Solving the Question
We're given:
3x-y=-6Find 4 solutionsWe can start by isolating one of the variables, like y:
[tex]3x-y=-6\\-y=-3x-6\\y=3x+6[/tex]
Now we can find four solutions by plugging in any number for x:
[tex]y=3x+6\\y=3(1)+6\\y=3+6\\y=9[/tex]
First solution: (1,9)
[tex]y=3x+6\\y=3(2)+6\\y=6+6\\y=12[/tex]
Second solution: (2,12)
[tex]y=3x+6\\y=3(3)+6\\y=9+6\\y=15[/tex]
Third solution: (3,15)
[tex]y=3x+6\\y=3(4)+6\\y=12+6\\y=18[/tex]
Fourth solution: (4,18)
Possible AnswersFirst solution: (1,9)
Second solution: (2,12)
Third solution: (3,15)
Fourth solution: (4,18)
Write a two-column proof.
Given: QR ≅ SR ≅ WR ≅ VR
Prove: QT ≅ WU
We can conclude that line QT ≅ WU.
What exactly is meant by a triangle's congruency?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given: QR ≅ SR ≅ WR ≅ VR
To Prove: QT ≅ WU
Line VRS ⊥ WRQAs ∠UWR and TQR = 90°.So, UW and QT ⊥ WRQTherefore, we can conclude that line QT ≅ WU.
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A wide receiver starts from his 15-yard line on the right hash mark and runs a route that takes him 12 yards to the left and down field for a gain of 17 yards. Write a translation vector to describe the receiver's route.
A translation vector describing the receiver's path < -12, 17 >.
What is termed as translation vector?The distance vectors that almost all atoms in the grouping are translated through just to form another cluster inside the solid are defined by translation vectors.
Tv can be in either Cartesian or internal coordinates. If a Tv is described in Cartesian coordinates, it is directly used. If it is defined in internal coordinates, it is converted to Cartesian coordinates as well as the Cartesian coordinates of atom 1 (real or dummy) are subtracted from it at run time. If atom 1 is at the origin, i.e. (0.0, 0.0, 0.0), then the coordinates defined by Tv are indeed the translation vectors; this simplifies visualizing this same translation vectors using a GUI because a line drawn from atom 1 to Tv would represent this same translation vector.Now, as per the stated question;
The horizontal (lateral, x) change is represented by the number 12. This same player runs 12 yards to the left.
The vertical (up/down, y) transition is represented by the number 17. In addition, the player runs 17 yards up the field.
When you put it all together, you get < -12, 17 >.
Therefore, the receiver's route is defined by translation vector < -12, 17 >.
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solve for -7x-3x+2=-8x-8
In linear equations, x = 5 is value of x .
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.-7x-3x+2=-8x-8
-7x -3x + 8x = -8 - 2
-10x + 8x = -10
-2x = -10
x = 5
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HELP FIND THE AVERAGE RATE OF CHANGE
The average rate of change of a function [tex]f(x)[/tex] as [tex]x[/tex] varies from [tex]x=a[/tex] to [tex]x=b[/tex] is given by the so-called difference quotient
[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]
If we plot [tex]f(x)[/tex], this difference quotient would correspond to the slope of the line through two points [tex](a,f(a))[/tex] and [tex](b,f(b))[/tex] and intersecting with the curve [tex]y=f(x)[/tex].
(a) The average rate of change of height from 0 to 6.6 seconds is
[tex]\dfrac{H(6.6) - H(0)}{6.6 - 0}[/tex]
and is measured in m/s.
Consult the table for the values of [tex]H(t)[/tex] - it tells us [tex]H(0)=0[/tex] and [tex]H(6.6)=198[/tex]. So the average rate of change of height in this time is
[tex]\dfrac{198 - 0}{6.6 - 0} \dfrac{\rm m}{\rm s} = \boxed{30\dfrac{\rm m}{\rm s}}[/tex]
(b) Similarly, the average rate of change of height from 8.8 to 13.2 seconds is
[tex]\dfrac{H(13.2) - H(8.8)}{13.2-8.8} \dfrac{\rm m}{\rm s} = \dfrac{0 - 44)}{4.4} \dfrac{\rm m}{\rm s}= \boxed{-10 \dfrac{\rm m}{\rm s}}[/tex]
Will the product of an integer and a natural number always be an integer? Why or why not? Justify your answer with two examples.
