Mathematics High School

solve 14x^2 + 42x + 70 = 0

Answers

Answer 1

Answer:

x = -3/2 ± i(√11)/2

Step-by-step explanation:

The quadratic formula can be used directly, but I find it convenient to divide by 14 first:

x^2 +3x +5 = 0

The solution to ...

ax^2 +bx +c = 0

is given by the formula ...

x = (-b ±√(b^2 -4ac))/(2a)

Here, we have a=1, b=3, c=5, so the formula gives the solutions ...

x = (-3 ±√(3^2 -4·1·5))/(2·1) = -3/2 ± i(√11)/2 . . . . . solutions are complex

Related Questions

Evaluate the expression (ab)2 for a = 4 and b = 3.

a.81
b.36
c.24
d.144

Answers

The answer is 24.
(ab)2 = (4x3)x2 = 12x2 = 24

A sample value that lies very far away from the majority of the other sample values is _____.

Answers

The answer to the missing word on the statement in this problem is an outlier.An outlier is a value that lies outside most of the other values in a set of data. It also means it is much smaller or larger than most of the values in a set.For example, in this given score set {24,29,2,32,88,33,26,28}. The scores 2 and 88 are outliers.

Answer:

It would be an outlier

Step-by-step explanation:

Fernando is starting at new sales job and needs to decide which of two salary plans to choose from for Plan A he will earn $100 a week plus 15% Commission on all sales for Plan B he will earn 150 week plus 10% Commission on all sales

Answers

The expression for each salary plan if s is Fernando's total weekly sales, would be:

Expression A: S= 100+ 100(0.15y) y=Commission
Expression B: S= 150+ 150(0.10y)

What amount of weekly sales us plan B better than plan A, the answer would be:Plug in the numbers for Y and use the outcomes as the sales stay to increase. For example, start with 5 sales, then go to 10 then 15, and so on and so forth.

The perimeter of a rectuangler pool is 130 ft. the width is 4 times the length. find the length and width of the pool

Answers

The width is 52ft and the Length is 13ft.

butch, harry, and nicky are playing a game. Harry has half as many points is butch. Nicky has 5 fewer points than Harry. Together, the three players have 31 points. How many points does Harry have?

Answers

Harry has 9 points. First, make some expressions to show what you know. I'll use the variables b, h, and n to represent the number of points each player has h = b/2 n = h - 5 b + h + n = 31 Substitute h - 5 for n in the 3rd expression b + h + h - 5 = 31 Now substitute b/2 for the h's in that expression b + b/2 + b/2 - 5 = 31 Now solve for b, first add the b terms together 2b - 5 = 31 Add 5 to both sides 2b = 36 Divide both sides by 2 b = 18 We now know that Butch has 18 points, so plug that value into the formula for Harry's points h = b/2 h = 18 / 2 h = 9 And we now know that Harry has 9 points.

The water level at Lake Penny changed −1 1/10 in. this year. Next year, it is predicted to change another −1 2/5 in. What is the total change that will likely occur in 2 years? Enter your answer as a simplified mixed number in the box. 20 POINTS

Answers

add 1 1/10 + 1 2/5

first get both fractions with the same bottom number: 2/5 = 4/10 ( multiply both numbers by 2)

so now you have 1 1/10 + 1 4/10 = 2 5/10

5/10 reduces to 1/2

so answer is 2 1/2 inches, and since the level is going down it would be negative 2 1/2 inches

Answer:

-2 1/2 inches is your answer

Stan, a local delivery driver is paid $3.50 per mile driven plus a daily amount of $75. On Monday he is assigned a route that is 30 miles longer. How much is he being paid for that day? Independent and dependent variables?

Answers

3.50m+75 for the 30 miles, he is being paid 105 plus the daily amount of 75 which equals to 180$.

PLEASE HELP!!!!! How does “rationalizing the denominator” use the form of 1?

Answers

"Rationalizing the denominator" of a number is exactly what its title implies: turning its denominator into a rational number.

For an example, let's take the fraction 1/√2. We call √2 irrational because it cannot be expressed as a ratio of two integers. Oftentimes when we have irrational numbers like √2 in the denominator, it helps to perform a little bit of algebraic manipulation on them to make the denominator rational. Here's where that "form of 1" comes in. Remember that, as a rational number, 1 can be expressed as n/n, where n is any number. We can use this fact to rationalize the denominator of 1/√2 by multiplying it by √2/√2, which is equivalent to 1.

When we multiply the two together, we get:

[tex] \frac{1}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}= \frac{\sqrt{2}}{(\sqrt{2})^2}= \frac{\sqrt{2}}{2} [/tex]

Crucially, multiplying by 1 in the form of √2/√2 keeps the fraction's value the same, since 1 times any number just equals that same number. If we weren't multiplying but some form of 1, we'd change the number entirely, making the whole attempt at rationalizing the denominator pointless.

