**Formula **for the trigonometry is** y = b sin ( πx/2 - π/2) + 4**

**y = A sin( ωx + δ) + b**

period: t = 4

ω = 2π/t = 2π/4 = π/2

A = 10 -(-2)/ 2

= 6

b = (10-2)/2

= 4

y = b sin (πx/2 + δ) + 4

x = 0, y = bsinδ + 4 = -2

sinδ = -1 => δ = -π/2

y = b sin( πx/2 - π/2) + 4

Therefore the **formula** for the** trigonometry function is y = b sin(πx/2 - π/2) + 4.**

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Your phone plan charges you an initial fee, and then a certain amount depending on the amount of data you use. They send you periodic updates of your usage andyour current bill cost. After using 3 GB of data you owe $30. After 5 GB of data, you owe $40. What is the initial fee prior to the data usage charge?A.$15B.$5C.$2.50D.$10

If for 3 Gb we get a bill for $30 and for 5 Gb we get a bill of $40. It implies that every Gb costs $5, therefor the equation we have use 3 Gb is

[tex]30=3\cdot5+b[/tex]where b is the initial fee. Solving this for b we get that

[tex]b=30-15=15[/tex]so the initial fee is $15

use the function f=8v to find the value of f when v =8

EXPLANATION

Given the function f= 8v

And the v-value = 8

Replacing this on the equation:

f= 8*8 = 16

**Answer: f=16**

Which equation is equivalent to −(5−x)=5−x? Responses −5−x=5−x − 5 − x = 5 − x −5+x=5−x − 5 + x = 5 − x 5−x=5−x 5 − x = 5 − x 5+x=5−x

**The equation** is equivalent to −(5−x) = 5−x is -5+x = 5-x

The given equation −(5−x) = 5−x

**The distributive property** states that multiplying the sum of two or more variables by a number gives the same result as when each variable is multiplied individually by the number and the products are added together.

The distributive property of **addition **

A(B+C) = AB + AC

The distributive property of **subtraction**

A(B-C) = AB - AC

The given equation is −(5−x) = 5−x

Apply distributive property in the equation

−(5−x) = 5−x

-5+x = 5-x

Hence, The equation is equivalent to −(5−x) = 5−x is -5+x = 5-x

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Write a rational expression to determine how many cubbies high the book shelf will be.

**Answer:**

[tex]\frac{x^2-8x-65}{x+1}[/tex]

**Explanation:**

The height of each small division is x + 1, and the total height is x² + 6x + 5. Then, the number of small division is the total height divided by the small division height.

Simplify completely (7x²+11x-6)/(7x²-10x+3)

One way of simplifying the given expression is by factoring them, and then simplifying the common terms.

So, we need to write:

[tex]\begin{gathered} 7x^{2}+11x-6=7(x-a)(x-b) \\ \text{and} \\ 7x^{2}-10x+3=7(x-c)(x-d) \end{gathered}[/tex]The constants a and b are the zeros of the first expression, and the constants c and d are the zeros of the second expression.

So, we can find those zeros using the quadratic formula. We obtain, for the first expression:

[tex]\begin{gathered} x=\frac{-11\pm\sqrt[]{11^{2}-4(7)(-6)}}{2(7)} \\ \\ x=\frac{-11\pm\sqrt[]{289}}{14} \\ \\ x=\frac{-11\pm17}{14} \\ \\ a=\frac{-11-17}{14}=-2 \\ \\ b=\frac{-11+17}{14}=\frac{6}{14}=\frac{3}{7} \end{gathered}[/tex]And, for the second expression, we obtain:

[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[]{(-10)^{2}-4(7)(3)}}{2(7)} \\ \\ x=\frac{10\pm\sqrt[]{16}}{14} \\ \\ x=\frac{10\pm4}{14} \\ \\ c=\frac{10-4}{14}=\frac{6}{14}=\frac{3}{7} \\ \\ d=\frac{10+4}{14}=1 \end{gathered}[/tex]Then, we can write:

[tex]\begin{gathered} 7x^2+11x-6=7(x-(-2))(x-\frac{3}{7})=7(x+2)(x-\frac{3}{7}) \\ \\ 7x^2-10x+3=7(x-\frac{3}{7})(x-1) \end{gathered}[/tex]Thus, the given function can be simplified as follows:

[tex]\frac{7x²+11x-6}{7x²-10x+3}=\frac{7(x+2)(x-\frac{3}{7})}{7(x-\frac{3}{7})(x-1)}=\frac{x+2}{x-1}[/tex]Therefore, the answer is:

[tex]\mathbf{\frac{x+2}{x-1}}[/tex]11. It takes 4 hours to type 8 memos. How long will it take to type 56 memos?

