The equation for the line parallel to y=1/4x+1 that passes through the point (6,-2) is x-4y=14 as the slope for both lines are equal and using slope-point form of equation.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
What is Slope-Point form?The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Here,
The slope for the line will be 1/4 and the given points will be (6,-2) so the equation for the line is
y-y1=m(x-x1)
y+2=1/4(x-6)
4y+8=x-6
x-4y=14
Given that both lines have an equal slope and using the slope-point form of equation, the equation for the line parallel to y=1/4x+1 passing through the point (6,-2) is x-4y=14.
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What is the Process for performing the transformation on a coordinate plane using rigid transformations
Flipping and Stretching is the Process for performing the transformation on a coordinate plane using rigid transformations.
A rigid transformation of a geometric object preserves distance between each pair of points of the object. In other words, rigid transformations preserve the shape and size of an object. For example, a rigid transformation of a triangle preserves both the measure of the angles and the lengths of the sides of the triangle. Think of rigid transformations of a shape as being like taking a cardboard cutout of the shape. The shape can be moved around, rotated, and flipped from one side to the other, but the shape itself does not change.
There are rules associated with rigid transformations. A rigid transformation is some function F from a set X to itself such that F preserves the distances between two points. Let d(x ,y) be the distance between two points. Then, to write the definition in mathematical notation, if d(x ,y) = d(F(x),F(y)) for all points x and y, then F is a rigid transformation.
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a dog walks due east 180 feet at a corner after turning through an angle of 81.5 the dog walks 329 feet to the second corner. then the dog walked back to the starting point. what is the area of the triangle formed by his path
The area of the triangle formed by his path is mathematically given as
Area = 29284.886 ft^2
This is further explained below.
What is the area?Generally, the equation for the defining cosine rule is mathematically given as
[tex]b^2 = a^2 + c^2 - 2ac cos B[/tex]
where
b = side B of the triangle
a = side A of the triangle
c = side C of the triangle
Therefore
[tex]b^2 = 180^2 + 329^2 - 2(180 * 329)cos 81.5[/tex]
b^2 = 32400 + 108241 - 17506.55
b = 350.91 ft
We calculate the area of the triangle using heron's formula.
Area = [tex]\sqrt{(p(p - a)(p - b)(p - c))}[/tex]
b = side B of the triangle
a = side A of the triangle
c = side C of the triangle
p = path
Where
p = (a + b + c)/2
p= (180 + 350.91 + 329)/2
p= 429.955 ft
Area = [tex]\sqrt{(429.955(429.955 - 180)(429.955 - 350.91)(429.955 - 329)}[/tex]
Area = 29284.886 ft^2
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Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 into the form (x − p)2 = q?
[p and q are integers]
Step 1 x2 + 10x + 24 − 1 = 0 − 1
Step 2 x2 + 10x + 23 = −1
Step 3 (x + 5)2 = −1
Step 1 x2 + 10x + 24 − 2 = 0 − 2
Step 2 x2 + 10x + 22 = −2
Step 3 (x + 5)2 = −2
Step 1 x2 + 10x + 24 + 2 = 0 + 2
Step 2 x2 + 10x + 26 = 2
Step 3 (x + 5)2 = 2
Step 1 x2 + 10x + 24 + 1 = 0 + 1
Step 2 x2 + 10x + 25 = 1
Step 3 (x + 5)2 = 1
The correct steps to transform equation x² + 10x + 24 = 0 into the form (x - p)² = q are:
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
In this question, we have been given an equation x² + 10x + 24 = 0
We need to transform given equation x² + 10x + 24 = 0 into the form (x - p)² = q
x² + 10x + 24 = 0 .............(Given equation)
x² + 10x + 24 + 1 = 0 + 1 ............(Add 1 to each side)
x² + 10x + 25 = 1
x² + 2(5)x + 5² = 1
(x + 5)² = 1
Therefore, the correct steps to transform equation x² + 10x + 24 = 0 into the form (x - p)² = q are:
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
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Look at the image for the problem, also round to the nearest hundredth if necessary.