Yes, the product of an integer and a natural number will always be an integer.
A natural number refers to a whole number that does not have any kind of fraction or decimal. Some examples of natural numbers are 1, 2, 3, 4, and so on. Zero is not a natural number.
Integers refer to all numbers that can be positive and negative. It should not have a fractional part or a decimal part in the number. Integers can be depicted by the positive or the negative sign. Zero is an integer.
Whenever we are multiplying a natural number with an integer, we are ultimately getting the result as a positive number, negative number, or zero. Thus, it will become an integer.
Example 1: We can take the natural number 10 and the integer -5. Its product will be -50. Thus, it is an integer.
Example 2: We can take the natural number 16 and the integer 0. Its product will be 0. Thus, it is an integer.
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In captivity, a male lion grows to weight about 420 lbs with a standard deviation of 35 lbs. A zoo would like to have a lion that is in the largest 25% of male lions based on weight. How much should a male lion weigh for the zoo to obtain the male lion?
456.25 male lion weigh for the zoo to obtain the male lion.
what is Normal distribution?Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Given:
A male lion grows to weight about 420 lbs with a standard deviation of 35 lbs.
A zoo would like to have a lion that is in the largest 25% of male lions based on weight.
So,
z= (x- [tex]\mu[/tex])/[tex]\sigma[/tex]
Now substituting the value
1.036 = X-420/35
36.25= X- 420
X= 36.25 + 420
X= 456.25
Hence, 456.25 male lion weigh for the zoo to obtain the male lion.
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here for the solution We have here, that jet is equal to 0.52. Their score corresponding to 30 area under standard normal distribution. By using jet table to the right up ahead here, X is equal to zero multiplied by sigma plus mu. Here by substituting the value for the next step, we get 0.52 dataset, multiply by sigma. That is 35 plus mu, That is four 20. By simplifying this, we get the value is 4 83.2, which is approximately equal to 4 38.4. Which is our Answy for the answer is 4:38.4 is the correct choice for the answer. So here is the solution. The answer. Please go through this.
Relations, Domains
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Select all numbers that are in the domain.
The domain are -3, -1, 1 . The range is -2, 0, 2 .
What is relation and domain?A relation is a rule that relates an element from one set to the other set.The domain is the set of all first elements of the ordered pairs. The range on the other hand is the set of all second elements of the ordered pairs.A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x, y) is in the relation.The range of a relation is the set of the second coordinates from the ordered pairs.Note that both functions and relations are defined as sets of lists. In fact, every function is a relation. However, not every relation is a function. In a function, there cannot be two lists that disagree on only the last element.To know more about Relation visit:
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Answer: -3,-1, and 1.
Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.
10 Points
Use the figure below to answer questions #1-4. You can also use DESMOS to help you answer this question.
What are the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE
Using translation concepts, the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE are given by: (3,4).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
The rule for a 90º clockwise rotation is given by:
(x,y) -> (y, -x).
From the figure given for the problem, the coordinates of G are given as follows:
G(-4,3).
Applying the rule, we have that:
(-4,3) -> (3, 4), as y = 3, -x = -(-4) = 4.
Hence the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE are given by: (3,4).
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Translate the sentence into an equation.
Twice the difference of a number and 3 is equal to 5.
Use the variable v for the unknown number.
Answer:
2(v-3) = 5
Step-by-step explanation:
2(v-3) = 5
You are solving a measurement problem where the numbers 4.5160 x 10−3, 2.09 x 107, and 5.8 x 103 are multiplied. how many significant digits should the product have? 2 1 5 3
The number of significant digits the product should have = 2
The given numbers are:
[tex]4.5160 \times 10^{-3}\\ 2.09 \times 10^7\\ 5.8 \times 10^3[/tex]
We first multiply them.
