**Answer:**

f(x) = 1/7 * (x + 7)^2 - 2

axis of symmetry: x = -7

vertex: (-7 | -2)

**Step-by-step explanation:**

f(x) = 1/7 * (x^2 + 14x + 35)

f(x) = 1/7 * (x^2 + 14x) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 7^2) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 49) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2) + 5 - 7

f(x) = 1/7 * (x + 7)^2 + 5 - 7

f(x) = 1/7 * (x + 7)^2 - 2

Graph each function f(x)=1/4 x

**Graph f(x)=14.**

**Plot each graph on the same coordinate system.**

**f(x)=14x**

**image of graph**

there are 5 students in mun elligible for a particular event at the next conference however, only two can compete. they are equally qualified, so it is decided that the contestants will be randomly selected. what is the probability that the first two students alphabetically will be selected?

The **probability of selecting** two students has 10 ways

Total number of students = 5

Only two students can be selected for the conference who are equally qualified.

The probability that the first two students selected alphabetically is derived from the **combinations**.

Therefore, the final probability for selecting the students randomly is,

x = ⁵C₂

x = [tex]\frac{5!}{2!*(5 - 2)!}[/tex]

x = 10

Hence, the **probability** of selecting two students has 10 ways.

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Equivalent equation to 2(x +3)=16

Answer: x = 5Show your work!! = 2(x+3)=16Apply the Distributive Property2x+6=16Rearrange variables to the left side of the equation2x=16-6Calculate the sum or difference2x = = 10Divide both sides of the equation by the coefficient of variable10 2

∠A and ∠B are vertical angles. If ∠A = (x-29) and m∠B = (6x-11), then find the value of x.

The required **value** of x is -3.6 which is determined by the **substitute** that equals the **vertical** **angles**.

When two lines** intersect** at a location, **vertical** angles are generated. They are always equal to each other.

Since ∠A and ∠B are **vertical angles** then they are **congruent**, thus

⇒ (x - 29) = (6x - 11)

**Subtract** 6x from both sides of the above equation,

⇒ x - 29 - 6x = 6x - 11 -6x

⇒ -5x - 29 = - 11

**Add** 29 to both sides of the **equation**,

⇒ -5x - 29 + 29 = - 11 + 29

⇒ -5x = 18

**Divided** by 5 to both sides of the equation,

⇒ x = - 18/5

⇒ x = - 3.6

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On May 8, 2010, a team of kayakers sets a record time for 5h 19 min 17 sec to kayak across the length of Loch Ness, Scotland, UK, a distance of 20.5 mi. When the kayakers were four times as far from the starting point as from the finish, how many miles were traveled?

**Answer:**

16.4

**Step-by-step explanation:**

The time is irrelevant to the problem

fraction42 *20.5= 16.4

Hope this helps

I am confused my old teacher got fired so we are learning stuff completely different and I am rlly confused in this assignment please help me.

Hello!

First, let's analyze these two quadrilaterals:

• Notice that the quadrilateral AB'C'D is ,smaller ,than the quadrilateral ABCD.

Let's try to solve it using the lines AB and AB':

• The measurement of the ,line AB is 14 units,.

,• The measurement of the ,line AB' is 7 units,.

Knowing it, let's write the scale factor as:

[tex]\text{ScaleFactor}=\frac{AB^{\prime}}{AB}=\frac{7}{14}=\frac{1}{2}[/tex]Answer: **alternative D**.

List the first 5 multiples.

18:

20:

16:

32:

**Answer: 18: 18, 36, 54, 72, 9020: 20, 40, 60, 80, 10016: 16, 32, 48, 64, 80**

**32: 32, 64, 96, 128, 160**

**Step-by-step explanation:**

multiply each number by 1 2 3 4 5 respectivly to get the answer.

Megan is in a musical production. She was at practice for 2 3/4 hours yesterday and 3 1/2 hours today. Altogether she spent 1/3 of her practice hours dancing. How many total hours did Megan spend dancing yesterday and today?

Megan spent 2 1/12** hours** dancing both yesterday and today

Megan is involved in a musical production

Yesterday, she practiced for 2 3/4** hours**

Today she practiced for 3 1/2 **hours**

The first step is to calculate the total number of **hours** she spent at the practice

2 3/4 + 3 1/2

= 11/4 + 7/2

The LCM between both fractions is 4

11/4 + 7/2

11 + 14/4

= 25/4

Megan spent 25/4 **hours** yesterday and today practicing

Out of this 25/4 **hours**, she spent 1/3 **hours** dancing

Therefore the** hours** she spent dancing can be calculated as follows

= 25/4 × 1/3

= 25/12

= 2 1/12

Hence Megan spent 2 1/12** hours** dancing yesterday and today

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Help please I don’t knowwww

The **corn's height **when the** fertilizer** was applied is 13 centimeters and it grows at a rate of 13 centimeters each day.