ANSWER
[tex]V=3052.08ft^3[/tex]EXPLANATION
We want to find the volume of the sphere.
The volume of a sphere is given as:
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]where r = radius of the sphere.
Therefore, we have that the volume of the sphere is:
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot9^3 \\ V=3052.08ft^3 \end{gathered}[/tex]That is the volume of the sphere.
in 1 year the water level of a lake changes by -3/8 inch
Answer:
-3÷8 or -0.375
Step-by-step explanation:
-3÷8÷1=-3÷8×1÷1=-24÷8=-3
steven had $5 that his mom gave him to buy lunch at school he spent $5 on his lunch. plot a point on the number line to show how much money steven has after he spent $5 on food
If Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, then he will have $0 remaining, as plotted on the number line in the reference attachment hereby.
As per the question statement, Steven had $5 that his mom gave him to buy lunch at school and he spent all of the $5 on his lunch.
We are required to plot a point on the number line to depict how many dollars Steven has left with himself after spending on his lunch.
To solve this question, we simply need to subtract the amount Steven spent for his lunch, from the amount, his mother gave him to spend on lunch, and then plot the result of the said subtraction on the number line to obtain our desired answer.
Since, Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, he has $(5 - 5) = $0 left with himself after spending on his lunch.
That is, we will have to plot 0 on the number line, which is shown in the reference attachment hereby.
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Use the equation below to find a, if b=3 and h=4
1.8 as decimal in it simplest form
Answer:
1.8 = 9
5
= 14
5
as a fraction
Which is a correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” when n = 4?
The correct expression is StartFraction n cubed Over 16 EndFraction minus 2 + 8.
The correct expression is 2 minus StartFraction n cubed Over 16 EndFraction + 8.
One of the steps to determining the value when n = 4 is 1 minus 2 + 8.
One of the steps to determining the value when n = 4 is 2 minus 1 + 8.
The value when n = 4 is 6.
The value when n = 4 is 7.
The value when n = 4 is 9.
The value when n = 4 is 10.
The correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” is "StartFraction n cubed Over 16 EndFraction minus 2 + 8"
The correct answer option is option a
The value of the expression when n = 4 is 10. option D
How to write algebraic expressionThe unknown number = nQuotient means divisionquotient of a number cubed and sixteen
= n³ / 16
two less than the quotient of a number cubed and sixteen
= (n³ / 16 - 2)
two less than the quotient of a number cubed and sixteen, increased by eight”
= (n³ / 16 - 2) + 8
If n = 4
(n³ / 16 - 2) + 8
= (4³ / 16 - 2) + 8
= (64/16 - 2) + 8
= (4 - 2) + 8
= 2 + 8
= 10
In conclusion, the expression can be written as "StartFraction n cubed Over 16 EndFraction minus 2 + 8"
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Given the sequence:
5, 12, 19, 26, 33 ...
1. Determine the function that represents this sequence?
2. What is the 30th term of this sequence?
Answer:
Step-by-step explanation:
Work out the value of (6.31 x 10^5) + (2.6 × 10^1)
Give your answer in standard form.
Answer: 16,406,000
Step-by-step explanation:
First, multiply 6.31 and 2.6 to get 16.406. Then, add 10^5 and 10^1 to get 10^6.
It should now look like this, 16.406 x 10^6
The number has to be between 10 and 1 so you need to make it smaller by moving the decimal point over once to the left. It should now be 1.6406. But, you can't leave the exponent at 10^6 so, you need to make it bigger since you made the number smaller.
Your answer should now look like this, 1.6406 x 10^7
Since it needs to be in standard form, move the decimal point 7 times to the right since it is a positive number.
