Answer:
-6, 1
Step-by-step explanation:
You want the real roots of the quadratic x^2 + 5x = 6.
FactorizationThe roots are easily identified from the factored form of the equation. The factors will involve the constants that have a sum of +5 and a product of -6.
-6 = 6·(-1) = 3·(-2)
Sums of the factor pairs are 5 and 1. We will use the constants that have a sum of 5.
x^2 +5x = 6 . . . . . . given
x^2 +5x -6 = 0 . . . . . standard form
(x +6)(x -1) = 0 . . . . . . . factored form
Zero product ruleThe zero product rule tells us that a product will be zero if and only if at least one of the factors is zero. To find the values of x, we set the factors equal to zero and solve for x.
(x +6) = 0 ⇒ x = -6
(x -1) = 0 ⇒ x = 1
x = -6, or x = 1 . . . . . . . . roots of the quadratic
Find the quotient and write the answer in simplest form 2 4/3 ÷1 8/7 =
first off let's convert the mixed fractions to improper fractions and then divide.
[tex]\stackrel{mixed}{2\frac{4}{3}}\implies \cfrac{2\cdot 3+4}{3}\implies \stackrel{improper}{\cfrac{10}{3}} ~\hfill \stackrel{mixed}{1\frac{8}{7}}\implies \cfrac{1\cdot 7+8}{7}\implies \stackrel{improper}{\cfrac{15}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{10}{3}\div \cfrac{15}{7}\implies \cfrac{10}{3}\cdot \cfrac{7}{15}\implies \cfrac{10}{15}\cdot \cfrac{7}{3}\implies \cfrac{2}{3}\cdot \cfrac{7}{3}\implies \cfrac{14}{9}\implies 1\frac{5}{9}[/tex]
A 9-member team plans to run a 4-mile relay race. Distance markers are placed on the racecourse every 0.25 mile. a. Place an X on the number line at the approximate locations where the relay exchanges will take place. b. Will any of the relay exchanges take place at any of the 0.25-mile markers? If so, which one(s)? List the locations of all of the exchanges in decimal form.
Relay exchanges will not take place at any of the 0.25-mile markers
The calculated relay exchanges are
0.44440.88891.33331.77782.22222.66673.11113.55564How to find the relay exchangesThe number of team members which is 9 is equal to the number of relay exchanges in the 4-mile race.
This will result to the relay exchanges occurring at every 4/9, and repeated addition of 4/9 will give the other points, and the list is
4/9, 8/9, 4/3, 16/9, 20/9, 8/3, 20/9, 32/9, and 4 in fraction
In decimal form this will be listed in four decimal place
0.4444
0.8889
1.3333
1.7778
2.2222
2.6667
3.1111
3.5556
4
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Find the coordinates of point P that lies on the line segment MQ. M(-5, 3), Q(4. 9), and partition the segment at a ratio of to 3. Graph line segment MG and Pin the coordinate plane.
The coordinates of point P that lies on the line segment MQ is P(-11/4 , 9/2).
Given:
M(-5, 3), Q(4, 9), and partition the segment at a ratio of 1 : 3.
(x1,y1) and (x2,y2) in the ratio m:n then,
(x,y) = (mx2+nx1 / m+n , my2+ny1 / m+n)
= (1*4+3*-5 / 1+3 , 1*9+3*3 / 1+3
= (4 - 15 / 4 , 9 + 9 / 4)
= (-11/4 , 18/4)
= (-11/4 , 9/2)
Therefore the coordinates of point P that lies on the line segment MQ is P(-11/4 , 9/2).
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Miranda buys 5.1 pounds of avocados at the local store. How much does
one pound of the fruit cost if she is billed $16.83 for the purchase?
The cost of one pound is $3.3 or the rate of per pound fruits is $3.3.
What is meaning of one pound?
Pound is an unit to measure mass of an object. The plural form of pound is pounds.
What is the unitary method?