The equation that is given is known as a **linear equation. **A **linear equation **is an equation that has a single variable that is raised to the power of one.

A **linear equation **increases or decreases at a constant rate. When a **linear equation **is drawn on a graph, it is a straight line that curves either upward or downward.

A **linear equation **usually has this form y = mx + b

Where:

m = slope = rate of change of the equation with respect to x b = interceptH = 13 + 13t

Where:

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Work out 1 1/4 + 4 2/3 Give your answer as a mixed number where appropriate.

The **resultant **of the given **sum** of the **mixed** **number **1 1/4 + 4 2/3 will be 5 11/12.

The number system is a way to **represent **or express **numbers**.

Any of the multiple **sets** of **symbols **and the guidelines for **utilizing **them to **represent numbers **are included in the Number System.

As per the given **sum** of the **mixed** **number**,

1 1/4 + 4 2/3

⇒ 1 + 1/4 + 4 + 2/3

⇒ 1 + 4 + 1/4 + 2/3

⇒ 5 + 1/4 + 2/3

Take **LCM** of 1/4 and 2/3 as 12.

⇒ 5 + (3 + 8)/12

⇒ 5 + 11/12 = 5 11/12

Hence "The **resultant **of the given **sum** of the **mixed** **number **1 1/4 + 4 2/3 will be 5 11/12".

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I need help figuring out the answer … I’m confused

1st step. Calculate the area of the parallelogram

We can use the following formula:

[tex]A=b\cdot h[/tex]where,

base, b = 9 km

height, h = 5 km

Therefore,

[tex]A=9\cdot5=45[/tex]The area of the parallelogram is 45 km^2

2nd step. Calculate the area of the triangle

Let's use this formula:

[tex]A=\frac{b\cdot h}{2}[/tex]where,

base, b = 6 km

height, h = 3 km

Therefore,

[tex]A=\frac{6\cdot3}{2}=9[/tex]The area of the triangle is 9 km^2

3rd step. calculates the ratio of the area of the parallelogram to the area of the triangle

[tex]r=\frac{A_P}{A_T}=\frac{45}{9}=5[/tex]**Answer**: the area of the parallelogram is **5 times** greater than the area of the triangle.

(2x^2+3x+8) (x^2-x-4) multiply the polynomials and simplify the answer

**Step-by-step explanation:**

(2x² + 3x+8) (x²-x-4)

= (2x² + 3x+8) (x² +-x²+-4)

= (2x²) (x²) + (2x²) (-x) + (2x²) (-4) +(3x) (x²) + (3x) (-x) + (3x) (-4) + (8) (x²) + (8) (-x) + (8) (-4)

= 2x⁴ - 2x³ -8x² + 3x³ -3x² - 12x + 8x² - 8x - 32

=2x⁴ + x³ - 3x² - 20x - 32

A paintball court charges an initial entrance fee plus a fixed price per ball. Suppose it costs $18 to use 2 balls and $23 to use 4 balls. What is the entrance fee?

The** entrance fees i**s 13 dollars charges by the paintball court.

Let us assume that the **entrance fees is $X **and the actual cost of using one ball is** $Y** charged by the paintball court.

According to one situation,

**Total cost **of using to ball = Cost of **entry fees** + actual cost of using two ball.

So, we can write,

X + 2Y = 18

Let us say that this is our equation 1,

Also, it is provided,

Total cost of using 4 balls = cost of entry fees + actual cost of using four balls.

X + 4Y = 23

Let us say that this is our equation 2,

Both of our equations are** linear equations with two variables,**

Now, substracting equation 1 from equation 2,

X + 4Y -(X + 2Y) = 23 - 18

2Y = 5

Y = $2.5.

Putting the value of Y = 2.5 in equation 1,

X + 2(2.5) = 18

X = 18 - 5

X = $13.

So, the **entry fees **is 13 dollars.

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AB and BC are perpendicular lines.

Find the value of x.

X = 32.5

First put it into an equation:

25 + 2x = 90

Then subtract 25 from both sides:

2x = 65

Finally divide by 2 on both sides:

X = 32.5

First put it into an equation:

25 + 2x = 90

Then subtract 25 from both sides:

2x = 65

Finally divide by 2 on both sides:

X = 32.5

9. Put the following equation of a line into slope-intercept

form, simplifying all fractions.