So, your answer is: 16,406,000
(-8,5); y= -4x+2 find the parallel equation
Answer: y=-4x-27
Step-by-step explanation:
[tex]y=mx+b[/tex]
Lines are parallel if their slopes are equal
[tex]y=-4x+2[/tex]
⇒ m=-4
⇒ y=-4x+b
A line passes through (-8.5)
⇒ x=-8 y=5
[tex]5=-4(-8)+b\\5=32+b\\5-32=32+b-32\\-27=b[/tex]
So, y=-4x-27
4/6 - 3/6p=16/6 what is p
20 points
Answer:
-4
Step-by-step explanation:
4/6 - 3/6p=16/6
Multiply each side by 6
4 - 3p = 16
Subtract 4 from both sides
-3p = 12
Divide both sides by -3
p = -4
Answer:
-4
Step-by-step explanation:
Solving for 'p':[tex]\sf \dfrac{4}{6}-\dfrac{3}{6}p=\dfrac{16}{6}[/tex]
To find the value of 'p', isolate 'p',
[tex]\sf \dfrac{-3}{6}p=\dfrac{16}{6}-\dfrac{4}{6}\\\\[/tex]
[tex]\sf = \dfrac{12}{6}[/tex]
= 2
[tex]\sf p = 2* \dfrac{6}{-3}\\\\ p = 2 *(-2)\\\\p = -4[/tex]
Find the distance between each pair of points round to nearest tenth if needed
Answer: 10) √85 units 12) 4 units
Step-by-step explanation:
[tex]\boxed {l=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}}[/tex]
10) (8,5) (-1,3)
[tex]x_1=8\ \ \ \ x_2=-1\ \ \ \ y_1=5\ \ \ \ \ y_2=3\\\\l=\sqrt{(-1-8)^2+(3-5)^2} \\\\l=\sqrt{(-9)^2+(-2)^2} \\\\l=\sqrt{81+4}\\\\l=\sqrt{85}\ units[/tex]
12) (-6,-10) (-2,-10)
[tex]x_1=-6\ \ \ \ \ x_2=-2\ \ \ \ \ y_1=-10\ \ \ \ y_2=-10\\\\l=\sqrt{(-2-(-6)^2+(-10-(-10))^2} \\\\l=\sqrt{(-2+6)^2+(-10+10)^2}\\\\l=\sqrt{4^2+0^2} \\\\l=\sqrt{4^2} \\\\l=4\ units[/tex]
Solve one sixth times quantity x plus 18 end quantity equals negative 5.
x = −48
x = −138
x = 12
x = 18
pls hurry
Answer:
(a) -48
Step-by-step explanation:
You want the solution to the equation 1/6(x +18) = -5.
2 Step equationThe first step to solving this can be to multiply both sides by 6, eliminating the fraction:
x +18 = -30
The second step can be to isolate the variable by subtracting 18 from both sides.
x = -48
The solution is x = -48.
__
Additional comment
Sometimes you may want to simplify the equation before you start the solution process. Here, you can also start by eliminating parentheses:
1/6x +3 = -5
Now, subtracting 3 gives ...
1/6x = -8
Finally, multiplying by 6, we have ...
x = -48
<95141404393>
brian sells wholesome computer parts at a comission rate of 4% .what is his income last month if his total sales were 82,968.00
Brian's income last month t is $3,318.92
How to calculate the income ?The commission rate for the computer parts is 4%
The total sales for last month is 82,968.00
Brian income last month can be calculated as follows
Total sales × commission percentage
4/100 × 82,968
= 0.04 × 82,968
= 3,318.92
Hence Brian income for last month is $3,318.92
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4. Given Segment AC such that point B is between A and C. If AC = 2x + 21, AB = x + 9, and BC = 3x - 4. a. What is the value of x b. How long is AC
On solving the given statement, the length of AC equals 37.
What is meant by line segment?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that lie inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
According to the given statement,
AC = 2x + 21
AB = x + 9
BC = 3x - 4
As B is the mid point of the segment AC,
⇒ AB + BC = AC
⇒ x + 9 + 3x - 4 = 2x + 21
⇒ 4x + 5 = 2x + 21
⇒ 2x = 16
⇒ x = 8
Length of AC = 2 (8) + 21
= 16 + 21
= 37
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Raise 7 to the 2nd power, then add the result to b
(7)^2 +
2nd power means squaring a number and since you need to do that first, it goes in brackets.
answer: 49 + b, or just 7^2 + b
explanation: 7^2 = 7x7, so it is equal to 49. then add b to 49
Find and interpret the slope. The number of cubic feet of watery In a reservoir x hours after the water starts flowing into the reservoir Is a linear function. The points (40,2,000) and (60, 3,000) are on the line of the function. The slope ls which means that the amount of water in the reservoir is increasing at a rate of cubic feet each hour.what is the y- intercept? what is the x- intercept?