Answer:28

Step-by-step explanation:if the unknown hour is x

then it would be

4hr=8memos

x hr=56 memos

cross multiply that would be

4×56÷8=28

and to check this answer you can find how many hours it would take to write one memo and multiply it by 28(your answer) that would be

x hr=1 memo

4hr =8 memo

cross multiply that would be

8÷4=

and then check it by doing 28 × 2=56

The **time **taken to type 56 **memos **will be 28 hours.

**Expression **in maths is defined as the collection of numbers variables and functions by using signs like addition, **subtraction**, multiplication, and division.

Numbers (constants), **variables**, operations, functions, brackets, punctuation, and grouping can all be represented by **mathematical symbols**, which can also be used to indicate the logical syntax's order of operations and other features.

Given that it takes 4 hours to type 8 memos. The time taken to type 56 memos will be calculated as,

8 memos = 4 hours

56 memos = ( 56 x 4 ) /8

56 memos = 28 hors

Therefore, it will take 28 hours to type 56 memos.

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Reflect (1, -3) over the y-axis.

Then translate the result down 1 unit.

What are the coordinates of the final point?

The answer would be (1,2) because the reflection would result (1,3) then translate down

**Answer:**

(-1 , -4)

**Step-by-step explanation:**

Hello!

Refer to the graph for the **reflection** and **translation**.

The coordinates of the final point would be (-1,-4), given the x and y-values of the point.

The ------------- of a circle is a line segment that joins two points on the circumference of the circle and passes through the centre of the circle

**Solution**

The **Diameter** of a circle is a line segment that joins two points on the circumference of the circle and passes through the centre of the circle

Bobby can work at most 20 hours next week, but she needs to earn at least $150. Herdog-walking job pays her $6 per hour and her iob as a car wash attendant pays her $10 perhour. If d is the number of hours she walks dogs this week and w is the number of hours sheworks at the car wash, write a system of inequalities that represents Bobby's situation.

**Solution:**

Let **d** represent the number of hours Bobby walks dogs,

and **w** be the number of hours she works at the car wash.

Given that she can work at most 20 hours next week, this implies that the total number of hours she works is expressed as

[tex]d+w\leq20[/tex]If her dog-walking job pays her $6 per hour, this implies that for **d** number of hours, she will earn

and her iob as a car wash attendant pays her $10 per hour, similarly for **w **number of hours, she will earn

Given that she needs to earn at least $150, this implies that her total earnings will be expressed as

[tex]6d+10w\ge150[/tex]**Hence, the system of inequalities that represents Bobby's situation is:**

Factor the following expression completely.x4 - 16

**Given:**

**Required:**

To factor the given expression.

**Explanation:**

Consider the given expression

[tex]x^4-16[/tex]Now

[tex]\begin{gathered} x^4-16=(x^2)^2-(4^)^2 \\ \\ =(x^2-4)(x^2+4) \\ \\ =(x^2-2^2)(x^2+4) \\ \\ =(x-2)(x+2)(x^2+4) \end{gathered}[/tex]**Final Answer:**

Simplify the following exponent (x¹⁰ ÷ x²) x x³

**Answer:**

**x^6**

**Step-by-step explanation:**

**Given X¹⁰ ÷ (x² X x³ ÷ x) : Simplify.**

**We know the law of exponents which states that**

**a^m x a^n = a^m + n**

**a^m / a^n = a^m - n**

**So the problem is x^10 / (x^2 x x^3 / x)**

**So we have x^10 / x ^5 / x**

** x ^10 / x ^5 - 1**

** x^10 / x^4**

** x ^10 -**

**x^6**

**After simplifying we get x^6**

How do you know when an equation has one solution? A. The coefficients are differentB. The coefficients are the same and the constants are differentC. The coefficients are the same and the constants are same

SOLUTION

Given the question in the question tab, the following are the solution steps to answer the question.

