We are given the following quadratic equation

[tex]f(x)=2x^2+7x-10[/tex]The **vertex** is the maximum/minimum point of the quadratic equation.

The x-coordinate of the vertex is given by

[tex]h=-\frac{b}{2a}[/tex]Comparing the given equation with the general form of the quadratic equation, the coefficients are

**a =** **2**

**b =** **7**

**c =** **-10**

The y-coordinate of the vertex is given by

[tex]\begin{gathered} f(x)=2x^2+7x-10 \\ f(-1.75)=2(-1.75)^2+7(-1.75)-10 \\ f(-1.75)=2(3.0625)^{}-12.25-10 \\ f(-1.75)=6.125^{}-12.25-10 \\ f\mleft(-1.75\mright)=-16.13 \end{gathered}[/tex]This means that we have a **minimum** point.

Therefore, the **minimum** point of the given quadratic equation is

**Answer:**

Exact Form:x=±√6/2

Decimal Form:x=1.22474487,−1.22474487

**Step-by-step explanation:**

I need help with 3x-2y=24 find the y and x intercept and the slope

3x-2y=24

3x - 2y + 2y = 24 +2y Adding 2y to both sides of the equation

3x - 24 = 2y + 24 - 24 Subtracting 24 from both sides of the equation

(3x - 24)/2= 2/2y Dividing by 2 on both sides of the equation

3/2x - 12 = y

From this form of the equation we deduce **the slope** (coefficient of x) **is 3/2** and **the y-intercept is equal to -12.**

To find the x-intercept, we replace y= 0 in the equation and isolate x

3/2x - 12 = 0

3/2x - 12+12 = 0+12 Adding 12 to both sides of the equation

x= 12/(3/2) Isolating x

x= 8

**The x-intercept is 8**

Nathan loved learning about earthquakes in science class. He told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10

–

6 centimeters per minute. What would be the most appropriate unit for Nathan to use instead of centimeters per minute?

The most appropriate **unit** for Nathan to use instead of **centimeters** per minute is centimeters per year.

An **earthquake** simply means a rapid motion of the solid layer of the **Earth**.

In this case, **Nathan** told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.

Since the year is being discussed, the **unit** should be based on the year.

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1. What is the reciprocal of 5? 6 Show your work below! (click "Show Work Type a response OD

**Answer:**

1/5

**Step-by-step explanation:**

a reciprocal is the multiplicative inverse

**Answer:**

The reciprocal of 5 is 1/5

**Step-by-step explanation:**

The reciprocal of a number is the fraction flipped upside down

6/1 = 1/6

⇒ 5/1 = 1/5

Find the midpoint of the line segment with endpoints (13,-14) and (-13, 10).

**Answer:**

(0, -2)

**Step-by-step explanation:**

Add the x value and divide by 2

[tex]\frac{13-13}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0

Add the y value and divide by 2

[tex]\frac{-14 + 10}{2}[/tex] = [tex]\frac{-4}{2}[/tex] = -2

please help

Which graph represents the solution set of the system of inequalities?

{y≥12x+1y>−x−2

Responses

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.

Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.,

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.

Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.,

The **graph **that represents the **system of inequalities** is the **graph** attached below.

The **graph** that would represent the **system of inequalities** must be two lines that intersect each other and have the exact slope and y-intercept of each of the lines on the **graph**.

Determine the slope and y-intercept of each of the **inequalities**, and also determine their boundary lines based on which **inequality** sign they have.

The line that represents the **inequality**, y ≥ ½x + 1, will be a solid line that has a slope of ½, and a y-intercept of 1.

The second line that represents the **inequality**, y ≥ -x - 2, will be a dashed line that has a slope of 1, and a y-intercept of -2.

Therefore, the **graph **that represents the features stated above for both lines is shown in the diagram below.

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Help me rewrite this problem to satisfy the provided boxes please

**EXPLANATION**

Since we have the expression:

Removing the parentheses:

[tex]5x^2+6x+5+6x^2-6x-5[/tex]Rearranging terms:

[tex]5x^2+6x^2+6x-6x+5-5[/tex]Adding like terms:

[tex]11x^2+0x+0[/tex]The final expression is as follows:

[tex]undefined[/tex]i need help asp ;-;

Which of the following values is less than −|58|?

