It is calculated using the quadratic formula
[tex]x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In the equation
[tex]x^2-5x+1=0[/tex]a = 1, b = -5 and c = 1
Substitute the given to the quadratic formula
[tex]\begin{gathered} x\text{ = }\frac{5+\sqrt[]{21}}{2} \\ x\text{ = }\frac{5-\sqrt[]{21}}{2} \end{gathered}[/tex]two planes are flying torwards each other. in 45 minutes, the two planes will be 200 miles apart. in 1 hour, plane A will pass plane B. How far apart are the planes now.
800 miles is going to be the distance that separates the two aircraft. The distance between the two airplanes will be 1,300 kilometers at the very least.
What is the distance?It is important to keep in mind that the two aircraft's combined speed will be equal to the sum of their separate speeds when calculating their overall speed. In addition, the pilots of the two aircraft have one hour to find each other.
According to the information that was provided, the distance that separates the aircraft after they have flown for forty-five minutes is two hundred miles. As a result, the following will constitute the remaining distance:
= 1 hour - 45 minutes = 15 minutes.
When this occurs, the distance between the planes will be as follows:
= 200/15 × 60
= 200 × 4
= 800 miles
As a result, there will be a gap of 1300 kilometers between the two aircraft.
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Evaluate each expression using the values given in the table.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the question,
We have that:
[tex]\begin{gathered} a)\text{ f (1) =2 and g(1) =0} \\ We\text{ n}eed\text{ evaluate :} \\ (fog\text{ ) (1) = f(g(1)) = f (0) =-1} \\ \text{Then, (fog)(1) = - 1} \end{gathered}[/tex][tex]undefined[/tex]The values of each composite function are:
a) -1
b) -1
c) 2
d) 0
e) 2
f) -4
We have,
These are composite functions.
It is written as:
(f o g) (x) = f (g(x))
Now,
From the table, the values for each function f and g at specific values x are taken.
a.
(f o g)(1)
f(g(1)) = f(0) = -1
b.
(f o g) (-1)
f(g(-1)) = f(0) = -1
c.
(g o f) (-1)
g(f(-1)) = g(-2) = 2
d.
(g o f) (0)
g(f(0)) = g(-1) = 0
e.
(g o g) (-2)
g(g(-2)) = g(2) = 2
f.
(f o f) (-1)
f(f(-1)) = f(-2) = -4
Thus,
The values of each composite function are:
-1, -1, 2, 0, 2, and -4.
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Triangle ABC is translated T(x,y) --> (x + 2, y - 3). What are the coordinates of the image of triangle ABC after this translation?
The coordinates of the image of triangle ABC would be A (-1, -1), B (3, 2), and C (4, -6) after translation, and if the original coordinates are A(-3,2) B(1,5) C(2,-3).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
Let assume A(-3,2) B(1,5) and C (2,-3) are original coordinates
The following translation is being used: (x, y) ⇒ (x + 2, y - 3)
First, take your x-coordinates and add them by two because it is the translation utilized to solve for your x-coordinate.
You would receive the following for yours x's: A (-1, y ) B (3, y) C (4, y)
Next, remove three from each of your y-coordinates because it is the translation being utilized to solve for your y-coordinate.
You would receive the following for your y's: A (x, -1) B (x, 2) C (x, -6)
Finally, you would take each one and put it together, or piece it together.
Hence, the coordinates of the image of triangle ABC after translation would be A (-1, -1), B (3, 2), and C (4, -6).
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in serious need of help! i need the answer quick!
The coordinates of G is (d+c, b)
This is because the opposite sides of any parallelogram are equal in length, and so the length of side HG is equal to the length of side EF.
a) The length of side HG is equal to the horizontal distance (x2 - x1): xG - 0
The length of side EF is equal to the horizontal distance (x2 - x1): d - (-c) = d +c
Thus:
xG - 0 = d + c
xG = d + c
Therefore the x-coordinate of G is d + c
b) To find the y-coordinate of G, we also apply the idea that sides GF and HE are equal.
The length of side GF is equal to the vertical distance (y2 - y1): yG - 0
The length of side HE is equal to the vertical distance (y2 - y1): b - 0
Thus:
yG - 0 = b -0
yG = b
Therefore the y-coordinate of G is b
Finally, the coordinates of G is (xG, yG) = (d+c, b)
What was the distance of the first part of yuna's swim? round to the nearest tenth as needed. the distance in the first part of her swim was miles.