The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given that Miranda buys 5.1 pounds of avocados at the local store. The cost of the fruits is $16.83.
Apply unitary method to calculate the cost of 1 pound:
The cost 5.1 pounds fruit is $16.83.
The cost 1 pound fruit is $16.83/5.1 = $3.3.
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A local farmer had a mouse problem in his barn. He estimated there were about 800
mice to start with. He adopted some cats and noticed that the number of mice was
decreasing by 8%/wk. The graph models the number of mice x weeks after the
farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms
of this situation!
Answer: try a c and e
Step-by-step explanation:
If an arena charges $7. 50 to park in satellite parking and $12. 00 to park in an arena lot, how much will be made from parking 11,000 vehicles at the arena and 4,600 in satellites?.
Parking 11,000 automobiles at the venue and 4,600 in satellites will bring in total $166,500.
Define multiplication.One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.
Given,
If an arena charges $7. 50 to park in satellite parking and $12. 00 to park in an arena lot,
Multiplying:
$7.5 x 4,600 = satellite parking
$34,500 = satellite parking
The next step is to determine how much it will cost to park in the arena lot.
$11,000 ×12 = arena lot
$32,000 = arena lot
Let's now calculate the entire revenue from parking.
Total earnings equal $132,000 + $34,500.
Amount made in total is $166,500.
In conclusion Parking 11,000 automobiles at the venue and 4,600 in total satellites will bring in $166,500.
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PLEASE HELP
If Janice is building a garden and the perimeter is 20 (P = 20) and the length is 4 (L = 4), find w (the width)
Answer:
w = 6 units
Step-by-step explanation:
The perimeter is found by adding all the sides of a rectangle. The perimeter can be found using this equation:
[tex]P=2w+2l[/tex]
Where w represents width and l represents length.
To find the width, rearrange the equation so it is in terms of w:
[tex]P=2w+2l\\2w=P-2l\\w=\frac{P-2l}{2}[/tex]
Now, plug in the known values!
[tex]w=\frac{20-2(4)}{2}[/tex]
Simplify!
[tex]w=\frac{12}{2} \\w=6[/tex]
In 2010, there were 3,669 people living in Bridgeview, IL. Chicago, IL has 681 times as
many people. How many more people live in Chicago?
Answer:
There are roughly 2,488,600 more people living in Chicago.
a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. he wants the area to be 20,000 20,000 square feet. what is the least amount of fencing he can use to create the area for his sheep?
Using the concepts of area of rectangle, we got that 72 feet is the the least amount of fencing he can use to create the area for his sheep.
Lets, suppose that the length of rectangle as x feet,
and width of rectangle as y feet.
So perimeter of rectangle as 2×( length + breadth)
We are given perimeter of rectangle as 72 feet
So, length of two sides of rectangle + width of rectangle=72feet.
=>2x+y=72 feet----------(eq1)
Now, we know that area of rectangle is given by =(length × breadth),or
=>(x × y)=20000
Putting values of y from eq1,we get
=>x × (72-2x)=20000
=>72x-2x²=20000
We need to find the least amount of fencing, so we find the local minima by using the differentiation
=>d(72x)/dx-d(2x²)/dx=d(20000)/dx
=>72-4x=0
=>x=18feet
Therefore, y=72-2×18=72-36=36feet
Hence, length of rectangle is 18 feet, and width is 36 feet
Therefore, length of fencing is =2x+y=2×18+36=72 feet.
Hence, if a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. he wants the area to be 20,000 square feet, then the least amount of fencing he can use to create the area for his sheep is 72 feet.
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(Complete question) is:
a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. Perimeter of rectangle is given as 72 feet. He wants the area to be 20,000 square feet. what is the least amount of fencing he can use to create the area for his sheep?
unit 3 function notation and evaluating function homework gina wilson (all things algebra), 2013
Answer:
b
Step-by-step explanation:
it is the answer
After one day, you read 40 pages of a book. On each
following day, you read 10 more pages.
