The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.The intercept b represents the initial position.The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.x2(t) = 600 - 90t. (negative as they travel in opposite direction).They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?
Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.
The intercept b represents the initial position.
The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.
x2(t) = 600 - 90t. (negative as they travel in opposite direction).
They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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2. What number is a common multiple of
5 and 9?
hazar is having 4 friends over to play video games. Each person will spend $6 on game rental and $4 on drinks and snacks, Write two expressions for the total cost for hazar and his friends
Answer: Here are two possible expressions for the total cost for Hazar and his friends:
The first expression is to add the cost of game rental and drinks and snacks for all the four friends
6x + 4x =10x where x is the number of friends
Second expression is to calculate the cost for each of the 4 friends and then add it together
(6 + 4) * 4 = 40
Both the expressions represent the same outcome, that is the total cost of $40 for Hazar and his friends to play video games.
It's depend on how you want to represent it, both are correct and represents the same outcome.
Step-by-step explanation:
There are 9 players on a baseball team there are 6 teams in the league how many baseball players are in the league
Answer:
54
Step-by-step explanation:
Multiply 9 (players per team) and 6 (teams in the league) to find the total players in the league.
9 times 6 = 54
Convert the polar equation to rectangular form [tex]r=5cot(\theta)csc(\theta\))[/tex]
Answer:
[tex]\displaystyle x=\frac{1}{5}y^2[/tex]
Step-by-step explanation:
[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]
a parking lot contains only cars and motor bikes. if there are 18 vehicles and 50 tires in the parking lot, how many cars and bikes are there?
Answer:
Step-by-Step:5 cars and 14 bikes
100 points please answer
The best answer is to simplifying each of the identity separately to get the same expression on both sides. Option C
What are trigonometric identities?Trigonometric identities are described mathematically as equalities consisting of trigonometric functions that proves true for all the value of occurring variables for which both sides of equality are defined.
These involve certain functions of one, two or more angles.
They also are different from triangle identities, which involves angles and side lengths of a triangle.
To verify a trigonometric identity, we take the following steps;
Convert the equalities to terms of sine and cosine.Solve the identities at possible timesThen, simplify the left-hand side of the equation, before simplifying the right-hand side.Hence, the best option is C
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im getting confused on this part, i wasnt there the day for class to do this stuff
From the graph, it can be seen that it took 4 days to mow 30 lawns. 12 lawns can be mowed in 1 days.
A graph is what?Analyzing numerical data can be done using graphical representation. It uses a diagram to show the relationship between the data, ideas, information, and concepts. One of the most crucial learning strategies, it is also simple to understand. The kind of information in a particular domain is always a factor.
What are some examples of graphs?Examples include pictures, sketches, line art, graphs from mathematics, charts, diagrams, typography, numbers, symbols, geometric patterns, engineering drawings, or other images. Often, text, illustration, and color are combined in graphics.
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I need to know the first and last one
The lines FE and GH are parallel to each orther.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
Given that
ΔPEI = ΔGHI
here ∠pie = ∠gih
PI =HI
GI=EI
So both triangles are congruent
So the FE║GH.
Hence the lines FE and GH are parallel to each orther.
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Help ASAP PLSSS!! I’d really appreciate it! Thank youuu!
Which of the following is the slope of the line y - 3x =0
Answer:
-3
Step-by-step explanation:
Answer: The slope whould be 3
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope: 3
y-intercept:
(0,0)
x|y
----
0|0
1|3
Find a quartic function
The quartic equation y = x⁴ - x³ - 5 · x² - x - 6 has x = - 2 and x = 3 as its only real zeros. (Correct choice: C)
What quartic equation contains a given set of zeros?
Quartic equations are polynomials of grade 4, whose standard form is described below:
y = a · x⁴ + b · x³ + c · x² + d · x + e
Where a, b, c, d, e are real coefficients. A value of x is a zero of a polynomial when the result is equal to zero. The quickest way to find the polynomial is by evaluating each expression at x = - 2 and x = 3:
x = - 2
y = (- 2)⁴ - (- 2)³ - 5 · (- 2)² - (- 2) - 6
y = 16 + 8 - 20 + 2 - 6
y = 0
x = 3
y = 3⁴ - 3³ - 5 · 3² - 3 - 6
y = 81 - 27 - 45 - 3 - 6
y = 0
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simplify expression: 3f+8(2m-7)
After simplification we got the above expression in the form 3f + 16m -56
What is simplify in mathematics?
The word "simplify" implies to turn something in a simpler form.
In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.
How to simplify the above expression?3f + 8(2m-7)
we rearrange the expression by removing the parenthesis.
we remove the parenthesis by multiplying the factors.
3f + 8 × 2m - 8 × 7
3f + 16m -56
the above expression has no like terms to add or subtract so it is kept in this form.
Hence, 3f + 16m -56 is the simpler form.
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Help please! How do I write an equation in standard form using the information on the graph?
Answer:
3x -y = 2
Step-by-step explanation:
You want a standard form equation for the line through the points (0, -2) and (2, 4).