Using equations we now know that the distance of the first part of the Yuna's swim is 0.7 miles.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, let 'x' be the distance of the 1st part and 'y' be the time in hours of the 1st part.
1st part: 1/4 = x/y (Equation A)2nd part: 0.8 = 1.9 - x/2 - y (Equation B)Plot the equations on the graph as follows:
(Refer to the graph attached below)
Be obtain:
x = 0.7 milesy = 0.5 hoursTherefore, using equations we now know that the distance of the first part of the Yuna's swim is 0.7 miles.
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The complete question is given below:
In training for a triathlon, Yuna swam 1.9 miles in the open ocean, which took her 2 hours. For the first part of her swim, she averaged 1.4 miles per hour. For the second part of her swim, she swam against the current and started to tire, so her average speed decreased to 0.8 mph. What was the distance of the first part of Yuna's swim? Round to the nearest tenth as needed. The distance in the first part of her swim was miles.
Answer:
.7
Step-by-step explanation:
Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
Drag each description to explain each part of both expressions.
Both Adam and Rena re both correct regarding the expression.
What is an expression?An expression simply means an illustration that can be used to represent a scenario or situation.
From the information, Adam writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
In this case, they are both correct. This can be illustrated as:
= 1 - 0.75d
= 0.25d
Note that the information was answered based on the information given.
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In ▲ABC, side AC is extended through C to D. If m<dcb=50 which is the longest side of triangle abc?
Answer:
AB
Step-by-step explanation:
the angles DCB and ACB are supplementary angles (together 180°).
simply because the sum of all angles around a single point on one side of a line is suggests 180° (it represents a half-circle).
so, the inner angle ACB is
ACB = 180 - 50 = 130°
because the sum of all angles in a triangle is also always 180°, there are only 50° left for the other 2 angles.
so, the inner angle at C is clearly the largest angle in the triangle ABC.
the larger an angle, the longer the opposing side.
the largest angle has the longest opposing side in the triangle.
the opposing side of the inner angle C is AB. and that is therefore the longest side in the triangle ABC.
slope for point (7,2) and (1,-1)
Answer: The slope is [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
[tex]Slope = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-1-2}{1-7} =\frac{-3}{-6} =\frac{3}{6}=\frac{1}{2}[/tex]
How do I solve y-1=3(x-4)
Step-by-step explanation:
open the bracket
y - 1 = 3x - 12
add 1 to both sides
y = 3x - 11
I think that should be it
If you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved. What am I?
Answer: The moon
Step-by-step explanation:
The cone is the solid form that represents "If you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved."
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
∵ The volume of the cone (V )= 1/3πhr²
The number of faces of a regular cone is one, which we may partition vertically into two halves.
This means one base face and lateral face
Now, the number of faces in one half equals the number of faces in the original form.
This meets the conditions outlined in the question.
So, the cone is a solid form.
Thus, the cone is the solid form that represents "If you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved."
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Plot the ordered pair and state which quadrant or on which axis the point lies
Answer:
Explanation:
Given the ordered pair (-2, 4 1/2), where x = -2 and y = 4 1/2 = 9/2 = 4.5. Plotting this point, we'll have;
Note that quadrants are numbered in an anti-clockwise manner with the top right portion of the graph as Quadrant I. Looking at the plotted point, we can see that it lies in Quadrant II.
Given the points:
(5,2) and (3,-4)
Select the THREE equations that represent the line that passes
through them.
The equations of the line according to the given points will be:
3x - y - 13 = 06x - 2y - 26 = 012x - 4y - 52 = 0We know that,
The equation of a line passing through two points is:
( y -y 1) / ( x - x1 ) = ( y2 - y1 ) / ( x2 - x1 )
(y - 2) / (x - 5) = (-4 - 2) / (3 - 5)
=> (y - 2) / (x - 5) = -6 / -2
=> y - 2 = 3 (x - 5)
=> 3x - 15 - y + 2 = 0
=> 3x - y - 13 = 0
Some more equations of the same line can be calculated just by multiplying the coefficients of x and y so that they remain proportional to the previous equation.
