4. What is the equation of the midline of the sinusoidal function?

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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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:

The equation representing Total money spend being as a member is [tex]m = 60+7.6(b-1)[/tex]

Step-by-step explanation:

Given:

Memberships charges = $60

Cost of 1 book = $7.60

Let number of books be 'b'.

We need to find Total money 'm' spend yearly on buying books after becoming member.

Now we know that 1 book is free for a member.

Total money spend 'm' will be equal to Sum Memberships charges  and Cost of 1 book multiplied by number of books bought yearly minus 1.

Framing in equation form we get;

[tex]m = 60+7.6(b-1)[/tex]

Hence The equation representing Total money spend being as a member is [tex]m = 60+7.6(b-1)[/tex]

Therefore, the final expression for the total cost [tex]\( m \)[/tex] as a function of the number of booksx [tex]\( m \)[/tex] is:

[tex]\[ \boxed{m = \frac{262 + 38b}{5}} \][/tex]

The total cost \( m \) that a student spends after buying \( b \) books and a yearly membership can be calculated using the following formula:

[tex]\[ m = \text{Cost of membership} + (\text{Number of books} - 1) \times \text{Cost per book} \][/tex]

Given that the yearly membership costs $60 and each book after the first free book costs $7.60, we can substitute these values into the formula:

[tex]\[ m = \$60 + (b - 1) \times \$7.60 \][/tex]

Now, let's simplify the expression by converting $7.60 to a fraction to avoid decimals in our calculation:

[tex]\[ m = \$60 + (b - 1) \times \frac{760}{100} \][/tex]

[tex]\[ m = \$60 + (b - 1) \times \frac{38}{5} \][/tex]

[tex]\[ m = \$60 + \frac{38b - 38}{5} \][/tex]

To combine the terms, we need a common denominator, which is 5:

[tex]\[ m = \frac{\$60 \times 5}{5} + \frac{38b - 38}{5} \][/tex]

[tex]\[ m = \frac{300}{5} + \frac{38b - 38}{5} \][/tex]

[tex]\[ m = \frac{300 + 38b - 38}{5} \][/tex]

[tex]\[ m = \frac{262 + 38b}{5} \][/tex]

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:

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:

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:

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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.

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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We observe that a line will pass through 3 points, but to find a slope we only need two.

We see that it passes through points (assuming the scale of graph is 1 : 1) [tex]P_1(x_1,y_1)=P_1(0,1)[/tex] and [tex]P_2(x_2,y_2)=P_2(2,-1)[/tex].

We can use slope formula that applies for any line and produce the same slope for any two different points on the line

[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-1}{2-0}=-1[/tex]

So the slope is -1 also it intersects y-axis at [tex]n=1[/tex] so the general form of the linear function is

[tex]f(x)=mx+n[/tex]

That is in your case

[tex]\boxed{f(x)=-x+1}[/tex]

Hope this helps.

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

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.

[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

Learn more about coordinate geometry at:

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Answer:

-85

Step-by-step explanation:

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

Multiply

(42.5)(-2)

-85

Hope this helps :)

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:

Step-by-step explanation:

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

= 325/22 = 14.77%

Hi there! In this problem, two hundred and eighteen divided by thirty one would be 7.032258064516129‬. Like this:

   281 / 31 = 7.032258064516129‬

Hope this answers your question!

(P.S. I could really use Brainliest.....)

Answer:

200+18÷31=200.58062452

200÷31=6.451612903

18÷31=0.5806451613

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:

12/25 of the class are boys.

Step-by-step explanation:

12+13=25

12/25

Answer:

12/25, I hope this helped!

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.

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:

[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:

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]

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:

[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:

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:

My answer what I came up with is B And B

Answer:

A) (x-2)(x+4)

Step-by-step explanation: