The equation of the line r is y = ₋(10/9)x ₊ 7.
Given, parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope intercept form
equation of line q is y = ₋10/9x ₊ 2
it's already in slope intercept form.
hence slope is:
m = (₋10/9) from the above the equation.
we know that the second line will also have a slope of ₋10/9 and we are given the point (9 , ₋3). We can setup an equation in slope intercept form and use these values to solve for the y inetrcept.
y = mx ₊ b
₋3 = ₋10/9 (9) ₊ b
₋3 = ₋10 ₊ b
b = 7
plug the y intercept back into the equation to get our final answer.
y = ₋(10/9)x ₊ 7
hence we get the equation of the line r as y = ₋(10/9)x ₊ 7.
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Find the seventh term of each geometric sequence. 100,20,4, . . . . . . .
The seventh term of the given geometric sequence is: [tex]\frac{4}{625}[/tex].
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Given: 100, 20, 4, ....
Here, a₁ = 100, r = [tex]\frac{100}{20}=\frac{20}{4}=\frac{1}{5}[/tex], for the given geometric progression.
In the formula: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 7, a₇ = 100 ([tex](\frac{1}{5})^{7-1}[/tex]
=> a₇ = 100 [tex](\frac{1}{5})^6[/tex]
=> a₇ = 4([tex]\frac{1}{625}[/tex])
Hence, The seventh term of the given geometric sequence is: [tex]\frac{4}{625}[/tex].
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Look at the picture and help me figure how many planes are in the figure.
Answer: C
Step-by-step explanation:
6 planes
Answer: C, 6)
Step-by-step explanation: Area of square = a2 Square units, where a is the side length of square.
Area of rectangle = l × b Square units, where l is the length, b is the breadth.
Area of circle = π × r2 Square units, where r is the radius of a circle.
Write an equation of each line in point-slope form.
(0,0) and (-4,-5)
The equation of the line in point-slope form, which passes through the pair of points located at (0 , 0) and (-4 , -5), is y + 5 = 5/4(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (0 , 0) and (-4 , -5)
m = (y2 - y1)/(x2 - x1)
m = (-5 - 0)/(-4 - 0)
m = -5/-4
m = 5/4
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = 5/4 and (x1 , y1) = (-4 , -5)
(y - -5) = 5/4(x - -4)
y + 5 = 5/4(x + 4)
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Please help. im in need
3*3=9
4*3=12
9*12=108 sq feet
“Twice a number minus 5 is 7”
Answer: the number would be 6
Step-by-step explanation:
6 x 2 = 12, 12 - 5 = 7, so the number is 6
Make a conjecture about the measure of an exterior angle and the sum of the measures of its nonadjacent interior angles.
Here we can conjecture that :
The measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles.
What is interior and exterior angle ?The exterior angle of any polygon is defined as the angle which is at the outside boundaries of that polygon. whereas, the interior angle is defined as the angle which is inside the polygon. In the other words if the polygon has the point within the angle it is in the interior of the angle , but if the point is outside then is it said to be in the exterior of the angle.
What is Non adjacent interior angle ?Non adjacent angles are those angles which are not adjacent to each other. The non adjacent angles follow one of the properties which are listed below:
They do not share a common vertex or common side.They can share a side, but not share the common vertex.They share a common vertex, but not share the common side.In the given question,
taking a example say a triangle ABC with ∠A=64, ∠B = 45 and an external angle x to the side AC.
as sum of angles equal to 180
thus, ∠A + ∠B + ∠C = 180
64 + 45 + ∠C = 180
∠C = 180-109 = 71
now as x is external to ∠C,
therefore x = 180 - ∠C = 180 - 71
x = 109 = ∠A + ∠B
Hence we can make the conjecture that, the measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles.
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1. Solve the equation:
6(x + 1) = 3x - 14
Answer: x=-20/3
Step-by-step explanation:
6(x + 1) = 3x - 14
6x+6 = 3x - 14
6x-3x+6 = 3x-3x - 14
3x+6 = -14
3x+6-6=-6-14
3x=-20
x=-20/3
Look at the pattern shown.
144,72,36,. . .
a. What is a rule for the pattern?
Answer:
I hope it's helpful.........
(0,7) (1,5) (-1,13)
How to find the quadratic equation given only these points (standard form)
Answer:
(x - 1)^2 =1/2 ( y - 5) or 2x^2 - 4x - y + 7 = 0
Step-by-step explanation:
(x - 1)^2 =1/2 ( y - 5)
or
x^2 - 2x + 1 = y/2 - 5/2
2x^2 - 4x + 2 - y + 5 = 0
2x^2 - 4x - y + 7 = 0
Summit (1,5) = (h,k)
4p = 2
p = 1/2
(x - h)^2 = 1/2(y - k)
Determine the slope of the line that contains the given points.