**STEP 1: Define an equation with one solution**

You can tell that an equation has one solution if you solve the equation and get a variable equal to a number. A system of linear equations has one solution when the graphs intersect at a point.

**STEP 2: Examine the options**

An equation is said to have **"no solution"** when the coefficients are the same and the constants are different as seen below:

**When the coefficients are the same and the constants are the same, the equation is said to have "infinitely many solutions as seen below:**

**When the coefficients are different, the equation is said to have one solution as seen below:**

**Hence, the answer is:**

**"When the coefficients are different"**

Find the mean of these numbers: 5, 11, 2, 12, 4, 2Need solution :D

**SOLUTION **

We want to find the mean of the numbers 5, 11, 2, 12, 4, 2

To do this, we add the numbers and divide by the total numbers.

The numbers are 6 in numbers, so the mean

[tex]\begin{gathered} mean=\frac{5+11+2+12+4+2}{6} \\ =\frac{36}{6} \\ =6 \end{gathered}[/tex]**Hence the answer is 6**

8.1÷0.9+0.4^(3)÷0.8×30

**Answer:**

11.4

**Step-by-step explanation:**

**Answer:**

11.4

p.s you try it may help

Together, Nora and Addison own 152 shares of stock. Nora has 4 less than three times Addison's amount. How many shares does each girl have?

The number of **shares **that Nora has is 113.

The number of **shares **that Addison has is 39.

Let x represent the amount of **shares **that **Addison **has

**Shares **that **Nora **has = 3x - 4

The sum of **shares **they both have : 3x - 4 + x = 152

In order to determine the value of x, take the following steps:

Combine similar terms together: 3x + x = 152 + 4

**Add **similar terms: 4x = 156

**Divide **both sides by 4 : x = 156/ 4 = 39

**Shares **that **Nora **has = 3(39) - 4

117 - 4 = 113

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Hiro picks up four digits card, he says: I can make a multiple of 10 with these cards. I can also make a number that rounds to 5300 and a number where the digit 8 is worth 800?

I believe the numbers are 5, 2, 8, 0 if you round to the nearest hundred

PLEASE HELP

A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random, find the probability that it is yellow or green.

p(Yellow or not green)= ?

**Answer:**

I think the answer is 94/139

**Step-by-step explanation:**

**Answer:**

65/139

**Step-by-step explanation:**

Total number of candies - 139

No of yellow and green - 65

Thus probability - 65/139

Find the surface area of a cylinder with a height of 7 in and a base diameter of 8 in.

Use the value 3.14 for pi and do not do any rounding.

Be sure to include the correct unit.

The total **surface area **of the cylinder whose height is 7 units and diameter is 8 units is 226.08 units.

**What is surface area?**

The **surface area** of a solid item is a measurement of the total volume that the surface of the thing occupies. The mathematical definition of **surface area** in the presence of curved surfaces is considerably more complicated than the definition of arc length for one-dimensional curves or the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces. When smooth surfaces, like spheres, are represented as parametric surfaces, their surface area can be calculated. This definition of surface area, based on infinitesimal calculus methods, uses partial derivatives and double integration.

The formula to calculate the **total surface area **of a cylinder is:

[tex]S = 2\pi rh + \pi r^2[/tex]

Where, S = **surface area**, r = radius, and h = height

As given in the question,

height (h) = 7 units

diameter (d) = 8 units

Since, r = d/2

So, r = 8/2 = 4 units

putting these values in the formula:

[tex]S = (2\times 3.14 \times 4 \times 7)+( 3.14 \times 4^2)[/tex]

[tex]S = (2\times 3.14 \times 4 \times 7)+( 3.14 \times 16)[/tex]

[tex]S = 175.84 + 50.24\\[/tex]

**S = 226.08 units**

Therefore, **Surface area** of the cylinder is 226.08 units

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Using the idea of the Empirical Rule for a normal distribution, explain what percent of individuals would fall in the given range. iܒܫܡܗ Si The range of IQ scores from 80 to 120, when the mean IQ score is 100 and the standard deviation is 10.