For Example,
6x - 2y - 26 = 012x - 4y - 52 = 0Here we can see that the coefficients of x and y and also the constant term are proportional to every equation compared with each other.
These lines are also called coincident lines.
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Using Cramer's Rule, the solution to the system of equations
6x - 5y = -4
-7x + 3y = -1
can be written in the form
( Dx , Dy )
( D D )
What is the value of D?
Answer's
Step-by-step explant
On average, people breath 10,000 times per night with a standard deviation of 1400. You study 50 people and record how many breaths they take per night. What is the probability that the average of all participants in the study was fewer than 10,200 breaths each night?I want answer with step by step.
ANSWER
[tex]\begin{equation*} 0.84375 \end{equation*}[/tex]EXPLANATION
We want to find the probability that the average of all participants in the study was fewer than 10,200 breaths each night.
To do this, first, we have to find the z-score corresponding to the sample mean:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]where x = sample mean
μ = population mean
σ = standard deviation
n = sample size
Therefore, the z-score is:
[tex]\begin{gathered} z=\frac{10200-10000}{\frac{1400}{\sqrt{50}}}=\frac{10200-10000}{\frac{1400}{7.0711}} \\ z=\frac{200}{197.99} \\ z=1.01 \end{gathered}[/tex]Now, using the standard normal table, we can find P(z < 1.01).
Therefore, the probabilityis:
[tex]P(z<1.01)=0.84375[/tex]That is the answer.
You pick a card at random without putting the 1st card back you pick a second card at random what is the probability of picking an even number and then picking an even number
We will have the following:
First, we can see that the probability of picking an even number at first is:
[tex]P_1=\frac{3}{6}\Rightarrow P_1=\frac{1}{2}[/tex]And then, the probability of picking another even card without replacing the previous one will be:
[tex]P_2=\frac{2}{5}[/tex]Now, the probability of this happening one after the other will be:
[tex]\begin{gathered} P_3=P_1P_2\Rightarrow P_3=\frac{1}{2}\ast\frac{2}{5} \\ \\ \Rightarrow P_3=0.2 \end{gathered}[/tex]So, the probability will be of 20%.
The solution set of which of the following equations is the set of real numbers that are 3 units from -2?
A |x+2|=3
B|x-2|=3
C |x+3|=-2
D |x-3|=2
E |x+3|=2
The solution set of real numbers that are 3 units from -2 is :
|x +2| = 3
What is a solution set?Any value of a variable that makes the specified equation true is referred to as a solution. A solution set is the collection of all variables that satisfy the equation. To find the solution set of an equation with a given domain, first plug each domain value into the equation to obtain the respective range values. Make ordered pairs out of these values and write them down as a set. That set is our solution.Here
Function : |x +2| = 3
since ,
|x +2| = 3 => x + 2 = 3 ∨ x + 2 = -3
x = 3 - 2 ∨ x = -3 - 2
x = 1 ∨ x = -5
| - 2 - 1 | = | -3| = 3
| -2 -(-5) | = | -2 + 5 | = 3.
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28-6x=2x-84
Prove: x = 14
28-6x = 2x -84
Add 6x to both sides:
28 = 8x -84
Add 84 to both sides
112 = 8x
Divide both sides by 8
X = 112/8
X = 14
You are planning to place a bet on your local sports team, the red sparrows. the sparrow's have a past record of 4-5 (4 wins, 5 losses) at this venue. however you also know that their record is 2-7 in games where it rains and it has rained at 60% of their games this season. 4 if the red sparrows win their game what is the probability that it rained at that game?
The probability that it rained at that game is 0.49.
Probability is the the ratio of a particular event with total number of event. It tells the possibility that an event can occur.
Probability that it rains P(R) = 0.60
probability that it won't rain P(R') = 1-0.60
= 0.4
Red sparrows have a past record of 4 wins and 5 loses when it does not rain, that is
P( winning/R') = 4/9 (win% = 4/total that is 5+4 which is 9)
P( lose/R') = 5/9 (lose % = 5/total)
When it rain the past record is 2 wins and 7 loses
P( win/R ) = 2/9
P( lose/R ) = 7/9
P (win) = P(R)*P(win/R) + P(R')*P(win/R')
= 4/9*0.4 + 2/9*0.6
If red sparrows win, then the probability that it rained at game
P (R/win) = P ( R η win) / P (win)
= 0.49
Therefore, we can conclude that the the probability that it rained at that game is 0.49.