A. −48

B. 68

C. −68

D. 48

C is less that -l58l

**Answer:**

C. -68

**Step-by-step explanation:**

Using absolute value symbols, it makes any negative number a positive. But, the negative sign is outside the absolute value signs, making the number -58. -68 is the only number less than -58.

Find the length of the sloping side of the roof. Give your answer to the nearest foot. Show your work.

Given:

The triangle having two similar angles.

This is the isosceles traingle.

Draw the altitude to the given traingle,

D divides the side BC into two equal side having length,

[tex]\begin{gathered} \frac{45}{2}=22.5 \\ BD=22.5\text{ and DC=22.5} \end{gathered}[/tex]Now, use the tan ratio for right triangle ABD,

[tex]\begin{gathered} tan15^{\circ}=\frac{AD}{BD} \\ 0.268=\frac{AD}{22.5} \\ AD=6.02=6\text{ f}eet \end{gathered}[/tex]Using the pythagorean theorem,

[tex]\begin{gathered} AB^2=AD^2+BD^2 \\ =6^2+22.5^2 \\ =542.25 \\ =23.286 \\ =23.3 \end{gathered}[/tex]The length of the sloping side of the roof is 23.3 feet.

Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential

200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP HELP I WILL GIVE BRAINLIEST AND 100 POINTS

!!

The **solution** for the inequality is** 11.746 ≤ x ≤ 24.44**

Kali earns a 15.75 plus a flat fee of 50 from her job.

She wants to earn between 200 and 400.

Let 'x' denote her **earning potential**.

Then the **inequality** for her earning potential is given by,

200 ≤ 15.75x + 50 ≤ 400

We solve this **inequality** for x.

Subtract 50 from the** inequality,**

⇒ 200 -15 ≤ 15.75x ≤ 400 -15

⇒ 185 ≤ 15.75x ≤ 385

Divide by 15.75,

⇒** 11.746 ≤ x ≤ 24.44**

is the solution for the** inequality**.

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if y =3x^3 + 2x^2 - 5x + 2, find d^3y/dx^3

**Answer****:**

18

**Step-by-Step**** ****Explanation****:**

[tex]\frac{dy}{dx}=9x^2 + 4x-5 \\ \\ \frac{d^2 y}{dx^2}=18x+4 \\ \\ \frac{d^3 y}{dx^3}=18[/tex]

Using FUNCTION NOTATION, assume you are given the function: y = 3x - 2. This can be rewritten as ________ = 3x - 2, since y can be replaced with _______.

The **complete statement** is:

This can be rewritten as _f(x)_ = 3x - 2, since y can be replaced with _f(x)__.

How to use function notation?A general **relation **is written as:

y = something that depends of x.

This is a relation that relates the **variable **y with the **variable **x, where we define x as the input and y as the output.

If this is a **function**, we can use the notation:

y = f(x).

(or any letter of x, f(x) is the most common notation used)

in this case, we have:

y = 3x - 2

And in **function notation**, this will be writen as:

f(x) = 3x - 2

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A car that travels from Las Vegas to Los Angeles averages about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles. Write a function to represent the distance d remaining on the trip t hours after departure.

The **distance** remaining is given by the** equation** d = 270 - 60t

Speed is the** ratio **of **distance **travelled to** time ta**ken. It is given by:

Speed = distance / time

Let d represent the **distance** from Las Vegas to Los Angeles and t represent the **remaining time **after departure.

A car travels from Las Vegas to Los Angeles at about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles.

Hence distance remaining is:

d = 270 - 60t

The **distance** remaining is d = 270 - 60t

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Name the point that lies on this line: y = 2 + 5(x + 7)

(1, 42)

1) Since we have an equation of the line y = 2 + 5(x + 7) let's find one point that ∈ to this line.

2) Let's plug into that for x, the value of x=1

y= 2+ 5(1+7)

y= 2 +5(8)

y= 2 +40

y= 42

3) So one of the points that lie on this line is (1, 42) i.e. belong to that line.