**SOLUTION**

**Answer = 95.5%**

From this information given.

We have a mean value of 100 and a standard deviation value of 10

To obtain the range from 80 to 120.

This will be moving 2(S.D) to the left and 2(S.D) to the right of the mean.

From theory, values within 2S.D from the mean, represent 95.5% of the given data.

**Therefore, the percent of individuals that would fall in the given range is **

**95.5%**

Which expression is equivalent to -5/3 x

**Answer:**

-1 2/3 x

**Step-by-step explanation:**

This is not that difficult. But I suggest that you provide answer options.

pls mark brainliest

Dean started with 5 metersof yarn. He used 300millimeters of yarn each dayfor 5 days. How manymeters of yarn does Deanhave left?

**Given:**

Dean started a yarn with 5 meters. He used 300millimeters of yarn each day for 5 days.

**Required:**

Find how many meters of yarn Dean has left.

**Explanation:**

We know that 1 meter = 1000milimeters

Dean used meters of yarn in the five days

[tex]\begin{gathered} =\frac{300\times5}{1000} \\ =\frac{3}{2}\text{ meter} \end{gathered}[/tex]The left meters are:

[tex]\begin{gathered} =5-\frac{3}{2} \\ =\frac{10-3}{2} \\ =\frac{7}{2} \\ =3.5 \end{gathered}[/tex]**Final Answer:**

Thus 3.5 meters of yarn left

= 186x – 30y5х – 25y= 15

**Answer:**

There are infinitely many solutions

**Explanation:**

Given the system of linear equations:

[tex]\mleft\{\begin{aligned}6x-30y=18 \\ 5x+25y=15\end{aligned}\mright.[/tex]To solve using Matrices, we write the equation in the form:

Ax = b

Where A represent the matrix of the coefficient of the variables x and y

x represent the matrix of the variables x and y

and b represents the matrix of the constants on the right hand side.

In matrix form, we have:

[tex]\begin{bmatrix}{6} & {-30} \\ {5} & {-25}\end{bmatrix}\begin{bmatrix}{x} \\ {y}\end{bmatrix}=\begin{bmatrix}{18} \\ {15}\end{bmatrix}[/tex]**We must have a nonzero determinant for A**

The determinant of A is:

[tex]\begin{gathered} (-25\times6)-(-30\times5) \\ =-150+150 \\ =0 \end{gathered}[/tex]**The determinant of A is zero, without going far, we conclude that the system has infinite number of solutions.**

What's 2,412 Divided by 25

**Answer:**

96.48

**Step-by-step explanation:**

The answer is 96.48.

**Answer:**

96.48

**Step-by-step explanation:**

2,412 divided by 25 equals 96.48

PLS HELP I HAVE LESS THAN 20 MINUTES!!!!

The statement "Samuel will get **25** or **more** for mowing the** **lawn" can be represented using the **inequality →** **x ≥ 25 **and the **graph number [2] **represents the correct graph.

In mathematics, an inequality is a relation which makes a **non-equal comparison** between two numbers or other **mathematical expressions. **There are two types of **inequalities** namely **strict** and **slack** inequalities.

Given is the following** statement **- "Samuel will get **25** or **more** for mowing the** **lawn".

The **given statement** is -

Samuel will get $**25** or **more** for mowing the** **lawn.

Assume that Samuel gets **$x** for mowing the lawn.

Then according to the question, we can write the **inequality** as -

**x ≥ 25**

**" ≥ "** sign to represent either **25 **or **more**.

So, the inequality can be written as **x ≥ 25** and the **graph number [2] **represents the correct graph.

Therefore, the statement "Samuel will get **25** or **more** for mowing the** **lawn" can be represented using the **inequality →** **x ≥ 25 **and the **graph number [2] **represents the correct graph.

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Describe the graph of the quadratic function f (x) = -3x^2+ 6x + 5 by stating whether it opens upward or downward and stating how it is stretched or compressed when compared to the parent quadratic functionA. The parabola opens downward. It is compressed shorter by a factor of 3.B. The parabola opens upward. It is stretched taller by a factor of 3.C. The parabola opens downward. It is stretched taller by a factor of 3.D. The parabola opens upward. It is compressed shorter by a factor of 3.

