The possible coordinates of the other points are (3 + √7, -1) and (3 - √7, -1)
How to calculate the coordinates of the two points?From the question, we have
Points = (3, 2) and (x, -1)Distance = 4 unitsWhere (x, -1) represents the other points
The distance between the points is the number of units between them
It is calculated using the following distance formula
d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
Where x and y represent the coordinates of the given points
Substitute the known values in d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
So, we have
d = √[(3 - x)²+ (2 + 1)²]
Evaluate the expression
d = √[(3 - x)²+ 9]
Recall that d = 4
So, we have
√[(3 - x)²+ 9] = 4
Square both sides
(3 - x)²+ 9 = 16
This gives
(3 - x)² = 7
So, we have
3 - x = ±√7
Solve for x
x = 3 ± √7
Hence, the coordinates are (3 + √7, -1) and (3 - √7, -1)
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Write an equation of the line through (-3,- 6) having slope17/16Give the answer in standard form.The equation of the line is
The equation of a line in Standard form is:
[tex]Ax+By=C[/tex]Where "A", "B" and "C" are Integers ("A" is positive).
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case you know that:
[tex]m=\frac{17}{16}[/tex]And knowing that the line passes through the point
[tex]\mleft(-3,-6\mright)[/tex]You can substitute values and solve for "b":
[tex]\begin{gathered} y=mx+b \\ -6=(\frac{17}{16})(-3)+b \\ \\ \\ -6=-\frac{51}{16}+b \\ \\ -6=-\frac{51}{16}+b \\ \\ -6+\frac{51}{16}=b \\ \\ b=-\frac{45}{16} \end{gathered}[/tex]Then, the equation of this line in Slope-Intercept form is:
[tex]y=\frac{17}{16}x-\frac{45}{16}[/tex]Now that you have this equation, you can write it in Standard form as following:
[tex]\begin{gathered} y+\frac{45}{16}=\frac{17}{16}x \\ \\ \frac{45}{16}=\frac{17}{16}x-y \\ \\ \frac{17}{16}x-y=\frac{45}{16} \end{gathered}[/tex]The answer is:
[tex]\frac{17}{16}x-y=\frac{45}{16}[/tex]v - 4 > 22 solve the inequality of v and simplify your answer as much as possible. plsssss do this!!!
Answer:
v > 26
Step-by-step explanation:
v > 22 + 4
v > 26
there is no qouificient ( I don't know how to spell that) of v so that's your answer
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A (4, 5), B (12,9); 3 to 1 The coordinates of P are:
By applying line ratio, the coordinates of P are: [10, 8].
How to determine the coordinates of P?Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Given the following parameters:
Point A (4, 5)Point B (12, 9)m:n = 3:1Substituting the given parameters into the formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(3(12) + 1(4))/(3 + 1)], [(3(9) + 1(5))/(3 + 1)]
P(x, y) = [(36 + 4)/4], [(27 + 5)/4]
P(x, y) = [40/4, 32/4]
P(x, y) = [10, 8].
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Hi may you please help me
The value of x is 85° when a pair of parallel lines intersects another pair of parallel lines.
According to the question,
We have the following information:
A pair of parallel lines intersects another pair of parallel lines.
We have a figure where an angle is given as 85°.
Now, the following theorems would be helpful in finding the value of x:
When a pair of parallel lines is intersected by another line then the sum of two consecutive interior angles is 180°. (1)
When a pair of parallel lines is intersected by another line then the alternate interior angles are equal. (2)
Vertically opposite angles are equal. (3)
(Now, we will refer to these theorems by the number given in the brackets.)
Now, by theorem 3, we have vertically opposite angle as 85°.
Now, its alternate interior angle will also be 85°.
Now, 85° and x° are vertically opposite angles.
So, by theorem 3, we have the value of x as 85°.
Hence, the value of x is 85°.