E(6,3), F(-6,3)
The slope of the line that contains the given points E(6,3) and, F(-6,3) is 0.
It is given in the question that the line contains the points E(6,3) and F(-6,3).
We know that:-
The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-
m = (d-b)/(c-a)
Here, we have
m = slope of the line
(a,b) = (6,3)
(c,d) = (-6,3)
Hence, putting the values of (a,b) and (c,d) , we get
Slope of the line that contains the given points E(6,3) and, F(-6,3) is given by:-
(3-3)/(-6-6) = 0/-12= 0
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Two angles form a linear pair. The measure of one angle is 3.5 times the measure of the other angle. Find the measure of each angle.
Given that the two angles form a linear pair, the measure of each angle is 40° and 140°.
What is the measure of each angle?The sum of angles of a linear pair is always equal to 180°.
Given the data the data in the question;
Let x represent the measure of the first angle.
Measure of angle 1 = xMeasure of angle 2 = 3.5xSince the sum of angles of a linear pair is always equal to 180°.
m∠1 + m∠2 = 180
x + 3.5x = 180
Solve for x
4.5 = 180
x = 180/4.5
x = 40
Hence,
Measure of angle 1 = x = 40°
Measure of angle 2 = 3.5x = 3.5(40) = 140°
Given that the two angles form a linear pair, the measure of each angle is 40° and 140°.
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Bronson is creating a right triangular flower bed. If two of the sides of the flower bed are 7 feet long each, what is the length of the third side to the nearest foot?
The length of the third side of the right triangular flower bed is 10 feet.
A right-angled triangle is a triangle with one of its interior angles equal to 90°. The side opposite to the right angle is the largest side and is referred to as the hypotenuse. Hypotenuse is always greater than any of the other two sides.
If two of the sides of the flower bed are 7 feet long each, then these are the sides adjacent to the right angle. We are to find the length of the third side, which is the hypotenuse, using the Pythagorean theorem.
Pythagorean Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two other sides.
c^2 = a^2 + b^2
where a and b are the adjacent sides to the right angle
c is the hypotenuse
c^2 = 7^2 + 7^2
c^2 = 49 + 49
c^2 = 94
c = 9.899
Hence, he length of the third side of the right-angled triangular flower bed is 10 feet.
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Write a recursive definition for each sequence. -2,7,16,25, . . . . .
The recursive formula for the arithmetic sequence [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
A recursive formula is a sequence in which terms are defined using one or more previous terms which are given. If we know the nth term of an arithmetic sequence and you know a common difference, d, we can find the (n+1)th term using the recursive formula.
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
The sequence -2, 7, 16, 25,.... is in arithmetic sequence and its common difference is 7 - (-2) = (16-7)= 9 .
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The equation for the change of position of a train starting at x = 0 m is given by . the dimensions of b are what?
It involves determining the fundamental quantities and units of measurement and tracking these dimensions while computations or comparisons are made.
What is meant by Dimensional Analysis?Dimensional analysis is the study of the relationships between various physical quantities in engineering and science. It involves determining the fundamental quantities and units of measurement and tracking these dimensions while computations or comparisons are made. Dimensional Analysis is a problem-solving technique that makes use of the fact that any number or statement may be multiplied by one without changing its value. It is also known as the Factor-Label Method or the Unit Factor Method.Now, in that equation above, b represents the velocity of the motion. Now, the formula for velocity is;
Velocity = Distance/Time
Now, distance is also named Length and represented by L in basic parameters units while Time is represented by T.
Thus, the dimensions of b are; L/T or expressed as LT⁻¹.
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An airplane on a long-distance flight flew the first 1295 miles of it's journey on 3 hours and 33 minutes. After that, the wind changed, and it took the plane 1 hour and 47 minutes to cover the remaining 738 miles. What was the plane's average speed during the flight?
Round to the nearest tenth
The plane's average speed during the flight is 381.43 miles per hour.
What is the average speed?The average speed is the quotient of the total distance covered during the flight divided by the total time used.
The Average Speed is the scalar quantity that shows the rate of change in displacement from one point to another.