To support a shelf, the diameter of a bolt can be measured anywhere from 0.2 cm less than 1.5 cm to 0.2 greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt

Answers

In the question "To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?" The values from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm are values from 1.5 - 0.2 to 1.5 + 0.2 = 1.3 cm to 1.7 cm The graph is a graph on the number line starting from the point 1.3 to 1.7.

Answer:

The answer is A.

Step-by-step explanation:

We use filled in dots because it can be anything .2 and less or, .2 or more.

The declaration opens with a rational statement of its purpose. in a document with such radical intent, its is not surprising that supporting details often use emotionally laden language.Find at least 5 details in the document that use loaded words to cite factual support . What emotions are revealed in the use of charged language ?

Answers

The Declaration of independence is full of loaded language. It invokes the will of god to support its cause and talks of the power of man and nature. It uses words that conjure visual thoughts, such as dissolving the political bands that held the two nations together. With this language you can visualize these tethers being dissolved. It speaks of equality and drums up feelings of self and National pride.

Final answer:

The document uses emotionally loaded language to support its claims. This creates a strong emotional impact on readers and helps persuade them.

Explanation:

When analyzing a document, it is important to pay attention to emotionally loaded language used as factual support. Here are five details in the document that use loaded words:

Quoting from interviews with government workers and bystanders who were hiding behind locked doors and had no police protection, appealing to the emotion of fear.Recreating images with vivid descriptions and concrete language of lone officers overwhelmed by crowds of people and beaten, appealing to the emotions of fear and empathy.Using nonaggressive language to address opposing views, showing empathy and attempting to convince others to support the author's position.Adhering to descriptive diction and employing sensory detail, creating a rhetorical effect.Refuting counterclaims and appealing to readers' logic and emotions, demonstrating fairness and advanced skill at persuasion.

The use of emotionally charged language reveals the emotions of fear, empathy, conviction, and persuasion in the document.

Mike bought 4 new baseball trading cards to add to his collection. the next day his dog ate half of his collection. there are now only 42 cards left. how many cards did mike start with

Answers

(4 + x) / 2 = 42
(2) (2)

4 + x = 84
-4 -4

x = 80

Mike started with 80 cards

Hope I helped :)

The office manager ordered145 packs of printer paper. Based on average daily use, she knows that the paper will last 65 days. What graph represents this situation? How many packs of printer paper should the manager expect to have after 25 days?

Answers

The first or third graph represents the situation
After 25 days he would expect to have , i would say 88 packs left
I cant make out the bottom figure below third graph

Find the total amount in the compound interest account.
$1740 is compounded daily at a rate of 12% for 5 years. Let 1 yearequals=365 days.

=$

Answers

[tex]\bf \qquad \textit{Compounding Continuously Earned Amount}\\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$1740\\ r=rate\to 12\%\to \frac{12}{100}\to &0.12\\ t=years\to &5 \end{cases} \\\\\\ A=1740\cdot e^{0.12\cdot 5}[/tex]

bear in mind that the continuously compounding interest is just that, a daily compounding cycle, taking a year as 365days.

How would you convert 9 km/hour to feet/minute? Oh, and please show the steps you took to get there. Thank you. (This is worth extra points btw)

Answers

keeping in mind that

there are 1.609 kms in 1 mile

5280 feet in 1 mile

and 60 minutes in 1 hr.

[tex]\bf \cfrac{9~\underline{km}}{\underline{hr}}\cdot \cfrac{\underline{mile}}{1.609~\underline{km}}\cdot \cfrac{5280~ft}{\underline{mile}}\cdot \cfrac{\underline{hr}}{60~mins}\implies \cfrac{9\cdot 5280~ft}{1.609\cdot 60~mins} \\\\\\ \cfrac{47520~ft}{96.54~mins}\approx 492.2311995\frac{ft}{min}[/tex]

A line passes through the point (3,2) and (6,2) a write an equation for the line in point-slope form rewrite the equation in standard form usung integers

Answers

(3, –2) and (6, 2)First, we must establish slope...m=(y-y1)/(x-x1)m=(-2-2)/(3-6)m=-4/-3m=4/3Point slope formula is...y-y1=m(x-x1)Let's select either coordinate. I randomly select the first (3, –2)...y--2=4/3(x-3)Subtracting a negative number is the same as adding a positive number...y+2=4/3(x-3)This corresponds to the first answer.Standard form...Ax+By=Cy+2=(4/3)x-4y=(4/3)x-6-(4/3)x+y=-6Multiply both sides by 3...-4x+3y=-18This also corresponds to the first answer. How about the second coordinate, (6, 2)...y-y1=m(x-x1)y-2=(4/3)(x-6)Let's convert it into standard form..y-2=(4/3)x-8y=(4/3)x-6-(4/3)x+y=-6Multiply both sides by 3...-4x+3y=-18

Triangle STU has been reflected over line m to form triangle S'T'U'. what is the value of y

Answers

Where is y? Is there a figure?