Let f(x) = 2x^2 – 3 and g(x) =x+1/2Find the value of (fof )(-1)A -1B-3C 0.5D 95

[tex]undefined[/tex]

Is the answer correct if no please let me know

Answer: 57

Given:

[tex]S_n=4n-3[/tex]We are asked to find the 15th term, meaning n = 15

[tex]S_n=4n-3[/tex][tex]S_{15}=4(15)-3[/tex][tex]S_{15}=60-3[/tex][tex]S_{15}=57[/tex]Therefore, the 15th term is 57.

A company has 40 salespeople. A board member at the company asks for a list of the top 5 salespeople, ranked in order of effectiveness. How many such rankings are possible?

The number of **rankings** that are possible when the company has 40 **salespeople** is 78960960.

Based on the information given, **permutations** will be used. The formula is illustrated thus:

**Permutations** = n! / (n – r)!

N is the number of things you are choosing from,

r is the number of items.

“!” is a factorial of a **number**

The company has 40 **salespeople** and the board member at the company asks for a list of the top 5. This will be;

= 50! / (40 - 5)!

= 40! / 35!

= 40 × 39 × 38 × 37 × 36

= 78960960

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Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?

Hence, the minimum **number** of** **sets of knives kaj should buy is 48** sets**.

Given this, a restaurant must have at least 736 knives.

At the moment, it possesses 155 knives.

Every set includes 12 knives.

Let the** number** of knife sets be.

Reason: Minimum **number** of sets indicates ≥

This means ≤ the maximum amount of sets

Step: 2

In light of the inquiries,

[tex]155+s*12\geq 736[/tex]

[tex]12s\geq 736-155[/tex]

[tex]12s\geq 581[/tex]

[tex]s\geq \frac{581}{12}[/tex]

[tex]s\geq 48.42[/tex]

Step 3: Count the number of knife **sets** [tex]s\geq 48.42[/tex]

that is greater than or equal to 48

Therefore, the required minimum is 48 **sets** of knives.

What are **sets**?

In mathematics, a set is a well-defined collection of objects. Sets are named and represented using capital letters. In the **set theory**, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.

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In which pair do both decimals represent rational numbers? O A. 9.0032812373025549382... and 0.12333.. OB. 0.115 and 0.12333... O C. 3.10382947305718274... and 0.123 O D. 9.0032812373025549382... and 0.115

Rational numbers can be formed by dividing 2 integers. It can be represented in this format x/y where y is not 0. Rational numbers, in decimal form are not repetitive and unending.

Therefore,

A quiz consists of two true false questions and two multiple-choice question with three choices each. How many different sets of answers are there?There aredifferent sets of answers.

We know that

• There are two true/false questions.

,• There are two multiple-choice questions with three choices each.

In the true/false questions, there are 4 ways to answer since each question has only two choices.

In the multiple-choice questions, there are 6 ways to answer since there are 3 choices per question.

Therefore, there are 10 ways to answer in total.i would appreciate so much if you could answer this and atleast explain a little how you did it (optional)

**Answer:**

**a.**

Fee of whole band = Fee of writer + guitarist + singer

Fraction of fee of whole band = 4/12 + 1/12 + 1/12

= 4+1+1/12

=6/12

=1/2

**b.**

Fee of writer= 4/12 of £3000

=3000 × 4/12

= £1000

Fee of singer= 1/12 of £3000

= 3000 × 1/12

= £250

Fee of guitarist= Fee of singer

= £250

HELP PLEASE.

Either Table A or Table B shows a proportional relationship.

Plot the points from the table that shows a proportional relationship.

( If you can, can you save the image as and edit it it will help me out a lot)

**Answer: Table A has a proportional relationship**

**See the diagram below**

==================================================

Explanation:

Table A has a proportional relationship because all the points are on the same straight line. That line in this case is y = 2x

Whatever x is, multiply it by 2 and you'll get the y value

Example: If x = 4, then y = 2*x = 2*4 = 8 which gives the point (4,8)

Another phrase for "proportional relationship" is "direct variation".