Write an equation in point-slope form to model the number
of pages you have read, y, after a days.
Then use your equation to determine the number of pages
of the book will you have read after 9 days.
pages
The equation of the number of pages is y = 40 + 10x and for 9 days, you read 130 pages
How to determine the equation of the number of pages?From the question, we have
Initial number of pages = 40
Rate per day = 10 pages per day
The equation of the number of pages is then represented as
y = Initial number of pages + Rate per day x Number of days
Substitute the known values in the above equation, so, we have the following representation
y = 40 +10 * x
Evaluate
y = 40 + 10x
For 9 days, we have
x = 10
This gives
y = 40 +10 * 9
Evaluate
y = 130
Hence, the number of pages is 130
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There are 20 people in a room. 4 of them are people you know. When 2 people are selected at random at the same time, what is the probability that at least one of them is someone you know?
(this is a basic question but its 4am, my brain isnt working properly)
Answer:
4/20=1/5 or 20% or 0.2
Step-by-step explanation:
if u write 4/20 simplify it which becomes 1/5
u can write in percentage or in decimal depending on what the question wants
Solve (x – 3)2 = 49. Select the values of x.
Answer:
27.5
Step-by-step explanation:
2x-6=49
2x=55
x=27.5
A polynomial function P(x) with rational coefficients has the given roots. Find two additional roots of P(x)=0. 17+7 and 2i
The two additional roots are:-0.17-7i and -2i
Given,
A polynomial function P(x) with rational coefficients has the given roots.
P(x) = 0.17+7i and 2i
we are asked to determine the two additional roots of the given P(x).
we know that a+bi is a root of P(x)=0, then a-bi is also a root of P(x)=0
we have:
0.17+7i and 2i are two roots pf P(x)
so, -0.17-7i and -2i are two additional roots of P(x).
Hence we get the required roots.
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pls help sjajgdjsiaysgdhwiudhh
Answer:
scalene acute
Step-by-step explanation:
scalene = 2 sides are the same and one is different
acute = all three angles are smaller than 90
in the diagram below of triangle KLM, N is the midpoint of KM and O is the midpoint of LM if NO equals 3+ 7X and KL equals 4X +16 what is the measure of no
If O is the midpoint of LM and N is the midpoint of KM then the measure of NO is 10.
What are Linear equations?Linear equations are a combination of constants and variables where the value of the variable is calculated using mathematical operations.
We have given that Triangle KLM, N is the midpoint of KM and O is the midpoint of LM if NO equals 3+ 7X and KL equals 4X +16, we are supposed to find the measure of NO.
Using the Midpoint theorem, we can say that in Triangle KLM;
NO = KL / 2
Substituting values,
3+ 7X = 4X +16/ 2
3+ 7X = 2X + 8
7x - 2x = 8 - 3
5x = 5
x = 1
NO = 3+ 7X
NO = 3+ 7(1) = 10
NO equals 10
Hence the measure of NO is 10.
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What is the least angle measure by which this figure can be
rotated so that it maps onto itself?
• 45°
•90°
•180°
•360°
The least angle at which given figure maps onto itself is 180°. This can be understand by using magnitude of symmetry.
What is symmetry?
In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more precise definition of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Although these two interpretations of "symmetry" can occasionally be distinguished from one another, they are intricately linked and are therefore discussed jointly in this article. Aspects of mathematical symmetry can be seen in abstract objects like theoretical models, language, and music, as well as in the passage of time, as a spatial relationship, through geometric transformations, and in other types of functional transformations.
A figure in the plane has rotational symmetry if the figure can be mapped into itself by a rotation between 0° to 360° about the center of figure.
The given figure has one line of symmetry,
figure is divided into two parts that can overlap
angle will be = 360/2=180° .
So, the smallest angle is 180°.
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You operate a theme park and want to use the temperature outside and the day of the week to predict how many people will be in attendance each day. While testing this model, you also want to see if the relationship between temperature and theme park visitors will be curvilinear. You decide not to test for interactions. How many betas will be in your model aside from the y-intercept?.
