Answers
We are given the following function:
\(y=x^2+2x-8\)This is a quadratic equation since the greater exponent of the independent variable "x" is 2.
Every quadratic equation follows the general form:
\(y=ax^2+bx+c\)To put it in the form:
\(y=(x-h)^2+k\)We will use a technique called "completing the square". This consist in adding and subtracting the following term:
\((\frac{b}{2a})^2\)In the given equation these terms are:
\(\begin{gathered} a=1 \\ b=2 \end{gathered}\)Therefore, the term we need to use is:
\((\frac{2}{2(1)})^2=1\)Therefore, we need to add and subtract 1 to the given function:
\(y=x^2+2x-8+1-1\)Associating terms terms we get:
\(\begin{gathered} y=x^2+2x+1+(-8-1) \\ y=(x^2+2x+1)-9 \end{gathered}\)Now we factor the expression inside the parenthesis using trinomial factoring. We take the square roots of the first and third term, we add them and we square them, like this:
\(y=(x+1)^2-9\)And thus we have put the function in the desired form where:
\(\begin{gathered} h=-1 \\ k=-9 \end{gathered}\)Related Questions
What is the equation for this word problem?:
Salma has 18 cars available to rent.
Last C be the number of cars she would have left after renting R of them.
Help!!!
Answers
Answer:
equation: C = 15 - R
C = 15 - 7
C = 8
Step-by-step explanation:
Okay first of all stan the karl pfp
rovide an appropriate response.
Determine the number of classes in the frequency table below.
tableau3 ( (Class Frequency)(23-24 7)(25-26 2)(27-28 6)(29-30 4)(31-32 1) )
2
5
6
20
Answers
There are 5 classes in the frequency table.
What is frequency table?The frequency of each data point or interval in a dataset is displayed in a frequency table. It is a technique for arranging data such that patterns and connections within the data may be examined. Two columns are normally present in the table: one for the intervals or data points (referred to as classes) and the other for the frequency of recurrence for each class. The classes may be intervals of equal size or they may be determined by the data's relevant categories or values.
From the given table we have:
Class 1: 23-24 (frequency of 7)
Class 2: 25-26 (frequency of 2)
Class 3: 27-28 (frequency of 6)
Class 4: 29-30 (frequency of 4)
Class 5: 31-32 (frequency of 1)
There are 5 classes in the frequency table.
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\( \frac{1}{2 \sqrt{x} } \geqslant \frac{1}{16} \)
Answers
Answer:
\(0\le x\le 64\)
Step-by-step explanation:
\(\dfrac{1}{2\sqrt{x} } \geq \dfrac{1}{16}\)
Using substitution
\(\sqrt{x} = t\)
\(\dfrac{1}{2t} \geq \dfrac{1}{16}\)
Multiply both sides by 2
\(\dfrac{1}{t} \geq \dfrac{1}{8}\)
Multiply both sides by \(t\). We can do it because \(t > 0\)
\(1 \geq \dfrac{t}{8}\)
Multiply both sides by 8
\(8 \geq t\)
As \(t=\sqrt{x}\)
\(8 \geq \sqrt{x}\)
So
\(x\le 64\cap x\ge 0\)
\(0\le x\le 64\)
I NEEDD HELPPP ASAPPPPPPPP
Answers
The value of sin (α + β) is,
⇒ sin (α + β) = - 135/377
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Angle α in quadrant 3:
y = opposite = 21 and x = adjacent = 20
Then, hypotenuse = √( 21² + 20²)
= √ ( 441 + 400)
= sqrt( 881)
So, sin α = 21/√881
= 21 × sqrt(881)/881
And, cos α = 20/sqrt(881) = 20sqrt(881) / 881
Since, Angle β in Quadrant 2:
Hence, adjacent = -5 and hypotenuse = 13
Then, by Pythagorean,
y = opposite = 12
So, sin β = 12/13, cos β = -5/13
as given,
And, tan β = -13/12
Since, We know that;
sin (α + β) = sin α cos β + cos α sin β
= 21/√881 × - 5/13 + 20/√881 × 12/13
= 1/√881 (- 105/13 + 240/13)
= - 1/√881 (135/13)
= - 135/377
Hence, The value of sin (α + β) is,
sin (α + β) = - 135/377
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If the triangles are similar, what is the value of x?
Answers
Answer:
\( 180 - 16 - 126 = 38\\ 13x = 180 - 16 - 38\\ 3x = 126 \\ 3x = 126 \\ x = \frac{126}{3} = 42\)
Coresponding angles of similar triangle are congruent.