At a party, there are 30 men, 16 of whom are without dates, and 30 women, none of of whom are without dates. Find the probability of picking someone at random and getting a person who is a woman or without a date?

For this type of probability question, there are different ways to solve the same question but let's analyze the situation and calculate as simple as possible.

For our question, there are two parts, the first one first is the probability to pick someone who is a woman. Once there are 60 people of which 30 are women, it means this probability is 30/60. Let's keep this probability.

Now let's move on to the second part. The situation where we pick someone who is without a date. once there are 60 people and all 30 women have a date and 16 men also have a date it means 30 + 16 - 60 = 14 people does not have a date. So the probability to pick someone without a date is 14/60.

Now once we have analyzed the two parts of the question, and we have two probabilities all we need is to sum our probabilities, as follows:

*But why do we sum and do not multiply?* Because we use the proposition **OR** at "Find the probability of picking someone at random and getting a person who is a woman **OR** without a date" If the proposition was **AND** we would have multiplied both probabilities.

Determine whether the function has a minimum or maximum value and then find that value.()=−^2+2−7

Given function is

[tex]f(x)=-x^2+2x-7[/tex]Now,

[tex]\begin{gathered} f(x)=-(x^2-2x+7) \\ =-(x^2-2x+1+6) \\ =-\lbrack(x-1)^2+6\rbrack \\ =-(x-1)^2-6 \end{gathered}[/tex]Being a perfect square,

[tex](x-1)^2\ge0[/tex]Therefore,

[tex]-(x-1)^2\leq0[/tex]So,

[tex]f(x)\leq-6[/tex]**Theerfore, the maximum value of the given function is -6.**

The radius of a circle is 14 cm. Find its circumference in terms of pie

Explanation.

The question wants us to determine the circumference of the circle.

Circumference of a circle simply means the perimeter of a circle, and the formula to be used is

[tex]\begin{gathered} C=2\pi r \\ where \\ r=radius=14cm \end{gathered}[/tex]100 points asap and brainliest

**Answer:**

68

**Step-by-step explanation:**

Althea needs 134 ounces of cold cuts for a party. How many pounds and ounces does she need?

The number of** pounds and ounces** that we have in 134 ounces is; 8 pounds 6 ounces

How to carry out units conversion?

We know that in** units conversion**, there are different units and their **conversion rates**. For example;

1 meters = 100 cm

1000 meters = 1 kilometer

1000 grams = 1 kilograms

100 cents = 1 dollar

Now, we want to **convert **ounces to pounds.

The conversion rate for ounces to pounds is;

1 ounce = 0.0625 pounds

We are given 134 ounces of cold cuts for a party. **Converting **that to pounds gives us;

134 * 0.0625/1 = 8.375 pounds

Now, we want it in pounds and ounces and so we **convert** the **decimal **part to ounces

1 pound = 16 ounces

0.375 pounds = 0.375 * 16/1 = 6 ounces

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3. Given: B is the midpoint of AC, AD = CD

Prove:

DAB = LDCB

Statements

1)

2) AB=CB

3) DB DB

4)

5) ZDAB=2DCB

A

1)

2)

3)

5)

Reasons

D

B

C

Using the** congruency **of the triangle we can prove all the conditions.

The **dimensions** of the sides and angles of two or more triangles determine whether they are **congruent**. A triangle's size and shape are determined by its three sides and three angles, respectively. Two triangles are said to be congruent if pairings of corresponding sides and corresponding angles are equal. They are the exact same size and form.

D is the **midpoint** of AC

so AB = BC

and also AD = CD

so the **triangle** ADB is congruent to triangle CDB

Therefore,

angle ADB = angle CDB

angle ABD = angle CBD

angle BAD = angle BCD

Using **congruency** of the triangle.

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Mr. Thomatos thinks that {3, 8} and [3, 8] represent the same set of values Is Mr. Thomatos correct? Why or why not? Explain. (giving brainliest)

{3,8} give the **values **of set that **implies **the set has two **elements **3 and 8. [3,8] give the range of **values **that can be used in any **functions **with values from 3, 4, 5, 6, 7, 8 both 3 and 8 included.