[tex]4.5160 \times 10^{-3}\times 2.09 \times 10^7\times 5.8 \times 10^3 = 54.743\times10^7[/tex]
In measurement problems, we usually write it as [tex]5.474\times10^7[/tex]
Significant digits are the numbers which decide the precision and accuracy in measurement problems.
The fewest number of significant digits in each factor of multiplication is considered as the significant digits of the product.
So number of significant digits in [tex]4.5160\times10^{-3}[/tex] = 5
Number significant digits in [tex]2.09\times10^7[/tex] = 3
Number of significant digits in [tex]5.8\times10^3[/tex] = 2
So the product should be rounded into 2 significant digits.
So the product, [tex]5.474\times10^7[/tex]= [tex]5.5\times10^7[/tex] with 2 significant figures.
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ASAP please
A rotating sprinkler is placed in one corner of a garden . If it has a reach of 8m and rotates through an angle of 30°, calculate the area of garden not being watered. Give your answer in terms of π
The area that is not covered by the sprinkler is 33.49 m².
The sprinkler is placed in one corner of the garden.
It has a reach of 8 m.
radius = r = 8 m
It means that it will form a segment of 90°.
So, the area it should cover will be:
Area that should be covered = 1 / 4 π r²
= 1 / 4 π (8)² m²
= 1/ 4 π (64) m²
= 16 ( 3.14 ) m²
= 50.24 m²
Now, it only rotates 30°.
It means that, it covers only 1 / 3 area.
So, the area actually covered = 1 / 3 × 50.24 m²
= 16.75 m²
The area that is not covered = 50.24 m² - 16.75 m²
The area that is not covered = 33.49 m²
Therefore, we get that the area that is not covered by the sprinkler is 33.49 m².
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what is 50 times 4
giving away points
Answer: 200
Step-by-step explanation: hope this helps!!!
hey don't ask it in this way
ask a easy real question
so mods won't take it down
thanks btw <3
A saleswoman earns 30% commission on all the merchandise that she sells. Last month she sold $800 worth of merchandise. How much commission (in dollars) did she earn last month?
Answer:
$240
Step-by-step explanation:
30% of 800 is 240
.30*800
The width of a 2-by-4 piece of wood is actually 3 1/2 inches. Find the total width of 30 2-by-4s laid side by side. Simplify your answer.
This is equivalent to 8.75 feet
====================================================
Explanation:
3 & 1/2 inches = 3.5 inches since 1/2 = 0.5
30 boards of this width total to 30*3.5 = 105 inches
This is equivalent to 105/12 = 8.75 feet. I'll leave the answer in inches since the original unit is inches. I would ask your teacher for further clarification.
i need this asap pls pls pls …
The zeros of the given polynomial equation are {-1, -2, -3}.
The given polynomial equation is g(a)=4a³+24a²+44a+24.
What is the Rational Zeros Theorem?The rational root theorem is also known as the rational zero theorems (or) the rational zero tests (or) rational test theorem and is used to determine the rational roots of a polynomial function. The general form of a polynomial function is [tex]f(x) = a_nx^n+a_{n-1}x^{n-1}+.......+a_2x^2+a_1x+a_0[/tex]. Here, the value(s) of x that satisfy the equation f(x) = 0 are known as the roots (or) zeros of the polynomial.
Now, g(a)=4a³+24a²+44a+24
⇒ 4a³+24a²+44a+24=0
⇒ 4(a³+6a²+11a+6)=0
⇒ a³+6a²+11a+6=0
Now, put ....-3, -2, -1, 0, 1, 2, 3,....in a³+6a²+11a+6=0 and simplify and check they are equal to 0.
Put a=-3 and check.
That is, (-3)³+6(-3)²+11(-3)+6=0
⇒-27+54-33+6=0
⇒0=0
So, -3 is the zero of the given equation.
Put a=-2 and check.
That is, (-2)³+6(-2)²+11(-2)+6=0
⇒-8+24-22+6=0
⇒0=0
So, -2 is the zero of the given equation.
Put a=-1 and check.
That is, (-1)³+6(-1)²+11(-1)+6=0
⇒-1+6-11+6=0
⇒0=0
So, -1 is the zero of the given equation.
Therefore, the zeros of the given polynomial equation are {-1, -2, -3}.