List the descriptors used to interpret a scatterplot and provide a brief explanation for each

Answers

The descriptors used to interpret a scatterplot are strength, association and trends. The strength determines how closely the dots fall to the line, the association is the general direction in which the dots fall, and the trend or shape lets one know if the graph is linear or non-linear.

Joe decides to take his six year old son to the planetarium the price for the child’s ticket it’s $5.75 less than the price for the adult ticket if you represent the price for the child’s ticket using the variable X how would you write the algebraic expression for the adult ticket price

Answers

Child's ticket x=y-5.75
Adult would be found by solving for y.
x=y-5.75
5.75+x=y-5.75+5.75
5.75+x=y

Y=x+5.75

answer: Y=x+5.75hope this helps:D

plz give bainiest

angle of elevation and depression worksheet

Answers

The angle of depression is the angle in which is looking down , so in this case it’s the angle from the top of the flag pole to the gold ball. Then you write in you opposite and hypotenuse and adjacent then write out your equation plug in. Then type your final answer in the calculator and you should get your answer .

For which value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers

Answers

The trick here is to find the discriminant, b^2-4ac, of the equation 2x^2 - 5x + k.
Here a=2, b=-5, and c=k.

So long as the discriminant is 0 or greater than 0, your roots will be real and rational numbers.

Thus, compute b^2-4ac: (-5)^2 - 4(2)(k)

Let this equal zero and solve for k: 25=8k; k=25/8.

So long as k is 25/8 or smaller, b^2-4ac will be 0 or greater, and the roots will be real and rational.

25/8 is the value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers

What is quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

We need to find the value of k will the roots of the equation 2x²-5x+k=0 be real and rational numbers.

A quadratic equation has real roots when the discriminant is positive or zero (not negative).

b²-4ac≥0

b=-5, a=2, c=k

(-5)²-4((2.k)≥0

25-8k≥0

25≥8k

Divide both sides by 8

25/8≥k

k≤25/8

Hence, 25/8 is the value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers

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How do I write this as a single rational expression?

[tex] \frac{1}{p-2} - \frac{1}{p+2} [/tex]

Answers

[tex]\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ \cfrac{1}{p-2}-\cfrac{1}{p+2}\impliedby \textit{so let's use the }\stackrel{LCD}{(p-2)(p+2)} \\\\\\ \cfrac{(p+2)~~-~~(p-2)}{(p-2)(p+2)}\implies \cfrac{\underline{p}+2~~\underline{-p}+2}{(p-2)(p+2)}\implies \cfrac{4}{p^2-2^2}\implies \cfrac{4}{p^2-4}[/tex]

A movie theater sells student tickets for $5 and adult tickets for $10. On Saturday night, 2,500 people go to the theater and ticket sales total $18,000. How many adults and children went to the theater on Saturday night? Which solution is reasonable? A) 2000 students and 1000 adults B) 1100 adults and 1400 students C) 3000 students and 0 adults D) 500 students and 1500 adults

Answers

The problem says that 2500 people went, out of all the answers choices which choice gives you the total of 2500 when you add the adults and children.

Answer is B because 1100 + 1400 = 2500

The reasonable solution is B) 1100 adults and 1400 students, as it satisfies both attendance and revenue criteria.

Consider a movie theater that sells student tickets for $5 and adult tickets for $10. On a Saturday night, 2,500 people attended the theater, and the total ticket sales amounted to $18,000. The goal is to determine the number of adults and students who attended, with multiple choices provided:

We can set up two equations to represent the information:

The total number of people who attended: S + A = 2500

The total ticket sales amount: 5S + 10A = 18000

Solving this system of equations gives the correct solution:

B) 1100 adults and 1400 students.

This solution satisfies both equations (S + A = 2500 and 5S + 10A = 18000). It is reasonable as it accounts for both students and adults attending, and the total revenue aligns with the given information. The number of students (1400) and adults (1100) adds up to the total attendance of 2500.

Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose a point on the line, such as (2, 5). Step 2: Choose another point on the line, such as (1, 3). Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is . Step 4: Substitute those values into the point-slope form. y – y1 = m(x – x1) y – 3 = (x – 1) Which of Talia’s steps is incorrect? Step 1 is incorrect because it uses a point that is not on the line. Step 2 is incorrect because it uses a point that is not on the line. Step 3 is incorrect because it shows an incorrect ratio for the slope. Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.