Sets are collections of well-defined objects or elements in mathematics. A set is denoted by a capital letter symbol, and the number of elements in a finite set is denoted by the cardinal number of a set enclosed in a curly bracket{...}.

What is Function?A function is defined as a **relationship **between a set of inputs that each have one **output**. A function is a relationship between **inputs **in which each input is related to **exactly **one output. Every function has a domain and a codomain, as well as a range.

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I don’t understand this paper and our sub has no idea, nor the other students so if someone could help me, that would be great.

By **Angle-Angle theorem** similarity ΔABC is similar to ΔA'B'C'.

Given two triangles are ABC and A'B'C'.

What is a dilation?**Dilation** is the process of resizing or **transforming** an object. It is a transformation that makes the objects **smaller** or **larger** with the help of the given **scale factor**. The new figure obtained after dilation is called the image and the **original image** is called the pre-image.

1) Triangle ABC is **reduced** to triangle A'B'C'

∠ABC=∠A'B'C'=90°

∠BAC=∠B'A'C'

So, by AA similarity

ΔABC≈ΔA'B'C'

2) Triangle ABC is **enlarged** to triangle A'B'C'

∠ABC=∠A'B'C'

∠BAC=∠B'A'C'

So, by AA similarity

ΔABC≈ΔA'B'C'

Therefore, by **Angle-Angle theorem** similarity ΔABC is similar to ΔA'B'C'.

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In a math class , there are 14 girls and 16 boys. Which of the following ratios does NOT represent between girls and boys?A. 14:16B. 14/16C. 7 to 8D. 2:9its not college mathematics its middle school

No. of girls = 14

No. of Boys =16

Therefore the ratio, from girls to boys is,

[tex]\frac{14}{16}[/tex]Which can also be written as,

[tex]\begin{gathered} 14\colon16 \\ 7\text{ to 8} \end{gathered}[/tex]Therefore, the wrong ratio is option D.

That is,

[tex]2\colon9[/tex]So, the answer is option D.

The expansion of the railroad directly to economic growth in the US because
A prospector graphed the locations of a gold vein and all of the gold dust strikes in the vicinity. He positioned the gold vein at ( 8 , 9 ) ( - 8 , 9 ) and the farthest gold dust strike at ( 7 1 , 9 ) . ( 7 1 , 9 ) . If each unit on the graph represents 1 m i l e , then how far away from the gold vein is the farthest gold dust strike?
The ratio of the length of Skylar's bridge to the length of Karen's bridge is 3.4. Karen's bridge measure 48 inches.How long is Skylar's bridge
The first time I listened to Taylor's new album, I didn't enjoy it nearly as much as her last one. But the more I played it, themore I got into it, and now I think it's just as good as her older music. Has this ever happened to you? A new song or flavordoesn't impress you at first, but the more you experience it, the more you like it? If it has, you've experienced the 'mereexposure effect. This effect explains why things 'grow on' us as we get used to them, and why advertisers play the same adsover and over again."Who is the intended audience for this paragraph and how does it shape the text?The audience is people searching for information on how the brain responds to new experiences. The text is written toconvey as much information about how the brain works as possible.The audience is people flipping through a magazine looking for light entertainment. The passage uses a personal story tocatch their attention and then asks them a question to pull them in further.The audience is musicians. The paragraph follows a timeline to help them understand how audiences and critics will changetheir opinions over time.The audience is psychology students. It uses everyday examples to show the students how to speak about complex ideaswith their patients.40F3aOct 139:05US
Me gusta invitar a mis amigos a mi casa para cenar. Para esta noche, yo (invitar) a tres amigos: Fernn, ngel y Clara. Ellos van a traer unos platos preparados antes, porque hoy no tengo tiempo para cocinar todo. Yo (cocinar) unas chuletas de y arroz. ngel y Clara (preparar) una ensalada y una sopa de tomate, y ngel prepar el : un flan de vainilla. Yo voy a servir a mis amigos una botella de tinto con la cena. Va a ser una cena muy deliciosa!
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Use the give piece wide function to answer the questions belowF(-4)= f(2)= f(6)= f(0)=