Data and Calculations:The distance for the first miles = 1,295 miles
The time it took the plane to cover the distance = 3 hours 33 minutes
The distance for the last lap = 738 miles
The time it took the plane to cover the last distance = 1 hour 47 minutes
The total distance covered for the journey = 2,033 miles (1,295 + 738)
The total time for the journey = 5 hours 20 minutes or 5.33 hours
Average Speed = 2,033/5.33
= 381.43 miles per hour
Thus, the plane's average speed during the flight is 381.43 miles per hour.
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The sum of k and 8 __ k + 8 ___
The algebraic expression of the mathematical statement is given as "The sum of k and 8" is k + 8
How to represent the mathematical statement as an algebraic expression?The mathematical statement is given as:
The sum of k and 8
In algebraic expression, "Sum" means +
This means that, the interpretation of the question is that we add k and 8
So, we have the following algebraic representation:
The sum of k and 8 ⇒ k + 8
Remove the mathematical statement in the above algebraic representation
i.e. k + 8
Hence, the algebraic expression of the mathematical statement is given as "The sum of k and 8" is k + 8
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In+terms+of+resale+value,+is+remodeling+a+kitchen+worth+the+cost?+at+the+5%+significance+level,+what+can+you+conclude?
The resale value is not significantly higher than the cost of remodeling a kitchen based on the computed p-value of 0.42 and 0.21.
What is the null hypothesis?Any variation between the selected attributes that you observe in a collection of data is thought to be the result of chance, according to the null hypothesis.For instance, any discrepancy between the average profits in the data and zero is caused by chance if the expected earnings for the gambling game are actually equal to zero.An assertion that there is no correlation between two population measures is referred to as a null hypothesis.To prepare the ground for additional experimentation or study that explains the position of interest, researchers reject or refute the null hypothesis.Both the p-values of 0.42 and 0.21 are greater than the level of significance of 0.05. Hence, we fail to reject the null hypothesis. So, the resale value is not significantly higher than the cost of remodeling a kitchen based on the computed p-value of 0.42 and 0.21.
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Solve each equation. Check each solution. 2/x = x/2
2 and -2 both are the solution of the equation x/2 = 2/x.
According to the given question.
We have an equation 2/x = x/2.
As we know that, as we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.
Therefore, the solution of the equation 2/x = x/2 is given by
2/x = x/2
⇒ 2 = (x/2)x (multiplying both the sides by x)
⇒ 2 = x^2/2
⇒ 2(2) = x^2 (multiplying by 2 both the sides by 2)
⇒ 4 = x^2
⇒ x^2 = 4
⇒ x = √4
⇒ x = ±2
⇒ x = 2 or -2
Now we will check 2 is the solution of the given equation or not.
Therefore,
LHS = 2/2 = 1
RHS = 2/2 = 1
Here, LHS = RHS. Therefore, 2 is the solution of the given equation.
Similarly, for -2
LHS = 2/-2 = -1
RHS = -2/2 = -1
Here. RHS = LHS. Therefore, -2 is also the solution of the given equation.
Hence, 2 and -2 both are the solution of the equation x/2 = 2/x.
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How is -89 represented using 8-bit two's compliment? (the answer should be 8 binary digits)
-89 can be represented by using 8-bit two's compliment as 10100111.
What is binary encoding?Binary encoding can be defined as a standard technique that is designed and developed to convert data in plain text (source alphabets) to a form that is easily used by different operating systems (OS), especially through the use of a binary digit (bit) or two-symbol system.
In Computer programming, two's complement of base-10 is generally easier to implement because it has a single representation of 0 only.
How to convert a binary (base-10) to decimal (base-2)?First of all, we would determine the positive version of -89, which is 89:
2 | 89
2 | 44 R 1
2 | 22 R 0
2 | 11 R 0
2 | 5 R 1
2 | 2 R 1
2 | 1 R 0
2 | 0 R 1
Next, you would read the decimal number (base-2) upward and this gives:
89₂ = 01011001.
For the negative integer number representation on 8-bits, we would replace all the 0s with 1s and the 1s with 0s as follows:
01011001 = 10100110
For the 8-bit two's complement, we would add 1 to the above number:
-89 = 10100110 + 1
-89 = 10100111.
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Find the measure of the missing angle
Answer: 55 degrees
Step-by-step explanation:
a+90+35=180 ==> a straight line measures 180 degrees and the angles a, a right angle, and 35 lie on that line. A 180 degree angle is called a straight angle. Also, if there is a tiny box in between an angle, that means that the angle is a right angle.
a+125=180
a+125-125=180-125
a=180-125
a=55 degrees
find the vertical asymptotes if any. f(x)= 1/x^2
Answer:
x = 0
Step-by-step explanation:
Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function
For f(x) set the denominator = 0 and solve for x
For [tex]\frac{1}{x^2}[/tex]
set x² = 0
x = √0 = 0 which is the vertical asymptote
Answer:
x = 0
Step-by-step explanation:
The Vertical asymptotes are vertical lines which correspond to zeroes of denominators.