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A rectangular gardan is surrounded by a walk of uniform width. The area of the garden is 200 square yards. If the dimensions of the garden plus the walkway are 18 yards by 26 yards, find the dimensions of the garden.
***NOTE*** This is a Quadratic Word Problem, so please use the Quadratic Method when solving and show all steps!!
Answer: [tex]6\sqrt{6}+4 \times 6\sqrt{6}-4[/tex] yards
Step-by-step explanation:
Let the length of the walkway be x yards. Then,
[tex](18-2x)(26-2x)=200\\\\4x^2 -88x+468=200\\\\4x^2-88x+268=0\\\\x^2 -22x+77=0\\\\x=\frac{22 \pm \sqrt{22^2 -4(77)}}{2}\\\\=11 \pm 3\sqrt{6}[/tex]
However, [tex]x=11+3\sqrt{6} > 18[/tex], which is illogical, so we take [tex]x=11-3\sqrt{6}[/tex].
So,
[tex]18-2x=18-2(11-3\sqrt{6})=6\sqrt{6}-4\\\\26-2x=26-2(11-3\sqrt{6})=4+6\sqrt{6}[/tex]
Hari's weekly allowance varies depending on the number of chores he does. He received $18 in allowance the week he did 20 chores, and $12 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.
The equation of his allowance in slope-intercept form is y = 0.5x + 8
He received $18 in allowance the week he did 20 chores.
He received $12 in allowance the week he did 8 chores.
The ordered pairs will be (8,12) and (20,18)
The slope intercept form is
y = mx + b
Where m is the slope
b is the y intercept
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
m = (18-12)/(20-8)
m = 6/12
= $0.5 per chores
Now we have to find b,
Substitute the value of any ordered pair in the slope intercept form
12 = 0.5×8+b
12 = 4+b
b = 12-4
b = 8
Hence, the equation of his allowance in slope-intercept form is y = 0.5x + 8
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Dylan enjoys ramen noodles and music downloads. His monthly budget for these two items is 15 dollars. If the price of a package of ramen noodles is $1.48 and the price of a music download is $1.15, what is Dylan's opportunity cost of a music download? (Round your answer to the nearest tenth. For example: 1.4).
Data:
• Monthly budget: $15
,• Price of a package of ramen: $1.48
,• Price of a music download: $1.15
Procedure:
[tex]\frac{15}{1.48}\approx10.1[/tex]Answer: 10.1
-0.01a^4*(-10a^5)^3[tex]-0.01a^4*(-10a^5)^3[/tex]
It seems there is some missing info on this question. However, if you are simplifying, then the simplified version of the given expression would be...
[tex]10a^1^9[/tex]
Hope this helps!
7. The vertices of a triangle are P(-7,-4), Q(-7, -8), and R(3, -3). Name the vertices of the
image reflected across the line y=x.
OP(4, 7), Q8, 7), R'(3,-3)
OP(4,-7), Q8, -7), R'(3, 3)
OP(-4,-7), Q(-8,-7), R'(-3, 3)
OP(-4, 7), Q(-8, 7), R'(-3,-3)
(1 point)
A place where two or more curves, lines, or edges converge is known as a vertex in geometry (plural: vertices or vertexes), and it is frequently identified by letters like,,,. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.
The solutions are:
P' = (-4,-7)
Q ' = (-8,-7) (-8,-7)
R ' = (-3,3) (-3,3)
All you have to do is flip the provided points P, Q, and R's x and y coordinates.
The common principle is (x,y) —-> (y,x)
Thus, when we reflect across the line y = x, something like P = (-7,-4) becomes P'= (-4,-7). The similar approach is taken with the other points.
How do you locate a triangle's vertices?
Finding the triangle's vertices on the line y = x as an image
The steps below are used to locate a triangle's vertices using its midpoints:
Identify the midpoints' x and y values;
Calculate the midpoint using the following equations: A = (x 1+ x 3 - x 2, y 1 + y 3-y 2); B = (x 1+x 2-x 3, y 1+y 2-y3); C = (x 2+x 3-x 1, y 2 + y 3 -y 1);.