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Sarah was explaining her first step in factoring, but made an error in her explanation.
Factor: 5x² - 4x - 9
Sarah said, "I need to find factors of -9 that add to -4"
What was the error in her thought process?
Answer:
-9
Step-by-step explanation:
her error was that -9 can't add up to -4
Answer:
she needs to find factors of -45 that add to -4
Step-by-step explanation:
You want to know the error involved when looking for factors of 5x²-4x-9 by considering only factors of -9.
Quadratic factorsConsider the product of factors (ax +b)(x +d):
(ax+b)(x +d) = ax² +adx +bx +bd = ax² +(ad+b)x +bd
You will notice the two parts of the sum that is the middle term coefficient have the product abd, which is also the product of the first and last coefficients.
Sarah needs to be looking for factors of (5)(-9) = -45 that have a sum of -4.
__
Additional comment
The factors Sarah needs are -9 and 5. These will give Sarah the equation ...
5x² -9x +5x -9
which can be factored pairwise to ...
x(5x -9) +1(5x -9) = (x +1)(5x -9)
Plsss help me
Ayuda, es de matemáticas
Answer:
Step-by-step explanation:
Determine whether the events are independent or dependent. Then find the probability.
A king is drawn, without replacement, from a standard deck of 52 cards. Then, a second king is drawn.
1/13 is probability of a second king is drawn.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective.Total cards = 52
a complete pack without jokers, then it is 4/52 = 1/13.
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Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
A(4,7,9) and B(-3,8,-8)
The midpoint is at (11/2, 15/2, 1/2)
In the given statement is
To find the midpoint of the line segment joining the pair of points
A(4,7,9) and B(-3,8,-8)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =( [tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} ,\frac{z_{1}+z_{2} }{2}[/tex] )
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points A(4,7,9) and B(-3,8,-8)
Solving for the midpoint , we have,
m = ([tex]\frac{4+7}{2} ,\frac{7+8}{2} , \frac{9+(-8) }{2}[/tex])
m = (11/2, 15/2, 1/2)
Therefore, the midpoint is at ( 11/2, 15/2, 1/2)
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Pablo bought a sweater on sale for 25% off the original price and another 40% off the discounted price. If the sweater originally cost 48 , what was the final price of the sweater?
a. 14.40
b. 21.60
c. 31.20
d. 36.00
When Pablo bought a sweater on sale for 25% off the original price and another 40% off the discounted price, if the sweater originally cost 48 then the final price of the sweater is $21.6
Given,
The Original cost of the sweater = $48
First,
Pablo bought a sweater on sale for 25% off the original price
Then,
[tex]48-48(\frac{25}{100} )[/tex]= $36
Then another 40% off the discounted price
Final price = [tex]36-36(\frac{40}{100} )[/tex]
=$21.6
Hence, when Pablo bought a sweater on sale for 25% off the original price and another 40% off the discounted price, if the sweater originally cost 48 then the final price of the sweater is $21.6.
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The midpoints of the sides of a triangle are located at (a, 0),(2 a, b) and (a, b). If one vertex is located at the origin, what are the coondinates of the other vertices? Explain your neasoning.
The coordinates of the other vertices are (2a, 2b) and (2a. 0) after using the mid-point theorem.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
From the data, we can draw a triangle as shown in the attached picture.
Let the coordination of B is at (0, 0)
The coordinate of point A:
A(x, y):
a = (x + 0)/2
x = 2a
y = 2b
A(x, y): (2a, 2b)
The coordinate of point C:
C(X, Y):
2a = (X + 2a)/2
4a = X + 2a
X = 2a
b = (Y + 2b)/2
Y = 0
Thus, the coordinates of the other vertices are (2a, 2b) and (2a. 0) after using the mid-point theorem.
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If f(x) = sqrt(4 - x ^ 2) then f(2)
Answer:
f(2) = sqrt(4 - 2 ^ 2)
f(2) = sqrt(4 - 4)
f(2) = sqrt(0)
f(2) = 0
Answer: 0
Step-by-step explanation:
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Find the distance between each pair of parallel lines with the given equations).
y=2 x-3
2 x-y=-4
Distance between parallel lines y=2x-3 and 2x-y=-4 is [tex]\frac{7\sqrt{5} }{5}[/tex] .
