied on the loan is 2.4%

Step-by-step explanation:

Given as :

The principal amount borrows as loan = p = $4200

The time period of loan = t = 5 years = 5 × 12 = 60 months

The monthly payment for loan = $78.40

So, The payment for 60 months = $78.40 × 60 = $4704

i.e Amount after 60 months = $4704

Let The rate of interest = r at simple interest

Now, From Simple Interest method

Simple interest = [tex]\dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}[/tex]

Or, s.i = [tex]\dfrac{\textrm p\times \textrm r\times \textrm t}{100}[/tex]

Or, (Amount - principal) = [tex]\dfrac{\textrm p\times \textrm r\times \textrm t}{100}[/tex]

Or, $4704 - $4200 = [tex]\dfrac{\textrm 4200\times \textrm r\times \textrm 5}{100}[/tex]

Or,504 × 100 = 21,000 × r

∴, r = [tex]\dfrac{50400}{21000}[/tex]

i.e r = 2.4

So, The rate of interest = r = 2.4%

Hence, The rate of interest applied on the loan is 2.4% Answer

Answer:

[tex]\large\boxed{y=-\dfrac{3}{4}x+\dfrac{29}{4}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\=================================[/tex]

[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\text{Calculate the slops:}\\\\(5,\ -1),\ (2,\ -5)\\\\m_1=\dfrac{-5-(-1)}{2-5}=\dfrac{-5+1}{-3}=\dfrac{-4}{-3}=\dfrac{4}{3}\\\\\text{Therefore}\\\\m_2=-\dfrac{1}{\frac{4}{3}}=-1\left(\dfrac{3}{4}\right)=-\dfrac{3}{4}\\\\\text{Put the value of slope and coordinates of the given point (-1, 8) }\\\text{to the equation of a line:}\\\\8=-\dfrac{3}{4}(-1)+b\\\\8=\dfrac{3}{4}+b\qquad\text{subtract}\ \dfrac{3}{4}\ \text{from both sides}\\\\7\dfrac{1}{4}=b\to b=\dfrac{29}{4}\\\\\text{Finally:}\\\\y=-\dfrac{3}{4}x+\dfrac{29}{4}[/tex]

Answer:

Step-by-step explanation:

percentage  spent on books = (325/2200) * 100

= 325/22 = 14.77%

Answer:

The length of the total 8 pieces in 0.8 meters = 6.4 meters

How many pieces there are in the remaining 0.4 meter = 6.5

Step-by-step explanation:

0.8 x 8 = 6.4

9 meters - 6.4 meters = the remaining 2.6 meters

2.6 x 0.4 = 6 1/2 pieces of ribbon in 0.4 meters.

To find a number that is 10 times greater than 7962, we can multiply.

7,962 * 10 = 79,620

79,620 is 10 times greater than 7,962.

Best of Luck!

Answer:

79,620

Step-by-step explanation:

7,962 (10) = 79,620

Answer:

My answer what I came up with is B And B