For f(x) set the denominator = 0 and solve for x
For \fract {1}{x^2}
you set x² = 0
x = √0 = 0 which is the vertical asymptote
Which describes the pilot’s distance in section i? zero constant decreasing increasing
The pilot's distance is increasing.
In the graph, we can see distance on y axis and time on x axis. It is clearly visible that at 2 minutes, the distance covered is 0.4 miles. Further, at 4 minutes, the distance covered increases to 0.8 miles. At 6 minutes, the distance covered again increases by 0.4 miles and is 1.2 miles. At 8 minutes, the distance covered in 1.6 miles, which again increases by 0.4.
Now, it is evident that distance is increasing.
We can further calculate the speed using given information -
Speed = distance/time
Total distance = 1.6 - 0.0
Total distance = 1.6 miles
Total time = 8 - 0
Total time = 8 minutes
Speed = 1.6/8
Speed = 0.2 miles per minute.
Hence, the distance of pilot is increasing at constant rate or speed of 0.2 miles per minute.
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The complete question and figure is attached -
The graph below represents the distance a pilot is from the home airport during a period of time. A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0.0, 0.4, 0.8, 1.2, 1.6. Which describes the pilot’s distance in section I? zero constant decreasing increasing
A car is traveling at a speed of 100 kilometers/hour. How many hours will it take to cover a distance of 750 kilometers?
Answer:
7.5 hours
Step-by-step explanation:
Answer:
7.5 hours
Step-by-step explanation:
A car is traveling at 100 km/hr. How many hours will it take to cover a distance of 750 km? 750km ÷ 100km/hr = 7.5 hrs.
(Give brainlist?)
Write 2.702x10^-7 as an ordinary number
Answer:
0.0000002702
Step-by-step explanation:
2.702 * 10^-7
Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. 49,64,81,100,121, ......
Answer:
The next two terms is 144 and 169
Simplify these ratios: a 24:36 b 12:2
c 16:4 d 18:3
Answer: 2:3, 6:1, 4:1, 6:1
Step-by-step explanation:
The first step is by finding the GCF. For 24:36 the GCF is 12. Once you divide you get 2:3. For 12:2 the GFC is 2. For 16:4 it is 4 and you get 4:1 and finally 18:3 the GCF is 3 and you get 6:1.
For f(x)=-4 x+1 , what is the output for the given input?
b. 0
f (0) = 1 is the output for the given input .
What is linear function ?
A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).f(x)= -4 x+1
Put x = 0 ⇒ - 4 × 0 + 1
⇒ 0 + 1
⇒ 1
Therefore f (0) = 1
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x-y=4 et xy=21 calculer x^3-y^3
Answer:
316 or -316.
Step-by-step explanation:
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
= 4(x^2 + y^2 + 21)
x - y = 4
xy = 21
Substitute x = 4 + y in the last equation
(4 + y) y = 21
y^2 + 4y - 21 = 0
(y + 7)(y - 3) = 0
y = 3, -7.
So, x = 7, - 3.
So, x and y are 7 and 3 or -7 and -3.
But x^2 + y^2 = 9 + 49 = 58 whichever is true,
So, x^3 - y^3
= 4(x^2 + y^2 + 21)
= 4 (58 + 21)
= 316,
If x = -3 and y = -7 , then the answer is
-316.
14 < -2a + 6-2a
What is the inequality
Answer:
a < -2.
Step-by-step explanation:
14 < -2a + 6-2a
14 < -4a + 6
14 - 6 < -4a
-4a > 8
Divide both sides by -4:
a < -2.
Note that the inequality flips because we are dividing by a negative number.
Suppose the flight leaves 30 minutes early. What function represents this transformation?
The function that represents the Transformation of the graph is F(X+1/2).
Different non-vertical lines have different slopes and/or y-intercepts. They are graphs of various linear functions. If there are two such lines, one can be considered a transformation of the other. There is a group of functions called the family, each function being a transformation of a special function called a parent. Linear functions form a series of functions. All linear functions are transformations of the function y = x. The function y = x is an upper linear function. Each family role is a transformation of a parent's role. The conversion type is translation. A translation moves the graph of the parent function horizontally, vertically, or both without changing shape or orientation. So, the function that represents this transformation is F(X+1/2).
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