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POSSIBLE POINTS
Write and solve the given inequality: twice the difference of three times a number and five is at most the sum of four times a number and six.
O [8,00)
O (8,00)
O(-0,8)
O(-0,8]
The inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]
Let the number be x,
Twice the difference of three times a number and five = 2(3x - 5)
The sum of four times a number and six is (4x + 6)
2(3x - 5) ≤ (4x + 6)
6x - 10 ≤ 4x + 6
6x - 4x ≤ 6 + 10
2x ≤ 16
x ≤ 8
x can be any positive number less than or equal to 8.
Therefore, the inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]
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solving one step inequalities using addition subtraction multiplication and division
To begin with
we have the inequality
[tex]4>x-2[/tex]To solve
Step 1: we will collect like terms
[tex]4+2>x[/tex]simplify the inequality above
[tex]\begin{gathered} 6>x \\ \text{Re}-\text{arranging} \\ x<6 \end{gathered}[/tex]Hence, the answer is
[tex]x<6[/tex]To draw the shape
Part B is correct
In the diagram below line FG is // to line HI, and line segments BC and AD intersect at E.
The measure of angle GBE = 3x+20, and the measure angle ECD = x.
The values of the angle x in the line segments is 40 degrees.
How to find the measure of angle?When parallel lines are are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the line FG is parallel to line HI. The line segment BC and AD are the transversal lines that cut across the parallel lines FG and HI.
Therefore,
3x + 20 + x = 180 (Same interior angles)
Same interior angles are supplementary. That is the angles sum up to 180 degrees.
Therefore,
3x + 20 + x = 180
4x + 20 = 180
4x = 160
divide both sides by 4
x = 160 / 4
x = 40 degrees
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PLEASE HELP URGENT HELP PLEASE!!!!!!!!!!!!!!!!
Answer:
[tex]y = \frac{w}{h - 5c^{3}}[/tex]
Step-by-step explanation:
separate y from everything
[tex]w = y(h - 5c^{3})[/tex]
now divide everything by the thing in the parenthesis
[tex]\frac{w}{h - 5c^{3}} = y[/tex]
now flip it
[tex]y = \frac{w}{h - 5c^{3}}[/tex]
that is your answer
m=p*Vwe have
p=m/V
Solve for m
That means-----> isolate the variable m
Multiply both sides by V
p*V=(m/V)*V
Simplify
p*V=m
rewrite
m=p*V
Using the properties of equality, the value for m in the equation is: m = pV.
How to Apply the Properties of Equality to Solve for a Variable?For any given equation, to solve for a variable in the equation, we have to isolate the variable to one side of the equation in order to determine its value. To do this, several properties of equality need to be applied to isolate the variable to one side of the given equation.
Given the equation, p = m/V, we need to isolate the variable m to one side of the equation in order to solve for m.
p = m/V
Multiply both sides of the equation by V
p × V = m/V × V [multiplication property of equality]
Simplify the equation:
pV = m
m = pV
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Jodi bough a new car with 14 gallon gas tank. Around the town she is able to drive 336 miles on one tank of gas. on her first trip traveling on highways, she drives 448 on one tank of gas.A: Write a compound inequality in compact from the represents how many miles Jodi can drive on a tank of gas. Let m represent the number of miles per gallon.B: Rewrite the compound inequality as two simply inequalities separate by either and or, or.C: Solve each simple inequality. Then write the solution in compact form.
We have the following:
A.
Let m represent the number of miles per gallon, the inequality would be as follows
[tex]\frac{336}{14}\leq m\leq\frac{448}{12}[/tex]B. In two simple inequalities we have this
[tex]m\ge\frac{336}{14}\text{ or }m\leq\frac{448}{14}[/tex]C.
[tex]\begin{gathered} m\ge24\text{ or }m\leq32 \\ 24\leq m\leq32 \end{gathered}[/tex]PLEASE ANSWER ALL THE QUESTIONS FOR 50 POINTS!!!!!