To find the missing angle of the triangle on the right you conplete the equation 180-126-16, which equals 38.
Since congruent angles of similar triangle are congruent, the leftmost angle on the triangle to the right is also 38.
After that you have to solve the equation:
180=16+38+3x.
180=54+3x
-54 -54
126=3x
/3 /3
42=x
Bigco Corporation is one of the nation’s leading distributors of food and related products to restaurants, universities, hotels, and other customers. A simplified version of its recent income statement contained the following items (in millions).
Cost of sales $ 11,571
Income taxes 249
Interest expense 23
Net earnings 1,442
Sales 16,400
Earnings before income taxes 1,691
Selling, general, and administration expense 3,543
Other revenues 428
Total expenses (excluding income taxes) 15,137
Total revenues 16,828
Prepare an income statement for the year ended June 30, current year. (Hint: First order the items as they would appear on the income statement and then confirm the values of the subtotals and totals.)
Answers
Step-by-step explanation:
I hope this answer is helpful ):
What is the value of v? v+48° v–46°
Answers
Answer:
Step-by-step explanation:
Add v and 48°v
49v−46°
Isabella's Flower Shop sells a variety of flowers. Roses cost $5 each. The shop gives a discount of $1 off per rose if more than 10 are bought. Daisies are sold in bunches of 6 flowers and cost $4 per bunch. • Nala bought 12 roses for her friend's going-away party. • Hector bought his mother 4 bunches of daisies for her birthday. • Petunias cost $2 more per bunch than daisies. Use the axioms to make three conclusions about the flowers Isabella sells.
Answers
Answer:
Isabella earned $48 from Nara. Isabella earned $16 from Hector. Isabella sells petunias for $6 per bunch (the number of petunias per bunch is unclear).
Step-by-step explanation:
Nala bought 12 roses which is greater than 10. So she received a $1 discount for each one. Nara spent 12*4=$48 dollars.
Hector bought 4 bunches of daisies meaning that Hector spent 4*4=$16.
Petunias cost $6 per bucnh.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
\(BC=5.1\)
\(B=23^{\circ}\)
\(C=116^{\circ}\)
Step-by-step explanation:
The diagram shows triangle ABC, with two side measures and the included angle.
To find the measure of the third side, we can use the Law of Cosines.
\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)
In this case, A is the angle, and BC is the side opposite angle A, so:
\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)
Substitute the given side lengths and angle in the formula, and solve for BC:
\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)
\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)
\(BC^2=49+9-42\cos 41^{\circ}\)
\(BC^2=58-42\cos 41^{\circ}\)
\(BC=\sqrt{58-42\cos 41^{\circ}}\)
\(BC=5.12856682...\)
\(BC=5.1\; \sf (nearest\;tenth)\)
Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:
\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)
Substitute the values of the sides and angle A into the formula and solve for the remaining angles.
\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)
Therefore:
\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)
\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)
\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)
\(B=22.5672442...^{\circ}\)
\(B=23^{\circ}\)
From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):
\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)
\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)
\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)
\(180^{\circ}-C=63.5672442...^{\circ}\)
\(C=180^{\circ}-63.5672442...^{\circ}\)
\(C=116.432755...^{\circ}\)
\(C=116^{\circ}\)
\(\hrulefill\)
Additional notes:
I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.
The Ozzie Chocolate Company is preparing to offer a new product in its candy offerings, the Minty Dark Chocolate Bite bar. Material costs per new candy bar are
$0.25 for chocolate, $0.02 for sugar, and $0.03 for mint flavoring. Labor costs of the new product are approximately $0.15 per bar. Adding a production line devoted to the new candy will cost $250,000 per year.
(a) If the sales price is $1.40 per candy bar, how many must the company make per year in order to break even? Assume that each bar made is sold at full price.
(b) What is the company's profit or loss if they make and sell 270,000 candy bars at the $1.40 price in the first year?
(c) About 20% of the food consumed in the U.S. is imported. Production in many industries has been offshored. What ethical issues do companies face when presented with the decision to move operations?