Answers

C - took the test on edgenuity

Answer:

Step 3 is incorrect because it shows an incorrect ratio for the slope.

Step-by-step explanation:

what is 4x-9=k solve for the x

Answers

solve for x by simplifying both sides of the equation than isolating the variable

x=9/4 + k/4

hope this helps and please rate below :)

Hey Johna!

4x - 9 = k
Add 9 to both sides
4x - 9 + 9 = k + 9
4x = k + 9
Divide both sides by 4
4x/4 = (k + 9)/4
x = (k + 9)/4

Good luck!

Find two numbers whose product is 20 and whose sum is 12

Answers

10 * 2 = 20
2 + 10 = 12

Answer 2 and 10

The numbers are 10 and 2 if the product is 20 and whose sum is 12 after making the two equations.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The product of two numbers is 20 and whose sum is 12

Let the numbers are x and y

xy = 20

x + y = 12

y = 12 - x

x(12 - x) = 20

x² - 12x + 20 = 0

After solving the above quadratic equation, we get:

x = 10, 2

y = 2, 10

Thus, the numbers are 10 and 2 if the product is 20 and whose sum is 12 after making the two equations.

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What is the meaning of life? What makes this world so great? Is there something to look forward to in the future?

Answers

well if your one of those people, this question is actually very easy to answer.the meaning of life too me is simply to live.and anything good is not bad so, anything you can think of that is good is what makes the world good.;)

42 is the joking answer here. No, there is meaning to life. It really depends who you are talking to . A Christian or Jew would say that it is to please God. A Buddhist would say to live life like a good person so as to be ascended. Most people agree, however, that life is assigned the meaning you give it. If you believe that life is made to serve you, go for it! The second question now. This world is great because of life. I'd like to refer you to the Galaxy Song by Monty Python. It talks about how incredible the universe is, how unlikely ot is for us to even exist. And answering your final question: yes. The future may appear grim due to what is seen on the news, but while there is evil, greatness occurs. Science is progressing faster than ever before. We are slowly eradicating terroristic threats, and the standard of life for all will increase. Life is amazing, and the future promises great things ahead.

The seventh grade math classes are going on a field trip. the field trip will cost $7 per student. write an expression to find the cost of the field trip for s students. what is the total cost if 26 students go on the trip?

Answers

cost = 7s; where s is the number of students who paid.

Plugging in 26:

cost = 7 * 26
cost = 182

Hope this helps!

7s is the expression to find the cost of the field trip for s students and 182 is the total cost if 26 students go on the trip

What is Expression?

An expression is combination of variables, numbers and operators.

Given,

The seventh grade math classes are going on a field trip.

the field trip will cost $7 per student.

Given s is number of students.

7s is the expression to find the cost of the field trip for s students.

When number of students are twenty six 26, i.e s=26

Total cost=7×26

seven times of twenty six

182

Hence 7s is the expression to find the cost of the field trip for s students and 182 is the total cost if 26 students go on the trip

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Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.

Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)

Part B: Write the equation obtained in Part A using function notation. (2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Answers

14.33 ( x) = y is for the first one sorry I could only do the that one.

Answer:

A: r-14x-1=0

B: r(x)=14x+1

C: x= left to right axis

y= up to down axis

domain= x,0

range= r,0

slope= 14

x-intercept= r=0 ==> 0=14x+1 ==>x=(-1/14,0)

r-intercept= x=0 ==> r=14(0)+1= (0,1)

make sure to right it in your own.

Solve for PQ 4x+19=2x+32

Answers

4x + 19 = 2x + 32

4x (- 2x) + 19 = 2x (- 2x) + 32

2x + 19 (-19) = 32 (-19)

2x = 13

2x/2 = 13/2

x = 13/2, or 6.5

hope this helps

All the Factor of 40

Answers

The factors of 40 are:
1,2,4,5,7,10,20,40

The factors of 40 are whole numbers that divide 40 without a remainder, including 1, 2, 4, 5, 8, 10, 20, and 40.

To find all the factors of 40, you need to identify all the whole numbers that can divide 40 without leaving a remainder. The factors of 40 are numbers that multiply together to give the product of 40. Here's how we can find them:

List the number 1 and the number itself (which is 40) because 1 and 40 are always factors of 40.Try dividing 40 by whole numbers starting from 2 onwards.If the division does not leave a remainder, then the divisor is a factor of 40.Repeat this process with increasing numbers until you reach the square root of 40

Therefore, the factors of 40 are: 1, 2, 4, 5, 8, 10, 20, and 40.

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