Answer:
a. 4.2 - 2.8 = 1.4
b. 72.1 - 45.6 = 26.5
c. 82.2 - 41.3 - 29.2 = 11.7
d. 17.1 - 11.7 - 0.8 = 4.6
e. 29.2 - 12.5 - 0.9 = 15.8
f. 21 - 14 = 7
g. 71 - 37 - 18 = 16
h. 50 - 19 - 8 = 23
i. 92 - 57 - 16 = 19
j. 44 - 18 - 9 = 17
Find the slope of each line.
1)2x-5y=20
2) 2x-3y=-9
Answer:
1)2/5
2)2/3
Hope this helps!
Answer:
1. m=2/5
2. m-2/3
Step-by-step explanation:
Use the equation one sixth plus s equals 21 over 30 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
(Its due in 45 minutes so help answer it plsss)
s is 4/15 of the equation one sixth plus s equals 21 over 30.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is
one sixth plus s equals 21 over 30
This can be written as
one sixth can be written as 1/6.
21 over 30 can be written as 21/30.
so the equation is 1/6+s=21/30.
Let us separate the variable s to find the value of s.
s=21/30-1/6
The LCM of 30 and 6 is 30
s=21-5/30
s=16/30=4/15
Hence s is 4/15 of the equation one sixth plus s equals 21 over 30.
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Determine if the equation is linear. If so graph the function (x+y=1)
Answer:
The equation is linear
Step-by-step explanation:
Make the equation in y=mx+b form
which is y=-x+1 and because the x is not the first power it must be linear
Graph:
HELP ASAP, IM DUE IN 4 HOURS
Rotate DEF 90° clockwise around the origin. Then translate D'E'F' to the right 5units and down 2 units. What are the coordinates of D''E''F''? Show and explain how you arrived at your answer.
Answer below and in attached graph Step by stepShow and explain:1) The rule for a rotation by 90° around the origin is (x,y)→(−y,x) so I moved the y to x and changed the sign, I moved x to y position. 2) to translate 5 units right and 2 units down, you add (+5, -2) to your current coordinates of D’ E’ and F’ giving D’’ E’’ F’’. Pre Image ➡️ D’ E’ F’ ➡️. D’’ E’’ F’’ (+5, -2)D (-5, -2) ➡️ (2, -5) ➡️ (7, -7)E (0, -2) ➡️ (2, 0). ➡️ (7, -2)F (-4, -6) ➡️ ( 6, -4). ➡️ (11, -6)Attached graph of pre image and transformations
A parabola can be drawn given a focus of (-5, -1) and a directrix of y=7. Write the equation of the parabola in any form.
A parabola with focus of (-5, -1) and a directrix of y=7 has the equation of the parabola as: (x + 5)² = 8 (y - 3)
How to write the equation of parabola with directrix of y = 7 and focus of (-5, -1)Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The focus
F (h, k + p) = (-5,-1)
h = -5
k + p = -1
P in this problem, is the midpoint between the focus and the directrix
P = (-1 - 7) / 2 = -4
p = -4
the vertex
v(h, k)
h = -5
k + p = -1, k = 3
v(h, k) = v(-5, 3)
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - -5)² = 4 * 2 (y - 3)
(x + 5)² = 8 (y - 3)
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15. Name the indicated parts of this diagram.AC __________________AE __________________DE __________________AB __________________ADE __________________________ACE = _______°CAB = _______°
SOLUTION:
We want to name the indicated parts on the diagram, their names are;
For the angles, we have;
[tex]\begin{gathered} \measuredangle ADE=22^o\text{ }(Inscribed\text{ }Angle) \\ \measuredangle ACE=44^o\text{ }(Central\text{ }Angle) \\ \measuredangle CAB=90^o\text{ }(Angle\text{ }between\text{ }radius\text{ }and\text{ }tangent) \end{gathered}[/tex]Solve the system using linear combination.