Answers
Answer:
a) 263,158
b) $164,500
c) Ethical issues companies face when deciding to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
Step-by-step explanation:
a)
Total cost = (0.25 + 0.02 + 0.03 + 0.15) x + 250,000
Total revenue = 1.40x
Setting the two equations equal to each other and solving for x, we get:
(0.45)x + 250,000 = 1.40x
0.95x = 250,000
x ≈ 263,158
b)
If the company sells 270,000 candy bars at $1.40 each, the total revenue generated is:
270,000 * $1.40 = $378,000
The total cost of producing 270,000 candy bars is:
(0.25 + 0.02 + 0.03 + 0.15) * 270,000 + $250,000 = $213,500
Therefore, the company's profit is:
$378,000 - $213,500 = $164,500
c)
Ethical issues companies face when presented with the decision to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
Chlorpheniramine 100 ml
Lidocaine 2 oz
Banana flavoring ½ tsp
Take 10 ml BID
How many days will this solution last?
Answers
The number of days that this solution will probably last would be = 8 days.
How to calculate the total number of days the solution will last?To calculate the number of days the solution will last the following is taken into consideration.
The parameters given which are not in ml should be converted to ml as follows;
2 Oz of Lidocaine to ml = 2×29.6=59.2ml
½tsp of banana flavouring;
= 1/2×4.92
= 2.5ml
Therefore the total volume of the solution = 100+59.2+2.5 = 161.7ml
But 2×10 = 1 day
20ml = 1 day
161.7ml = X
Make X the subject of formula;
X = 161.7/20
= 8.1
= 8 days.
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Write an algebraic expression for: 2 less than 1/2 of the points the Jaguars scored. Use "x" as your variable.
Answers
Let:
T = Total score
x = points
\(T=\frac{1}{2}x-2\)Simplify (3x + 1)2 using the square of a binomial formula.
A) x2 + 2x - 1
B) 9x2 + 6x + 1
C) 9x² - 6x-1
D) 9x2 + 2x + 1
Answers
Answer:
B) 9x² + 6x + 1
Step-by-step explanation:
(3x + 1)^2
(3x + 1) • (3x + 1)
9x² + 3x + 3x + 1
9x² + 6x + 1
A bag contains 3 gold marbles, 8 silver marbles, and 30 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
Answers
Answer: To calculate the expected value, we need to multiply each possible outcome by its probability and then add up the results.
The probability of selecting a gold marble is 3/41, the probability of selecting a silver marble is 8/41, and the probability of selecting a black marble is 30/41.
The winnings/losses associated with each outcome are $3 for gold, $2 for silver, and -$1 for black.
Step-by-step explanation:
Therefore, the expected value can be calculated as follows:
(3/41) x $3 + (8/41) x $2 + (30/41) x (-$1)
= $0.073
The expected value is $0.073, which means that on average, you can expect to win $0.073 per game if you play this game many times.
Therefore, if you play this game, you can expect to win a small amount of money on average, but it is not a guaranteed win.
References:
Grinstead, C.M. and Snell, J.L. (2006). Introduction to Probability. American Mathematical Society.
"Expected Value," Investopedia, accessed May 14, 2023, https://www.investopedia.com/terms/e/expectedvalue.asp.
-) Find the equation of the line that passes through (1,0) and (3,6).
Answers
The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.
To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.
Given points:
Point 1: (1, 0)
Point 2: (3, 6)
Step 1: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates:
m = (6 - 0) / (3 - 1)
m = 6 / 2
m = 3
Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).
Using Point 1 (1, 0):
0 = 3(1) + b
0 = 3 + b
b = -3
Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):
y = 3x - 3
Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.
This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.
Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.
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Hi, can you help me to solve and explain to me how to find the results please!
Answers
0. Irrational
,1. Irrational
,2. Rational
,3. Irrational
1) Considering that Rational Numbers are the ones that can be written as ratios like:
\(\begin{gathered} \frac{a}{b} \\ 1,\frac{3}{2},5,\text{ }\sqrt[]{4} \end{gathered}\)2) Then we can examine each row and each expression as well. So we can begin with:
\(3\sqrt[]{9}\cdot\sqrt[]{2}=3\cdot3\cdot\sqrt[]{2}=9\sqrt[]{2}=12.72792\ldots\)Since the square root of 2 yields an irrational number, 9 times that yields an irrational one as well.
Irrational
\(\frac{\sqrt[]{9}}{\pi}=\frac{3}{\pi}=0.9452\ldots\)Note that in the second row we have an irrational number as well, a decimal and not a repeating number.
Irrational
\(\frac{\pi\sqrt[]{24}}{\sqrt[]{6\pi^2}}=\frac{\pi\cdot2\sqrt[]{2}\cdot\sqrt[]{3}}{\pi\sqrt[]{2}\cdot\sqrt[]{3}}=2\)Since 2 is a rational number the same as 2/1. This is a Rational one.