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Make r the subject of m=√6a+r/5r
Answer:
r=√6a/5m-1
Step-by-step explanation:
m=√6a+r/5r
cross multiply
5mr=√6a+r
5mr-r=√6a
factorise
r(5m-1)=√6a
divide both sides by the coefficient of r
r=√6a/5m-1
hope it helps
please mark brainliest
Answer:
hope it helps u
MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER
3. Use your answer from #2 for x, and find the measure of both angles. Select 2 answers.
A
B
116
61°
64°
119⁰
2x-15
3x + 5
None of the available possibilities is an equivalent expression.
Supplemental methods add up to 180 degrees, just like all other options.
An equivalent expression is what?If two expressions function the same way while having different looks, they are said to be comparable. Two identical algebraic expressions have the same value when the same value(s) for the variable are entered (s).
No one in the available possibilities satisfies the requirement of a comparable expression.
2x - 15 + 3x + 15 = 180
2x - 10 + 3x = 180
5x - 10 = 180
5x - 10 + 10 = 180 +10
add the numbers
5x = 190
5x /5 = 190 5
x = 38
As a result, none of the possibilities shown are identical expressions.
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Listen to this on the day she was born, a baby leopard had 9 spots. Each day 4 more spots appeared. After 5 days, how many spots did the baby have?
Answer:29
Step-by-step explanation:
9+4 spots times five days
Part AType an equation to represent the cost of the topsoil.Part BHow does the cost of the topsoil compare to the cost of the mulch?
Step 1
Write the equation of a line in slope point form
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Where;
[tex]\begin{gathered} y_2=\text{ 60} \\ x_2=2 \\ y_1=\text{ 30} \\ x_1=\text{ 1} \end{gathered}[/tex]Step 2
Find the equation to represent the cost of the topsoil.
[tex]y-30=\frac{60-30}{2-1}(x-1)[/tex][tex]\begin{gathered} y-30\text{ = }\frac{30}{1}(x-1) \\ y-30=30x-30 \\ y=30x-30+30 \\ y=30x \end{gathered}[/tex]The equation that represents the cost of the topsoil is
y=30x
Step 3
Find how the cost of the topsoil compares to the cost of the mulch.
[tex]\begin{gathered} \text{The equation for the cost of the mulch y, in dollars is} \\ y=25x \\ \text{for x cubic yards of mulch} \\ \text{The equation for the cost of topsoil, y in dollars is} \\ y=30x \\ for\text{ x cubic yards of topsoil} \end{gathered}[/tex][tex]undefined[/tex]
Which of the following is the correct expansion of the binomial (x + y)6?
A.
x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6
B. x6 + 155y + 6x4y2 + 20x³y3 + 6x²y + 15xy5+y6
C. x6 + 6x55+ 15x4y4 + 20x³y3 + 15x²y² + 6xy¹+y6
D. x6 + 6x5y + 20x4y² + 15x³y3 + 20x²y4 + 6xy5+y6
Option a is correct using algebric formulas.
What is (x + y)³ and (x + y + z)² formula?(x + y)³ = x³ + y³ +3xy( x + y )
(x + y + z)² = x² + y² + z² + 2( xy + yz + zx )
So breaking it into
(( x + y )³)² = (x³ + y³ +3xy( x + y ))²
(x³ + y³ +3xy( x + y ))² = x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )
x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )
So after rearranging the terms
we get (x + y)^6 as
x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6
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Please help ASAP! Select all rational numbers.
The rational numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49
What is a rational number?A rational number can simply be described as a number that is expressed as the ratio of two even or odd integers.
The denominator of the fraction or ratio must be greater than zero.
Rational numbers are represented mathematically as a quotient, say x/y of two integers such that y ≠ 0, that is, the denominator is not equal r equivalent to zero.
It is formed from dividing on integer(whether odd or even) by another integer.
The numbers; √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49 are all rational numbers
Hence, the numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49
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Rule for Input/output table Input values: 1, 2, 3, 4, n Output values: -4,-2,0,2
Answer:
[tex]a_{n}[/tex] = 2n - 6
Step-by-step explanation:
there is a common difference between consecutive terms , that is
- 2 - (- 4) = 0 - (- 2) = 2 - 0 = 2
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 4 and d = 2 , then
[tex]a_{n}[/tex] = - 4 + 2(n - 1) = - 4 + 2n - 2 = 2n - 6
the rule is then 2n - 6