41
(5x + 3y
3x - 6y = 9
=
We want to eliminate the variable y. What number should we multiply times the first
equation, so that when we add the two equations, we can eliminate the variable y?
The solution of system of equation is x = 2 and y = 7. We should multiply first equation with 2 so that when we add the two equations, we csystem of equation an eliminate the variable y.
What is system of equation?
Two or more equations that share variables are said to be .
For instance, consider two equations where x and y are shared:
x + y = 6
3x + y = 2
We might be able to solve equations that have the same number of variables. Where the lines intersect in this case is the answer (1,5)
Given system of equation:
5x + 3y = 41,
3x - 6y = 9
Lets multiply the first equation with 2, we get
10x + 6y = 82
Adding these equation with second given equation we get,
10x +6y +(3x - 6y) = 82 + 9
13x = 91
x = 91/13
x = 7
putting the value of x in any one equation
3(7) -6y = 9
y = 2
Therefore, the x and y in the given system of equation are 7 and 2 respectively.
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A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
If a bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. The height of the 7th bounce of the ball is 0.7.
Determining the height of the ballGiven data:
First bounce = 3.75 feet
Successive bounce = 79% or 0.79%
Bounce = 7
Now let determine the height of thee 7th bounce of the ball using this formula
Height = First bounce × (Successive bounce) ^ Number of bounce
Let plug in the formula
Height = 3.75 × (0.79 ) ^7
Height = 0.7
Therefore the height is 0.7.
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Jennifer is thinking about getting an MBA. She will give up making $27,500 a year for the two years it takes to complete the MBA. She will also pay $45,000 in total costs to get the degree. Assume she will make $67,500 a year after she gets her MBA. How long will it take for Jennifer to recover her investment?
Answer:
un year
Step-by-step explanation:
You have discovered another alien. Find the correct rescue path before answering this question.
When the spaceship starts from a point on the y axis, what is the y-intercept of the line of travel?
the x-coordinate of the spaceship
the y-coordinate of the spaceship
the y-coordinate of the alien
the distance from the spaceship to the alien
From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
Given,
You have discovered another alien. Find the correct rescue path .
When the spaceship starts from a point on the y axis, we have to find the y intercept of the line of travel.
y-intercept;
A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
Here,
From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
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5-52: the first card selected from a standard 52-card deck is a king. a. if it is returned to the deck, what is the probability that a king will be drawn on the second selection? b. if the king is not replaced, what is the probability that a king will be drawn on the second selection? c. in part (b), are we assuming the card selections are independent? justify your answer.
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability.
The probability of getting a king card is 1/13 or 0.077.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: Total number of probability - 52
Now, the first selected card is king and it is returned to the deck.
So it contains no effect on the second selection card.
Then, we have to estimate probability to obtain a king
probability = favourable outcomes for a king / total possible outcomess
= 4 king cards / 52 cards in total
= 4 / 52 = 1 / 13
The probability of getting a king card is 1 / 13 or 0.077
Therefore, the correct answer is option B. 1/13, or 0.077.
The complete question is:
The first card selected from a standard 52-card deck was a king. It isreturned to the deck, what is the probability that a king will be drawn on the second selection?
A. 1/4 or 0.25
B. 1/13, or 0.077
C. 12/13, or 0.923
D. 1/3 or 0.33
E. None of the above
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Use the conditional statement "If it is January, then there is snow." for questic
17. Identify the hypothesis:
18. Identify the conclusion:
Hypothesis: It is January and Conclusion: There is snow
What is hypothesis and conclusion?The initial clause, or "if," of a conditional statement is the hypothesis. The second, or "then," component of a conditional statement is the conclusion. The theory led to the conclusion.
An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. As indicated, this is pq. Read this: if p, then q. If the hypothesis is correct but the conclusion is untrue, a conditional statement is false.
Conditionals are in the form if P, then Q.