Three betas will be in our model aside from the y-intercept.
In the given question, we have to find how many betas will be in your model aside from the y-intercept.
You operate a theme park and want to use the temperature outside and the day of the week to predict how many people will be in attendance each day.
While testing this model, you also want to see if the relationship between temperature and theme park visitors will be curvilinear.
You decide not to test for interactions.
From the given question,
We have y intercept that means our model well be
[tex]y=\beta_{0}+x_{1}\beta _{2}+x_{2}\beta _{2}+x_{1}x_{2}\beta _{12}[/tex]
where [tex]\beta _{1}[/tex] is for temperature and [tex]\beta _{2}[/tex] is day of the week.
3 betas are there aside intercept of y.
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Cooper's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 96
coffees in all, 72 of which were regular. What percentage of the coffees were regular?
Answer:
75%
Step-by-step explanation:
To solve this equation, we need to turn the fraction 72/96 into a percentage.
72 ÷ 96 = 0.75
0.75 as a percentage is 75%
Therefore, 75% of the coffees were regular.
Why is the product of two rational numbers always rational?
Select from the drop-down menus to correctly complete the proof.
Let ab and cd represent two rational numbers. This means a, b, c, and d are
Choose...
, and
Choose...
. The product of the numbers is acbd, where bd is not 0. Because integers are closed under
Choose...
, acbd is the ratio of two integers, making it a rational number. Integers or rational numbers.
The product of two rational numbers is always rational because (ac/bd) is the ratio of two integers, making it a rational number.
We need to prove that the product of two rational numbers is always rational. A rational number is a number that can be stated as the quotient or fraction of two integers : a numerator and a non-zero denominator.
Let us consider two rational numbers, a/b and c/d. The variables "a", "b", "c", and "d" all represent integers. The denominators "b" and "d" are non-zero. Let the product of these two rational numbers be represented by "P".
P = (a/b)×(c/d)
P = (a×c)/(b×d)
The numerator is again an integer. The denominator is also a non-zero integer. Hence, the product is a rational number.
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For this exponential
function,
what is the output value (y),
when the input value (x) is O?
y = 12.5x
*it’s not 1*
After solving the exponential function y = 12.5ˣ, the value of y = 1.
What is an exponential function?The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0.
The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
So, the exponential function:
y = 12.5ˣ
We know that x is 0.
The exponential function rule states that when the power is 0, the answer is always 1.
y = 12.5ˣ
y = 12.5⁰
y = 1
Therefore, after solving the exponential function y = 12.5ˣ, the value of y = 1.
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Correct question:
For this exponential function, what is the output value (y), when the input value (x) is O?
y = 12.5ˣ
Which of the following explains why (x + 3) = (x − 6))
has no solution?
Answer:
The is no number that I can substitue in for x to make the statement true.
Step-by-step explanation:
s + 3 = x -6 Subtract x from both sides
3 = -6 We get a false statement.
The perimeter of an isosceles triangle is 48 inches. Each leg is 6 inches less than two times the base.
Find the length of each side of the triangle.
The length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.
According to the question,
We have the following information:
The perimeter of an isosceles triangle is 48 inches. Each leg is 6 inches less than two times the base.
We know that in an isosceles triangle two sides are equal.
Let's take the base of the triangle to be x inches.
Other sides = (2x-6) inches
So, we have the following expression:
2x-6+2x-6+x = 48
5x-12 = 48
5x = 48+12
5x = 60
x = 60/5
x = 12 inches
Now, the other two sides of triangle:
2*12-6
24-6
18 inches
Hence, the length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.
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5.8, 6.328, 5.8042, 5.84 order these numbers from least to greatest
Answer:
Step-by-step explanation:
5.8, 5.8042, 5.84, 6.328
Calculate the next two terms in each of these Fibonacci-type sequences.
a) 1, 4, 5,
5, 9,
o task
b) 2,
9, 14, ...