The slope of a line (m) given two points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with (40,2,000) and (60, 3,000):
[tex]m=\frac{3000-2000}{60-40}=\frac{1000}{20}=50[/tex]The slope ls 50 cubic feet/hour which means that the amount of water in the reservoir is increasing at a rate of 50 cubic feet each hour.
Slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept. Replacing with m = 50 and point (40, 2000), e get:
200050()40
2000
2000 - 2000 = b
0 = b
Then the y-intercept is point (0, 0) which is also the x-intercept
The equation is:
y = 50x
When an integer is subtracted from 5 times the next consecutive odd integer,the difference is 22.find the value of the greater integer
The value of the greatest integers will be 5.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
'' An integer is subtracted from 5 times the next consecutive odd integer, the difference is 22''.
Now,
Write the mathematical expression for an algebraic expression as;
Let an integer = 2x + 1
Then, The next consecutive odd integer = 2x + 3
So, We can formulate;
5 (2x + 3) - (2x + 1) = 22
Solve for x as;
5 (2x + 3) - (2x + 1) = 22
10x + 15 - 2x - 1 = 22
8x + 14 = 22
Subtract 14 both sides, we get;
8x + 14 - 14 = 22 - 14
8x = 8
Divide by 8,
x = 8/8
x = 1
Since, The greatest integers = 2x + 3
Substitute x = 1, we get;
The greatest integers = 2x + 3
The greatest integers = 2 × 1 + 3
The greatest integers = 2 + 3
The greatest integers = 5
Therefore, The value of the greatest integers will be 5.
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True or false? If x>0, then x² > x.
Answer:
False
Step-by-step explanation:
It is false when x=1 because
[tex]1^{2} =1[/tex]
Omar has been training for the Candlewood Footrace. The first week he trained, he ran 7 days and took the same two routes each day: 3 miles around the track before work and a longer route through his neighborhood after work. By the end of the week, Omar had run a total of 63 miles.
Which equation can you use to find how many miles, x, Omar ran each day after work?
The equation that can be use to find the how many miles, x, Omar ran each day after work is x = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days after work
The total number of days he run = 7 days
Total distance he ran in one week = 63 miles
The distance he run before the work = 3 miles
The total distance he run before the work in one week= 7×3
= 21 miles
The total distance he run after the work = 63 - 21
= 42 miles
The equation that can use to find how many mile x, Omar ran each day after work = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7
Substitute the values in the equation
= 42/7
= 6 miles
Hence, The equation that can be use to find the how many miles, x, Omar ran each day after work is x = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days after work
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Passes through (9, 0) and (0, -3).
do you mind explaining with the answer so that i’ll understand it and be able to continue without being confused? thank you! :)
Answer: y = (1/3)x - 3
Step-by-step explanation:
It passes through -3 at 0, so we know the y = mx + b form will include -3
Next, we want to find the slope:
Change in y = 0 - -3 = 3
Change in x = 9 - 0 = 9
Change in y / Change in x = slope
3/9 = 1/3
micah is 111 of 282828 students in a class. micah's teacher is going to randomly select 333 students from their class to visit a classroom of younger students. what is the probability micah is included in the group of students chosen?
0.71% is the probability micah is included in the group of students chosen.
Describe probability using an example?
By dividing the number of favorable outcomes by the total number of possible outcomes, probability—the likelihood that an event will occur—is determined.The simplest example is a coin flip. When you flip a coin there are only two possible outcomes, the result is either heads or tails.the probability micah is included in the group of students chosen =
3/28 = 10.71%
The probability of her getting picked is unlikely.