Two lines a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.
Distance between two two parallel lines is given by [tex]\frac{|c1-c2|}{\sqrt{a^{2} +b^{2} } }[/tex].
In the given question
2x-y-3=0 and 2x-y+4=0
Given the coefficient of x and y is same in both the line therefore they are parallel.
given, a(coefficient of x)=2 , b(coefficient of y= -1 , c₁=-3 , c₂=4.
Substituting the values in the distance formula we get
[tex]d=\frac{|-3-4|}{\sqrt{2^{2}+(-1)^{2} } }[/tex]
[tex]=\frac{7}{\sqrt{4+1} } =\frac{7}{\sqrt{5} }[/tex]
on rationalizing we get
[tex]d=\frac{7\sqrt{5} }{5}[/tex]
Therefore , the distance between parallel lines y=2x-3 and 2x-y=-4 is [tex]\frac{7\sqrt{5} }{5}[/tex].
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Algebra solve the equation show work
Answer:
Step-by-step explanation:
3t + 4 = 12 + 3t
4 = 12 (subtract 3t from both sides)
0 = 8 (subtract 4 from both sides)
State the property that justifies each statement.
If m∠1+m ∠2=90 and m ∠2=m ∠3 , then m∠ 1+m∠ 3=90 .
Each assertion is supported by a property. The transitive feature of equality justifies this.
What exactly is meant about transitive property?If x, y, and z are the three quantities, and then if x is connected to y by some rule and y is related to z through the same rule, we are able to say x is related to z by the same rule.
According to the given data:m∠1+m ∠2=90
m ∠2=m ∠3
m∠ 1+m∠ 3=90 .
The property that justifies each statement is This is justified by the transitive property of equality.
because :
Transitive Property of Equality show If a = b and b = c, then a = c.
so in the given statement the m∠1+m ∠2=90 and ∠2=m ∠3 so m∠ 1+m∠ 3=90.
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5p − q − p; use p = 3, and q = 4
Step-by-step explanation:
5p − q − p; use p = 3, and q = 4
5*3-4-3
=15-7
=8
The band boosters sell cider and doughnuts at home football games.
Last week they sold 318 cups of cider at $0.75 per cup and 12 dozen
doughnuts at $1.25 per doughnut. What were the total sales?
318* 0.75= $238.5
12*12=144 doughnuts total
144*1.25= $180
238.5+180= $418.50
the total sales were $418.50
I need this answered and explained I missed a lesson from being sick and don’t understand this
a) 4, associative property
- This is the associative property of multiplication. When everything is multiplied, you can rearrange the parentheses.
b) 8, commutative property
- This is the commutative property. It means that when multiplying two numbers together, the order doesn't matter.
c) 0, zero property
- This is the zero property of multiplication. This states that anything times 0 is equal to 0. In this case, 0 times 3 is 0.
d) 8, identity property
- This is the identity property of multiplication. This means that any number times 1 is itself. In this case, 9 times 1 is 8.
Please note how a property is worded may differ per class.
Solve each equation. 12=2-k
The solution of the given linera equation in one variable 12=2-k is at k = 10.
According to the given question.
We have a linear equation in one variable 12 = 2 - k.
As we know that, linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Therefore, the solution of the linear equation in one variable 12 = 2 - k is given by
12 = 2 - k
⇒ 12 - 2 = -k (subtracting 2 from both the sides)
⇒ 10 = -k
⇒ k = 10
Hence, the solution of the given linera equation in one variable 12=2-k is at k = 10.
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16-19!!! NEED NOW!!!
Answer:
(15 solutions)[tex]2x + 9 = y \\ - 4x - 3 = y \\ so \: both \: equation \: is \: equal \\ 2x + 9 = - 4x - 3 \\ 2x + 4x = - 3 - 9 \\ 6x = - 12 \\ x = \frac{ - 12}{6} \\ x = - 2[/tex]
if this solution is correct then I'll solve another..... please reply my solution is correct or wrong