2x + 3y = 15

**Step-by-step explanation:**

slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

we have

2x + 3y = 15

3y = 15 - 2x

y = (-2/3)×x + 5

the Lim family are great mathematician.When asked howvold everyone are,the family replies : "our family of two adults and three childrens are 100years old altogether.The sum of father's age and son's age is 51.The father is 3 years older than mother while the twins daugthers are each 5 years younger than the brother" Can you work out everyone's age???

**Answer:**

Ages are as follows:

Father: 40

Mother: 37

Son: 11

Each twin daughter: 6

**Step-by-step explanation:**

Interesting puzzle!

Let

F denote the age of the father

M the age of the mother

S the age of the son

D the age of each of the twin daughters

Total of all ages is

F + M + S + 2D = 100 [1]

We also have

F + S = 51 ==> S = 51- F [2]

F - M = 3 ==> M = F - 3 [3]

S - D = 5 ==> D = S -5 [4]

==> D = (51-F) -5

==> D = 46 - F [5]

Substitute this in equation [1] to get

We now have everyone's age in terms of the father's age F

Substituting each of equations [2], [3] and [5] into [1] we get one equation in terms of F

F + (F-3) + (51-F) + 2(46-F) = 100

(F + F - F -2F ) + (-3 + 51 + 92) = 100

-F + 140 = 100

- F = 100 - 140

-F = -40

or

F = 40

From [3]

M = F - 3 = 40 - 3 = 37

From [2]

S = 51 - F = 51 - 40 = 11

From [4]

D = S - 5 = 11 - 5 = 6

Verify:

F + M + S + 2D = 40 + 37 + 11 + 2 x6 = 100

**Step-by-step explanation:**

a = father age

b = mother age

c = son age

d = daughters age

1. a + b + c + 2d = 100 (don't forget : twin-daughters)

2. a + c = 51

3. a = b + 3

4. d = c - 5

we need to transform the equations 2-4 to express 3 variables by the 4th, and then put that into the first equation and solve for that one variable.

once we have that, we can use again the equations 2-4 to solve for the other variables.

2. tells us that

c = 51 - a

3. tells us that

b = a - 3

4. and 2. tells us that

d = c - 5 = (51 - a) - 5 = 46 - a

with that we get in 1.

a + (a - 3) + (51 - a) + 2(46 - a) = 100

a + a - 3 + 51 - a + 92 - 2a = 100

2a - 3a + 48 + 92 = 100

-a + 140 = 100

-a = -40

a = 40

b = a - 3 = 40 - 3 = 37

c = 51 - a = 51 - 40 = 11

d = c - 5 = 11 - 5 = 6

so, the father is 40 years old

the mother is 37 years old

the son is 11 years old

both of the twin daughters are 6 years old.

Zack and Zane were floating down the river. They climbed to the top of the rock, which was 14.6 feet above the water level. When Zack jumped in, he got down to a depth of 6.8 feet underwater. What was the total distance from his highest point to his lowest point?

The **total distance **from his highest point to his lowest point is 21.8 feet.

**Height H **climbed by Zack and Zane is 14.6 feet.

The** depth D** underwater that Zack got down to is 6.8 feet.

The distance between the highest and the lowest point can be found by assuming the **coordinates axis.**

Let us assume the origin is on the water surface,

So, going by this logic, highest point is at +14.6 feet.

The lowest point is at -6.8 feet.

The **distance L** between lowest and highest point is,

L = H - D

L = 14.6 -(-6.8) feet

L = (14.6 + 6.8) feet

L = 21.8 feet

So the **distance L** is 21.8 feets.

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The store is trying to get rid of their Game of Thrones Season 8 sets and is marking them down by 25%. The original price was $55. What is the new price before sales tax?

The answer is $41.75

Samuel orders four DVDs from an online music store. Each DVD costs $9.96. He has a 25% discount code, and sales tax is 7.75%. Round sales tax amounts to the nearest cent. What is the total cost of his order?

The total cost of Samuel's order is $

Samuel's **order **will ultimately **cost $39.84.**

One DVD Samuel purchased cost** $9.96.**

He purchased four **DVDs in total.**

as a result, his total outlay will be **4 * 9.96 = $39.84.**

The** 7.75% sales tax **that must be paid is disclosed to us.