**Answer:**

B. The parabola opens upward. It is stretched taller by a factor of 3.

**Step-by-step explanation:**

You want to know **how the quadratic opens**, and how it is **stretched or compressed**, given its equation is **f(x) = -3x^2 +6x +5**.

The "leading coefficient" is the coefficient of the highest-degree term. That term is -3x^2, and its coefficient is -3.

The minus sign tells you the parabola **opens downward**.

The magnitude of 3 tells you the parabola is **stretched vertically (taller) by a factor of 3**.

i need help with this question

In the given expression

[tex]x^5+32y^3=\ln y[/tex]To differentiate it with respect to it, we will writ y' for every term of y

The differentiation of

[tex]x^5=5x^{5-1}=5x^4[/tex]The differentiation of

[tex]32y^3=32(3)y^{3-1}y^{\prime}=96y^2y^{\prime}[/tex]The differentiation of

[tex]\ln y=\frac{1}{y}(y^{\prime})=y^{-1}y^{\prime}[/tex]Now let us write all of them in one line

[tex]5x^4+96y^2y^{\prime}=y^{-1}y^{\prime}[/tex]Put the terms of y' on one side and the other term on the other side

[tex]96y^2y^{\prime}-y^{-1}y^{\prime}=-5x^4[/tex]Take y' as a common factor

[tex]y^{\prime}(96y^2-y^{-1})=-5x^4[/tex]Divide both sides by the bracket

[tex]y^{\prime}=\frac{-5x^4}{(96y^2-y^{-1})}[/tex]Since the given point is (-2, 1), then

x = -2 and y = 1

Substitute them to find y'

[tex]\begin{gathered} y^{\prime}=\frac{-5(-2)^4}{(96\lbrack1\rbrack^2-\lbrack1\rbrack^{-1})}=\frac{-5(16)}{(96-1)}=\frac{-80}{95} \\ y^{\prime}=-\frac{16}{19} \end{gathered}[/tex]**The value of y' is -16/19**

what is the exact value of tan (-3pi/4)

**Answer:**

1

**Step-by-step explanation:**

Write an equivalent expression for (x+2)+(x+2)

We will proceed as follows in order to get an equivalent expression:

[tex](x+2)+(x+2)=(x+x)+(2+2)=2x+4[/tex]So, one equivalent expression is 2x + 4.

Write the correct inequality for the following statement and then solve for the given number of

guests.

You are in charge of planning your mother's surprise party. You have

found a hall that rents for $225 and a caterer that will charge you $15 per

guest. Write an inequality to calculate your total cost (T) based on the

number of guests (g).

If you have a total budget of $1000 how many guests can you

invite?

The **inequality** that can be used to calculate total cost (T) based on the number of guests (g) is 225 + 15g ≤ 1000.

If you have a total **budget** of $1000, 51.67 guests can be invited.

Total cost = Cost of hall rent + Caterer's charge per guest(Number of guests)

225 + 15g ≤ T

If you have a total budget of $1000

225 + 15g ≤ T

225 + 15g ≤ 1000

15g ≤ 1000 - 225

15g ≤ 775

g ≤ 775 / 15

g ≤ 51.66666666666666

Approximately,

g ≤ 51.67

So therefore, the inequality to represent the situation is 15g ≤ 1000 - 225 and about 51.67 guests can be **invited** if you have a **budget** of $1000

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The graph compares the ages of 100 randomly selected visitors at a beach in January and in July. Select from the drop-down menu to correctly complete the statement. On average, visitors in January were Choose... years older than visitors in July.

From the given **box** and **whisker **plot, On average, visitors in January were 10 years older than visitors in July.

A **box **and** whisker plot** is a graph plot that indicates whether a distribution is **skewed** and whether there are potential unusual observations (outliers) in the data set.

Now, the way to interpret it is as follows;

The left side of the box is theNow, looking at the box and whisker plot for January and July, we can say that those in January are approximately 10 years older than those in July.

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