P is the hypothesis.
Q is the conclusion.
If It is January, then there is snow.
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Two 50 foot tall radio towers are 3000 feet apart. Find the angle of depression from the top of one tower to the base of the other.
Answer:
Explanation:
The diagram representing the two towers is given below:
Use the table to answer the question. Number of cases ordered Number of rolls of paper towels 1 12 3 36 5 60 10 120 A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair
Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls. 1:12 ratio does the proportionality constant appear at in the data table.
Given that,
There is a table.
Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls.
We have to find what ratio does the proportionality constant appear at in the data table.
The table is
Number of cases ordered | Number of rolls of paper towels
1 | 12
3 | 36
5 | 60
10 | 120
Therefore, 1:12 ratio does the proportionality constant appear at in the data table.
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Remington purchased a new cell phone for $350 and added an annual warranty plan that cost him $35 per year. In what year will Remington's average annual cost of owning the phone be $122.50? Type your answer....
Answer:
3 years and 6 months
Step-by-step explanation:
35 × 3= 105 + 17 = 122
2.916 a month × 6 = 17. 496. And round to the nears while number = 17.50 = 105 + 17.50 = 122.5 or 122.50 zero fir place holder.
A graph of a linear function has a slope of -1/3 and contains the point (0, 2). Which of these represents the equation of this function?
slope intercept equation is represented below
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 2=-\frac{1}{3}(0)+b \\ b=2 \\ y=-\frac{1}{3}x+2 \end{gathered}[/tex]Find the error in the calculations below, if there is one:
Line (1): -5x/4-7/2<-3/8
Line (2): 10x + 28<-3
Line (3): 10x < - 31
Line (4): x < -31/10
Line (5):
The error occurs in the second line, the correct solution is x > -5/2.
What is inequality?The relation between two unequal expressions is defined as inequality.
Given inequality is -5x/4 - 7/2 < -3/8.
The solution of the inequality is:
-5x/4 - 7/2 < -3/8
10x + 28 > 3
10x > -25
x > -25/10
x > -5/2
Hence, the error occurs in the second line, the correct solution is x > -5/2.
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Jayden multiples -4yx 1/5y and gets an answer of -4/5y. How can you tell without multiplying that his answer is incorrect
Multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, -4y × 1/5y:
The answer to this multiplication is -4/5y.Which is a wrong answer.We can easily observe in the second term that the denominator is 5y and in the 1st term there is no denominator, so 1 will be represented as a denominator.And y will not be present.Hence, multiplication is not possible with so similar variables in the denominator, in the given situation.Theefore, multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.
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given circle K with diameter IJ and radius KG. GH is tangent to K at G. If GH =6 and KH =8, solve dor KG. Round your answer to the nearest tenth if necessary. If the answer cannot be determined click cannot be determined.
EXPLANATION:
We are given a circle K with radius KG. Note here that line KJ and line KG are both radii of the circle given.
Also we know that a line tangent to a circle at the point of intersecting with the radius forms a 90-degree angle with the radius.
We can now extract the following triangle from the diagram provided;
We now have a right triangle which we shall solve by use of the Pythagorean theorem;
[tex]a^2+b^2=c^2[/tex]Where we have c as the longest side (hypotenuse) and then a and b are the two other sides. Substituting into the equation above now gives us;
[tex]\begin{gathered} a^2+b^2=c^2 \\ KG^2+6^2=8^2 \\ KG^2+36=64 \end{gathered}[/tex]Subtract 36 from both sides;
[tex]\begin{gathered} KG^2+36-36=64-36 \\ KG^2=28 \end{gathered}[/tex]Take the square root of both sides;
[tex]\begin{gathered} \sqrt[]{KG^2}=\sqrt[]{28} \\ KG=5.2915 \end{gathered}[/tex]Rounded to the nearest tenth, the answer is;
ANSWER:
[tex]KG=5.3[/tex]