And Finally:
\(-\sqrt[]{3}+2=0.2674\)Notice that the square root of 3 is already irrational so the sum of that with 2 yields another irrational number.
Irrational
3) Hence, the answer is:
0. Irrational
,1. Irrational
,2. Rational
,3. Irrational
A 99 ft length of wire is to be cut into 2 pieces, so that the longer piece is eight feet longer than six times the shorter piece. Fond the length of each piece.
Answers
9514 1404 393
Answer:
13 ft86 ftStep-by-step explanation:
Let s represent the length of the short piece. Then the long piece is 6s+8, and the total length is ...
s +(6s+8) = 99
7s = 91 . . . . . . . . subtract 8, collect terms
s = 13 . . . . . . . . . divide by 7
99 -13 = 86 = 6(13)+8 . . . length of long piece
The short piece is 13 feet long; the long piece is 86 feet long.
10. The number of people who have heard a rumor increases exponentially. If all who hear a rumor repeat it
to two people per day, and if 20 people start the rumor, the number N(t) of people who have heard the
rumor after t days is given by N(t) 20(2).
a. After what amount of time will 1000 people have heard the rumor?
=
1000 people will have heard the rumor
by 6 days.
1000 = 2012)
20
20
Soat
2t - 50
10g (50) = +
5.643856
b. What is the doubling time for the number of people who have heard the rumor?
+
Answers
Answer:
2000 is the answers.............
build and sketch 2x2+7x+6)
Answers
Answer:
Step-by-step explanation:
A water park sold 6 child tickets and 54 adult tickets. What percentage of the tickets sold were child tickets?
Answers
Answer: 10%
Step-by-step explanation:
Add 54 and 6 for the total.
54+6=60.
Now we find the percentage of 6 from 60.
6/60
0.1
So 10% of tickets sold were child tickets.
---
hope it helps
The vet said Lucy's cat Mitten weighs 8 2/6 pounds. This is 1 5/6 pounds more than Mittens weighed last year. How much did Mitten weigh last year?
Answers
Answer:She weighed 7 1/4
Step-by-step explanation: just took the test
please please help last text then finals l give brainliest
Answers
1. The x - intercepts of the parabola are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex of the parabola is at (5, 80).
What is a parabola?A parabola is a curved shape
1. Given the parabola above, to find the x - intercepts, we proceed as follows.
The x-intercepts are the points at which the graph cuts the x-axis.
They are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.
The plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex is the maximum point on the graph.
So, we see that the vertex is at x = 5 s and y = 80 ft
So, the vertex is at (5, 80).
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avenger Thor aiming for Loki launched his Mjolnir horizontally from the top of 20 meters cliff. If Loki is 36 meters away. At what speed did Thor throw his Mjolnir to reach Loki?
Answers
In 2010, the U.S. Congress passed the Tax Relief, Unemployment Insurance Reauthorization, and Job Creation Act of 2010. The act reduced the self-employment tax rate from 15.3% to 13.3%. Estimate the reduction in self-employment tax for an individual whose taxable earnings totaled $50,319.
Answers
Answer:A topic sentence is used to bring
to a paragraph.
Step-by-step explanation:
A topic sentence is used to bring
to a paragraph.
NO LINKS!!! URGENT HELP PLEASE!!!
The distance between Miami, Florida and Bermuda is about 1042 miles. The distance from Bermuda to San Juan. Puerto Rico is about 965 miles, and the distance from San Juan to Miami is about 1038 miles. Find the area of the triangle formed by the three locations.
Answers
Answer:
444523.45 square miles
Step-by-step explanation:
By using Heron's formula, we can easily find the area of the triangle formed by Miami, Bermuda, and San Juan, we need to use the lengths of the three sides of the triangle.
Let,
Side a: Distance from Miami to Bermuda = 1042 miles
Side b: Distance from Bermuda to San Juan = 965 miles
Side c: Distance from San Juan to Miami = 1038 miles
Now we can use Heron's formula to find the area of the triangle:
s =\(\frac{a+b+c}{2}\)
s = \(\frac{1042 + 965 + 1038}{2}=1522.5\) miles
A = \(\sqrt{s(s-a)(s-b)(s-c)}\)
A = \(\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}=444523.45\)
Therefore, the area of the triangle formed by Miami, Bermuda, and San Juan is approximately 444523.45 square miles.
Answer:
444,523.45 square miles (2 d.p.)
Step-by-step explanation:
To find the area of a triangle formed by the locations of Miami, Bermuda, and San Juan, use Heron's formula.