Adding 7.75% to **$39.84 yields**

39.84 x 7.75/(100) (100)

**= $3.0876**

Consequently, the total amount of** tax due is $3.0876.**

Using 25% of 39.84 to calculate a **25% discount,**

39.84 x 25/100

= 996/100

**=$9.96**

Consequently, the total discount on the total of **$39.84 will be $9.96.**

as a result, the updated purchase price will be,

39.84-9.96

**=$29.88**

adding the tax to the updated price,

9.96+29.88

**= $39.84**

Consequently, Samuel's order will ultimately cost **$39.84.**

One must **compute percentage **in order to determine the proportion of a whole that is stated in terms of 100. A percentage can be determined using one of two **methods**:

using the **unitary method**.

by changing the **fraction's denominator **to **100.**

It should be noted that the second method of **percentage **computation is not used when the denominator is not a factor of 100. In these circumstances, we make use of the **unitary approach**.

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Write the equation for g(x).

**Answer: **[tex]-\frac{x^2}{4}[/tex]

**Step-by-step explanation:**

The graph of g(x) is the graph of f(x) reflected over the x-axis and horizontally stretched by a factor of 2.

So, the equation is [tex]g(x)=-(x/2)^2 =-\frac{x^2}{4}[/tex]

Write an

equation of a parabola with the given vertex and focus.

vertex (5,-2); focus (5, -1)

**Answer:**

[tex](x-5)^2=4(y+2)[/tex]

Please note that alternative forms of this equation (vertex and standard) are in the explanation.

**Step-by-step explanation:**

Standard form of a parabola with a vertical axis of symmetry:

[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]

Vertex = (h, k)Focus = (h, k+p)Given:

Vertex = (5, -2)Focus = (5, -1)Therefore:

h = 5k = -2k + p = -1Calculate p:

[tex]\implies -2+p=-1[/tex]

[tex]\implies p=-1+2[/tex]

[tex]\implies p=1[/tex]

Substitute the values of h, k and p into the **formula **to create an **equation **of the **parabola **with the given parameters:

[tex]\implies (x-5)^2=4(1)(y-(-2))[/tex]

[tex]\implies (x-5)^2=4(y+2)[/tex]

In **vertex **form:

[tex]\implies y=\dfrac{1}{4}(x-5)^2-2[/tex]

In **ax² + bx + c** form:

[tex]\implies y=\dfrac{1}{4}x^2-\dfrac{5}{2}x+\dfrac{17}{4}[/tex]

Multiply.

40.631⋅1.07

Responses

4.347517

43.47517

434.7517

4347.517

**Answer: 43.47517**

**Step-by-step explanation:**

Considering orders of magnitude, we see that Option 2 is the only reasonable answer.

Write the following number in standard decimal form.six tenths

[tex]6\text{ }\times10^{-1}[/tex]Explanation:

**Rewriting the words mathematically:**

**Next we will write in standard decimal form:**

Write the equation of a line perpendicular to 8x−5y=−9 that passes through the point (−8,3).

Considering the definition of perpendicular line, the **equation** of a line perpendicular to 8x−5y=−9 that passes through the point (−8,3) is y=-5/8x-2 .

A linear equation o line can be expressed in the form **y = mx + b**

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you **multiply the slopes** of two perpendicular lines, you get **–1**.

In this case, the line is 8x-5y= -9. Expressed in the form y = mx + b, you get:

-5y= -9 - 8x

y= (-8x -9)÷ (-5)

y= 8/5x +9/5

The line has a slope of 8/5. If you multiply the slopes of two perpendicular lines, you get –1. In this case:

8/5× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (8/5)

*slope perpendicular line= -5/8*

So, the perpendicular line has a form of: y= -5/8x + b

The line passes through the point (-8, 3). Replacing in the expression for perpendicular line, you get:

3= -5/8× (-8) + b

3= 5 + b

3- 5 = b

*-2= b*

Finally, the equation of the **perpendicular line** is y= -5/8x -2 .

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how to find the greatest number of students to whom 135pens 225 books and 315 copies can be divided equally also find the shares of each item . maths

**Answer:**

The items can be equally shared between 45 students.

Each student will get 3 pens, 5 books and 7 copies.

**Step-by-step explanation:**

We have to find the **GCF (Greatest common factor) ** of 135 , 225 and 315.

135 = 5 * 3 * 3 * 3 = 45 * 3

225 = 5 * 5 * 3 * 3 = 45 * 5

315 = 5 * 3 * 3 * 7 = 45 * 7

GCF = 5 * 9 = 45

The items can be equally shared between 45 students.