SlopeThe slope of the line is the "rise" divided by the "run". The given point on the right is 3 grid squares above the one on the left. It is one grid square to the right. So, the slope is ...
m = (squares above)/(squares to the right) = 3/1 = 3
If we consider the actual x- and y-values represented by these grid squares, then the slope is ...
m = (4 -(-2))/(2 -0) = 6/2 = 3
InterceptThe point (0, -2) tells you the y-intercept is -2. That is where the line crosses the y-axis.
Slope-intercept equationWith this information, we can write the slope-intercept form equation for the line:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 3x -2 . . . . . . . . line with slope 3 and y-intercept -2
Standard formThe standard form of an equation for a line is ...
ax +by = c
where a, b, c are generally mutually-prime integers with a ≥ 0. If a=0, then b > 0.
We can rearrange the slope-intercept equation to put it into this form.
y = 3x -2
3x -y -2 = 0 . . . . . subtract y
3x -y = 2 . . . . . . . add 2. This is the standard-form equation of the line.
what is the quotient of g and 25
Answer:
the quotient of g and 25 is g/15.
elijah used 3/4 of the memory on his cell phone memory card if the memory card can hold 32 gigabytes how many gigabytes did elijah used
Elijah used 24 gigabytes memory on his cell.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Elijah used 3/4 of the memory on his cell phone memory card.
And, The memory card can hold 32 gigabytes.
Now,
Since, The memory card can hold 32 gigabytes.
And, She used 3/4 of the memory on his cell phone memory card.
Hence. The used memory = 3/4 of 32
= 3/4 × 32
= 3 × 8
= 24 gigabytes
Thus, Elijah used 24 gigabytes memory on his cell.
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PLS HELP ME!!!
COSINE RULE I THINK!!
please explain in some detail and will mark brainliest
Answer:
Step-by-step explanation:
if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then
[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]
B=101
a= 3 cm
b=y
c=1 cm
use formula for cos B
cos 101=cos(90+11)=sin 11
[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]
Answer:
2.16
Step-by-step explanation:
To find the length y:
Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.
Using the cosine formula:
a^2 = b^2 + c^2 - 2bc cos(A)
where b=1, c=3 and A=101
substitute these values in the formula:
a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)
a ^2 = 4.647970...
Square root to find a:
a = √4.647970...
a = 2.16
thus, y = 2.16 to 3sf
Aponi is a member of the Shoshone Native American Indian
tribe. Her name means "butterfly." Aponi uses beads to make
hair barrettes with a butterfly design. The number of beads she
uses is proportional to the number of hair barrettes she makes.
Aponi graphs a line that shows the number of hair barrettes
she makes and the total number of beads she uses. Two
points on the line are (2, 150) and (5, 375).
What does the slope of the line mean in this situation?
O Aponi uses 45 beads to make each hair barrette.
Aponi uses 75 beads to make each hair barrette.
Aponi uses 150 beads to make each hair barrette.
O Aponi uses 225 beads to make each hair barrette.
A line that shows the number of hair barrettes she makes and the total number of beads she uses is y = 75x.
What is the graph's line's equation?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, you must first determine the slope and y-intercept. The slope is the ratio of the change in y to the change in x. Find two locations on the line, and then draw a sloping triangle joining them.
What is the name for a straight line?A line is a perfectly straight, one-dimensional figure that extends infinity in both directions and has no thickness. To stress that a line has no "wiggles" anywhere along its length, it is sometimes referred to as a straight line or, more archaically, a right line.
Two points on the line are (2, 150) and (5, 375)
y - 150 = ( (375-150) / (5-2) ) (x-2)
y - 150 = 75 (x-2)
y = 75x
Equation of line is y = 75x
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Simplify to a single trig function
On solving the provided question we can say that - the value of the trignometric function will be -cos(t)+2cosec(t)
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
here,
(sint(t) + cos(t))[tex]^{2}[/tex] =(sint +cost)(sint - cost)
=| -cos(t)+2cosec(t) |
= -cos(t)+2cosec(t)
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Question
Enter a linear equation that models the situation.
A drugstore sells pens for $1.40 each and notebooks for $2 each. The owner would like to sell $40 of these
items each day. Use p for the number of pens and n for the number of notebooks.
A linear equation that models the situation is
= 40.
Answer:
1.40p+2n=40
Step-by-step explanation:
Find the value of x.
Answer: x = 4
Step-by-step explanation:
Based on the given distances and angle measures, DE is congruent to XY, DF is congruent to ZX, and EF and ZY are congruent.
This means that:
[tex](4x-1)=15[/tex]
Simplify and solve for x.
[tex]4x-1=15\\4x=16\\x=4[/tex]
So, x = 4
Use the defined variables for the verbal model to write an equation in slope-intercept form that relates the variables.
$2/pound × Pounds of peaches + $1.50/pound × pounds of apples = $15
Let x represent the number of pound of peaches.
Let y represent the number of pounds of apples.
An equation is y = ___
Graph the equation.
An equation is y = -4x/3 + 10.
A graph of the equation is shown in the image attached below.