\(\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}\)
Label the three sides of the triangle as 'a', 'b', and 'c', where 'a' is the distance from Miami to Bermuda (1042 miles), 'b' is the distance from Bermuda to San Juan (965 miles), and 'c' is the distance from San Juan to Miami (1038 miles):
a = 1042 milesb = 965 milesc = 1038 milesTo find the half perimeter, s, half the sum of the three side lengths:
\(\implies s=\dfrac{a+b+c}{2}=\dfrac{1042+965+1038}{2}=1522.5\)
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
\(\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}\\&=\sqrt{1522.5(480.5)(557.5)(484.5)}\\&=444523.4468348...\\&=444523.45\; \sf miles^2\;(2\;d.p.)\end{aligned}\)
Therefore, the area of the triangle formed by the three locations is 444,523.45 square miles, to two decimal places.
If 400 x 300 = 120,000
And 40 x 30 is 1,200
Fill in the blanks and show your work
*_____ x ______ = 12,000?
Answers
Answer:
this list
Step-by-step explanation:
1×12000=12000
2×6000=12000
3×4000=12000
4×3000=12000
5×2400=12000
6×2000=12000
8×1500=12000
10 ×1200=12000
12 ×1000=12000
Find the acute angle between the lines. Round your answer to the nearest degree. 9x − y = 4, 8x + y = 6
Answers
Answer:
\(\approx 13^\circ\)
Step-by-step explanation:
Given two lines with the equations:
\(9x - y = 4\\ 8x + y = 6\)
First of all, let us learn the formula for finding the angle between the two lines with given equations:
\(tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}\)
\(m_1, m_2\) are the slopes of the two lines respectively.
Let us convert the given equation to point intercept form.
Point intercept form of a line is given as:
\(y = mx+c\)
\(y = 9x-4\\y =-8x+6\)
Comparing with slope intercept form, we get:
\(m_1 = 9\\m_2 = -8\)
Using the above formula:
\(tan\theta =\dfrac{9 -(-8)}{1+9(-8)}\\\Rightarrow tan\theta = -\dfrac{17}{71}\\\Rightarrow \theta = -13.46^\circ\\\)
Therefore, the acute angle between the two lines is \(\approx 13^\circ\)
The acute angles between the equations is 13.46 degree.
To find the acute angles between the two equation, let's write out the individual slope of each equation.
Given Data
9x - y = 48x + y = 6Equation of lineThe given equations can be rearranged into equation of line.
\(9x-y=4\\ y=9x-4\\ slope=m_1=9\)
The second equation can also be rearranged as and solving for the slope
\(8x+y=6\\ y=6-8x\\ y=-8x+6\\ slope = m_2 = -8\)
Since we have the slopes of the two equation, we can now find the acute angle between them.
θ = \(tan^-^1[\frac{m_1-m_2}{1+m_1m_2}]\\ \)
substituting the values and solving for the angle
\(x = tan^-^1[\frac{9-(-8)}{1+(9*-8)}]\\ x = tan^-^1[17/-71]\\ x=-13.46 = 13.46^0\)
The acute angle between the equations is 13.46 degree
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There are three times as many fiction books as non-fiction books in a library. 120 fiction and 24 non-fiction books are loaned out. There are now twice as many non-fiction books as fiction books. How many books were in the library?
How do I work this out step by step?
Answers
Answer:
672
Step-by-step explanation:
If we call the number of non-fiction books as x, the number of fiction books would be 3x. Therefore: we can write the following equation:
3x - 120 = 2(x - 24) ← the 3x - 120 and x - 24 represents the new number of books
3x - 120 = 2x - 48
x - 120 = 48
x = 168 which means 3x = 3 * 168 = 504, therefore the total number of books is 168 + 504 = 672.
Dimensions of a building are 728 feet by 800 feet. If 1 inch represents 8 feet, what are the dimensions of the building on the drawing?
Answers
Answer:
91in by 100in
Step-by-step explanation:
Find the sum.
10 + 12 + 14 + ... + 80
Answers
Answer:
1620
Step-by-step explanation:
The amount of even integers between 10 and 80 inclusive is 36 (5 for each interval of 10 [e.g., 10-19 has 5, 20-29 has 5] and one extra for 80).
Since the numbers are consecutive even numbers, we can use the fact that the sum of the numbers is equal to the average of the numbers, times the number of numbers.
The average of the numbers is 45, since \(\frac{10+80}{2}=45\). We can use only the two outer numbers to determine the average since the numbers are all evenly spaced as they are consecutive even numbers.
\(45\times36=1620\), so the sum is 1620.