Each student will get 3 pens, 5 books and 7 copies.

Noah is studying a type of sea sponge that grows at a constant rate. They measured the age and height of 333 pieces of the sponge. Here's what they found:

**Answer:**

a = h/2 would be the answer.

Step;-

Find slope:-

m = rise/run = (16-8)/(8-4) = 8/4 = 2

Now,

y = mx + b

or, 8 = 2(4) + b

so, b = 0

So,

y = mx + b

or, h = 2a + 0

so, h = 2a

hence,a = h/2.

**The sea sponges's height grows 2cm every 1 year, so you can write an equation to find the height at any age **[tex]a = \frac{h}{2}[/tex]

I dont understand this

Identify all pairs of parallel segments. Arrange letters in

C

ALPHABETICAL

orders (AC. DF)

)//(

)//(

)//(

All pairs of **parallel** **segments** are given below.

Lines in a plane that are consistently spaced apart are known as parallel lines. **Parallel** **lines** don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees. Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

Given,

a) **Line** **segment** = AC and FD

**Parallel** = AC ║FD

b) Line segment = AE and BD

Parallel = AE ║BD

c) Line segment = EC and FB

Parallel = EC ║FB

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Anna spent half her weekly allowance at the movies to earn more money her parents let her wash the car for $8 what is her weekly allowance if she ended with $18

This situation can be expressed by the** equation** [tex]x-\frac{x}{2} +8=18[/tex], her weekly allowance is $20.

What is an **equation**?

Let the weekly allowance of anna be = X

Allowance spent on movies= X/2

The extra money from the car wash = 8

Allowance retained with anna = 18

This situation can be expressed by the **equation**,

[tex]x-\frac{x}{2} +8=18[/tex]

Solving the above **equation**, we get,

[tex]\frac{x+16}{2} =18[/tex]

x+16=36

x=20

Therefore, her weekly allowance is $20.

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Help pls ASAP

1a. When a lot of people are swimming in a pool, the water become cloudy. Explain why?

b. The water in an empty pool is very clear. is it still a mixture?

Explain why?

a. Inadequate **chlorine **levels cause cloudy or creamy **swimming pool **water.

b. Even though water represents the most ample substance on the planet, it is rarely encountered in its pure form in nature.

What is defined as the term mixture?A mixture is a compound composed of a number of chemical components that aren't chemically linked to one another. A mixture is a physical combination of two or more compounds that retain their individuality and are blended as solutions, suspensions, and colloids.**Part a:** Cloudy or milky** pool water **is ended up causing by seven major issues: insufficient chlorine, an imbalanced pH and alkalinity, extremely high calcium hardness (CH), a faulty or clogged filter, and the initial phases of algae, ammonia, as well as debris.

Methods for Cleaning Cloudy Pool Water

Balance the levels of**Part b: **A swimming pool mixture of water as well as chlorine is made reference to as a h**omogenous mixture** even though water and chlorine cannot be separated back to one‘s distinct materials once mixed together.

Because chlorine as well as water diffuse between each other, they cannot be kept separate into their pure forms again.

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Answer for bothering x and y giving brainliest. Need help asap!!!

**Answer: x = 77 - 2y y = -x/2 + (77/2)**

**Step-by-step explanation:**

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A pitcher claims he can throw a 0.145-kg baseball with as much momentum as a 3.00-g bullet moving with a speed of 1.50 x 103 m/s. What must the baseballs speed be if the pitchers claim is valid?
Two electromagnetic waves are traveling through a material. Wave 1 has a maximum electric field strength that is three times the maximum field strength of wave 2. How do the average intensities of the waves compare?.
The passage below (paragraph 5) adds to the development of the essay mainly by showing: 1. That Jabeen wants to be a poet when she grows up 2. That Jabeen is friends with Anna3. That this passage takes place in 1990 4. That Russian spies are an active concern among Jabeen and the other students at her school Passage: I nodded along as Anna spoke, pulling textbooks from my backpack and stacking them in my locker where the poetry collection I had written for third period English sat visibly on the bottom shelf. SMERSH the title of the collection said, which was also the name of Stalins counterintelligence agency. Below it was the subheading, Death to Spies. It was 1990, and though the Cold War had recently smashed into pieces, wall by wall, mallet by mallet, we still spoke its language. It was no surprise to me that things like the USSR, KGB, dead drops, poisoned lipsticks and perestroika would find their way into the stanzas of my electric typewriter-printed pages.