How to write an equation to model this situation?In order to write and graphically solve an equation that model this situation, we would assign variables to the number of pound of peaches and number of pounds of apples respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pound of peaches.Let the variable y represent the number of pounds of apples.Next, we would translate the word problem into an algebraic equation as follows;
$2/pound × Pounds of peaches = 2x.
$1.50/pound × pounds of apples = 1.50y
Combining the two expressions above, we have the following:
2x + 1.50y = 15
Making y the subject of formula, we have:
1.50y = 15 - 2x
y = (15 - 2x)/1.50
y = -4x/3 + 10
Therefore, an equation in slope-intercept form that relates the variables is y = -4x/3 + 10.
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3p-3p+2s-6s+2q-3q+8r-7r
Is it ok to not put the p in this equation as the 3p is minus
Answer:
- 4s - q + r
Step-by-step explanation:
that's right. You do not put the p since 3p and -3p cancel out to give zero. I'll solve the question for you:-
⇒3p-3p+2s-6s+2q-3q+8r-7r
add or subtract the like terms(terms having same variables), then out of the two like terms, put the sign of the greater number, for e.g. 2q-3q = -1q
⇒0 - 4s - 1q + 1r
⇒- 4s - q + r Answer
hope that helps...
One solution.
2x - 1 = ____x - 1
the blank space must be 2 or x must be zero, I don't know what you mean by one solution
the blank must equal 2 because on the right side the coefficient of x is 2 so it must be same
please help me plsssssssssssssss
Answer:
this should help you out
is y= 2x3 an exponential function?
Answer:
No it is not an exponential function
Prime numbers are the _______ _______of all numbers
The numbers which have only two factors either 1 and the number itself are called prime numbers.
What is prime numbers?Prime number is a natural number greater than 1 that is not a product of two smaller natural numbers while a natural number greater than 1 that is not prime is called a composite number
Therefore a prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
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Wilmer cashed his paycheck at Check Express. The fee at Check Express is 9% of the amount of the check. His paycheck was $291. How much was the fee for Wilmer to cash his paycheck?
Answer:
$26.19
Step-by-step explanation:
9% as a decimal is 0.09.
So, the fee is [tex](291)(0.09)=\$26.19[/tex].
Answer:
$26.19
Step-by-step explanation:
.09 x 291 = 26.19
Anyone knows the answer ?
The solution for the question found using the double angle formula for cosine is -[tex]\frac{7}{25}[/tex].
What are double angle formulae?
There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.
The double angle formula for cosine is
Cos 2θ = Cos²θ - Sin²θ
=2Cos²θ – 1
= 1 – 2Sin²θ
Given sinθ = [tex]\frac{4}{5}[/tex]
cos(2θ) = 1-2sin²θ = [tex]1-2[/tex]×( [tex]\frac {4}{5}[/tex])² = [tex]1-[/tex] [tex]\frac{32}{25}[/tex] = [tex]\frac{-7}{25}[/tex]
Therefore Cos(2θ) fund using double angle formula is -[tex]\frac{7}{25}[/tex]
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The solution for the question found using the double angle formula for cosine is -.7/-25
What are double angle formulae?There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.
What is angle?An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex. The size of an angle is typically measured in degrees or radians, with one full rotation around a point (360 degrees or 2π radians) being equal to a full circle.
The double angle formula for cosine is
Cos 2θ = Cos²θ - Sin²θ
=2Cos²θ – 1
= 1 – 2Sin²θ
Given sinθ = 4/5
cos(2θ) = 1-2sin²θ = 1-2×(4/5 )² = 1-32/25 = -7/25
Therefore Cos(2θ) fund using double angle formula is -
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Divide the polynomials. If there is a remainder, enter the remainder in fraction form. x^4+3x^3-x-2/x+1
The polynomial x⁴ + 3x³ - x - 2 will have a remainder of 1 when divided by x + 1 and the result can be written in the form (x³ + 2x² + 2x - 3) + 1/(x + 1).
How to divide the polynomialUsing the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder
We shall divide the polynomial x⁴ + 3x³ - x - 2 by x + 1. as follows;
x⁴ divided by x equals x³
x + 1 multiplied by x³ equals x⁴ + x³
subtract x⁴ + x³ from x⁴ + 3x³ - x - 2 will result to 2x³ - x - 2
2x³ divided by x equals 2x²
x + 1 multiplied by 2x² equals 2x³ + 2x²
subtract 2x³ + 2x² from 2x³ - x - 2 will result to 2x² - x - 2
2x² divided by x equals 2x
x + 1 multiplied by 2x equals 2x² + 2x
subtract 2x² + 2x from 2x² - x - 2 will result to -3x - 2
-3x divided by x equals -3
x + 1 multiplied by -3 equals -3x - 3
subtract -3x - 3 from -3x - 2 will result to a remainder of 1.
Therefore, the polynomial x⁴ + 3x³ - x - 2 divided by x + 1 gives a quotient x³ + 2x² + 2x - 3 and a remainder of 1 and can be written as (x³ + 2x² + 2x - 3) + 1/(x + 1).
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i have been trying to figure this out for hours-
answer choices:
SSS
SAS
ASA
AAS
HL
Not Congruent
Answer: The answer is SAS