4, 6, 10, 16,
Watch video
Ans
The next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.
What is Fabonacci type sequence ?
The first two terms are already defined in the this sequence. The nth term of a Fabonacci type sequence is given by the following expression:
[tex]F_n=F_{n-1}+F_{n-2}[/tex]
(a)
In this case 5 terms are given hence, calculate the 6th term.
[tex]F_6=F_5+F_4\\F_6=9+5\\F_6=14[/tex]
Now, calculate the 7th term.
[tex]F_7=F_6+F_5\\F_7=14+9\\F_7=23[/tex]
(b)
Calculate the 4th term.
[tex]F_4=F_3+F_2\\F_4=14+9\\F_4=23\\[/tex]
Calculate the 5th term.
[tex]F_5=F_4+F_3\\F_5=23+14\\F_5=37[/tex]
(c)
The series is 4, 6, 10, 16, ...
[tex]F_5=F_4+F_3\\F_5=16+10\\F_5=26[/tex]
[tex]F_6=F_5+F_4\\F_6=26+16\\F_6=42[/tex]
Hence, the next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.
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a boat travels 12 miles up the river in the same amount of time it takes to travel 32 miles down the same river. if the current is 5 miles per hour, what is the speed of the boat in still water?
Answer:
11 mi/h
Step-by-step explanation:
You want the speed of the boat when it travels 12 miles upstream against a current of 5 mph in the same time it travels 32 miles downstream with the current.
TimeThe relation between time, speed, and distance is ...
time = distance/speed
If b represents the speed of the boat, the times upstream and downstream are the same, so we have ...
(12 mi)/(b -5) = (32 mi)/(b+5)
Multiplying by the product of the denominators gives ...
12(b+5) = 32(b-5) . . . . . . also divided by "mi"
12b +60 = 32b -160 . . . . multiply by (b+5)(b-5)
220 = 20b . . . . . . . . . . . . add 160 -12b
11 = b . . . . . . . . . . . . . . . . . divide by 20
The speed of the boat in still water is 11 miles per hour.
__
Additional comment
Each trip took 2 hours.
can someone help me, please?
Answer:
I would say answer D is correct since it is closest to 1,760 yards.
Step-by-step explanation:
;)
f(x) = x^2. What is g(x)?
Answer:
[tex]\textsf{B.} \quad g(x)=-x^2-2[/tex]
Step-by-step explanation:
Transformations
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]
From inspection of the given graph, we can see that g(x) is function f(x) reflected in the x-axis and translated 2 units down.
Given function f(x):
[tex]f(x)=x^2[/tex]
Reflected in the x-axis:
[tex]-f(x) \implies g(x)= -x^2[/tex]
Translated 2 units down:
[tex]-f(x)-2 \implies g(x)=-x^2-2[/tex]
Therefore:
[tex]g(x)=-x^2-2[/tex]
Note:
If the leading coefficient of a quadratic function is positive, the parabola opens upwards.
If the leading coefficient of a quadratic function is negative, the parabola opens downwards.
Therefore, as g(x) opens downwards, the term in x² will be negative.
a pollster wishes to estimate the proportion of united states voters who favor capital punishment. how large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 5%?
The sample size must be 543 so the sample proportion is will not differ by 5%
We are given the following in the question:
Margin of error = 5%
Confidence interval:
p ±z√(p'(1 - p')/n)
Margin of error =
p = ±z√(p'(1 - p')/n)
Since no particular proportion is given, we take
p' = 0.5
Z critical at α 0.02 is ± 2.33
Putting values, we get,
p = ±z√(p'(1 - p')/n)
2.33 x √(0.5(1 - 0.5)/n)
√n = 2.33x 0.5/0.05
n = 542.89 = 543
Thus, the sample size must be 543 so the sample proportion is will not differ by 5%
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What is the slope? (15,-4) & (-50,16)