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The complete question is -
Micah is 1 of 28 students in a class. Micah's teacher is going to randomly select 3 students from their class to visit a classroom of younger students. What is the probability Micah is included in the group of students chosen?
Given the function f(x) = 3x + 1 and the linear function g(x), which function has a greater slope?
The function that has the greater slope is the function g(x) that is represented by the graph.
How to Determine the Slope of a Function?The slope (m) of a function using two points on a graph can be calculated as:
Slope of the line (m) = change in y/change in x
If we are given the equation of the line using function notation as .f(x) = mx + b, the slope of the function is represented in the equation as "m". The value of "m" is the slope of the function given.
Given the function, .f(x) = 3x + 1, the value that represents "m" which is 3. Therefore, the slope of the function .f(x) = 3x + 1 is: 3.
Find the slope of the function of the graph using two points on the line, say (2, 3) and (3, 7):
Slope of the function (m) = change in y / change in x = (7 - 3)/(3 - 2)
Slope of the function (m) = 4/1
Slope of the function (m) = 4
The larger the value of the slope, the greater the slope of the function.
Therefore, the function g(x) that is represented by the graph has a greater slope.
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Answer: B
Step-by-step explanation:
Simple
If f (x) = 4x² + 3x - 5, then f(x+h)-f(x)/ h is equal to which of the following?
Answer:
Option 3
Step-by-step explanation:
[tex]f(x)=4x^2 + 3x-5 \\ \\ f(x+h)=4(x+h)^2+3(x+h)-5 \\ \\ =4(x^2+2xh+h^2)+3x+3h-5 \\ \\ f(x+h)-f(x)=4(x^2+ 2xh+h^2)+3(x+h)-5-(4x^2+3x-5) \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{4(x^2+ 2xh+h^2)+3(x+h)-5-(4x^2+3x-5)}{h}[/tex]
C
A
O 49°
50°
B
If mBD = 23°, and mZBED=16°, what is mï?
27.5°
55°
D
DE
The arc angle AC is measured as 55 degrees.
How to find arc angle?If two secant intersect in the exterior of a circle, then the measure of the angle formed is half the positive difference of the arcs intercepted.
Therefore, the secants intersect outside the circle at point E.
The arc angle AC can be found as follows:
Therefore,
m∠BED = 1 / 2 (arc angle AC - arc angle BD)
arc angle AC = x
arc angle BD = 23 degrees.
m∠BED = 16 degrees.
m∠BED = 1 / 2 (arc angle AC - arc angle BD)
16 = 1 / 2 (x - 23)
16 = 1 / 2x - 23 / 2
16 + 11.5 = 0.5x
27.5 = 0.5x
x = 27.5 / 0.5
x = 55 degrees.
Therefore,
arc angle AC = 55 degrees.
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Simplify 3(2x-5) - (1-3x)
6x-15 - 1 - 3x
6x - 16
Why is this wrong
Answer:
6X-15-1-3X=3X-16
6-3=3
Find n(A) when
A = {14, 16, 18, 20, 22, 24}
n(A) is 6 when A = {14, 16, 18, 20, 22, 24}
What is set?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things. Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
Given Data
A = {14, 16, 18, 20, 22, 24}
We are aware that the cardinality, which is represented by the letter n, is the number of items in any set A.
n(A) = number of elements in set
n(A) = 6
n(A) is 6
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Is 9 11/13 bigger than 9.79
[tex]9\frac{11}{13}[/tex] is bigger than 9.79
The mixed fraction = [tex]9\frac{11}{13}[/tex]
The mixed fraction is the fraction that expressed with its quotient and remainder. The mixed fraction is the combination of a whole number and a simple fraction
Simple fraction is the fraction that has whole numbers as the numerator and denominator.
The decimal number is a number that has whole and the fractional parts are separated by a decimal point
First we have to convert the mixed fraction into simple fraction
[tex]9\frac{11}{13}[/tex] = 128/13
Next we have to convert the simple fraction into decimal form
Divide 128 by 13
The result will be
128/13 = 9.85
Hence, [tex]9\frac{11}{13}[/tex] is bigger than 9.79
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