The linear equation that passes through the two given points is:
y = (-1/4)*x - 2/4
Which is the equation of the line?A general linear equation is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
m = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, -1/4) and (1, -3/4)
Then the slope is:
m = (-3/4 + 1/4)/(1 + 1)
m = (-2/4)/2 = -2/8 = -1/4
the line is:
y = (-1/4)*x + b
To find the value of v we can replace the point (1, -3/4) so we get:
-3/4 = (-1/4)*1 + b
-3/4 + 1/4 = b
-2/4 = b
The linear equation is:
y = (-1/4)*x - 2/4
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the population of white-tailed deer is growing rapidly in the united states. in 1905 the population was approximately 5x10^5 and in 2000 the population was approximately 2x10^7 how many times larger was the population of white tailed deer in 2000 than it was in 1905
Answer:
40
Step-by-step explanation:
2 x 10⁷/5 x 10⁵ = 2/5 x 10^5-7 = 2/5 x 10² = 2 x 100/5
There were 40 times more white-tailed deer in 2000 than in 1905
What is the solution to -4(8-3x) ≥ 6x - 8?
O
4
x²--1/32
O x≤
xs--1/72
Ox≥4
Ox≤4
Answer:
x ≥ 4
Step-by-step explanation:
-4 ( 8 - 3x ) ≥ 6x - 8
First, solve the brackets.
- 32 + 12x ≥ 6x - 8
Subtract 6x from both sides.
- 32 + 12x - 6x ≥ - 8
- 32 + 6x ≥ - 8
Add 32 to both sides.
6x ≥ - 8 + 32
6x ≥ 24
Divide 6 by both sides.
x ≥ 4
SOMEONE HELP GEOMETRY THXX
The lines p and q are parallel.
What are alternate exterior angles?Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines, but on opposite sides of the transversal.
Given a figure,
Since, ∠ 1 ≅ ∠ 5 and they are alternate exterior angles, then we can conclude that p║q by alternate exterior angles theorem.
Hence, The lines p and q are parallel.
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Find the angle between each of these pairs of vectors:
A = -2.00 i + 6.00 j and B = 2.00 i - 3.00 j
The angle of pairs = 170.
The characteristics of the scalar product allows to find the angle between the two vectors is:The scalar product is the product between two vectors whose result is a scalar.
A . B = |A| |B| cos θWhere A and B are the vectors, |A| and |B| are the modules of the vectors and θ at the angle between them.
The vector is given in Cartesian coordinates and the unit vectors in these coordinates are perpendicular.
i.i = j.j = 1 i.j = 0 A . B = (4 i - 4j). * -5 i + 7j) A . B = - 4 5 - 4 7 A. B = -48We look for the modulus of each vector.
|A| = 4 √2 |B| = 8.60We substitute. -48 = 4√2 8.60 cos θ -48 = 48.66 cos θ θ = cos⁻¹ θ = 170ºIn conclusion using the dot product we can find the angle between the two vectors is:
Hence, the angle θ = 170º
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A cube has a volume of 125 cubic inches. What us the length of each adge? Enter your answer in the box
5 inches
I just randomly guessed
The Americans with Disabilities Act (ADA) gives businesses and cities requirements, rules, for making sure that people in wheelchairs and scooters can use slopes. The ADA requires a 1:12 slope for wheelchairs and scooters. (This means that for every one unit of vertical distance, the ramp must have 12 units of horizontal distance.) Mrs. Giles has a small business. She wants to make sure she builds the entrance to her building correctly. The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store. According to the ADA rules, how long (horizontal distance) does the ramp need to be, in feet?
The length of the horizontal distance of the ramp if The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store is 28 feet.
What is ratio?Comparing one quantity to another is what it is. For instance, the weight ratio is 1:3 if you weigh 30 kg and your father weighs 90 kg.
Given:
The ratio of vertical and horizontal distance = 1:12,
The vertical distance of Mrs. Giles's business = 28 inches,
If for every one unit of vertical distance, the ramp must have 12 units of horizontal distance, so or 28 inches vertical distance the horizontal distance would be = 28 × 12 = 336 inches,
([tex]1 feet = 12inches[/tex])
= 336 / 12 = 28 feet
Therefore, The length of the horizontal distance of the ramp if The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store is 28 feet.
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26³ +5=2(3)³ +5 7
please help me solve this lol
Answer:
(simplify 26³)
26³ = 17,576
= 17,576 + 5 = 3³+57
(simplify 3³)
3³ = 27
= 17,581 = 27+57
= 17,581 ≠ 84
Differentiate the function with respect to x.
The differentiation of the given function is [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex].
In the given question we have to differentiate the given function with respect to x.
The given function is f(x)= [tex]tan(x^4)\cdot(3x^3+2)[/tex].
We have to differentiate the given function so we differentiate using the Product Rule.
The Product Rule of Differentiation is
d/dx[h(x)g(x)]=h(x) d/dx g(x)+g(x) d/dx h(x)
In the given function the value of
h(x) = [tex]tan(x^4)[/tex] and g(x) = [tex](3x^3+2)[/tex]
So;
f'(x)= [tex]tan(x^4)[/tex]d/dx [tex](3x^3+2)[/tex] + [tex](3x^3+2)[/tex] d/dx [tex]tan(x^4)[/tex]............(1)
We firstly find the value of d/dx [tex](3x^3+2)[/tex] and d/dx [tex]tan(x^4)[/tex].
We firstly find the value of d/dx [tex](3x^3+2)[/tex]
As we know that d/dx of x^n =nx^(n-1) and d/dx a=0
So;
d/dx [tex](3x^3+2)[/tex]= 3 d/dx [tex]x^3[/tex]+d/dx 2
d/dx [tex](3x^3+2)[/tex]=3(3[tex]x^2[/tex])+0
d/dx [tex](3x^3+2)[/tex]=9[tex]x^2[/tex]
Now finding the value of d/dx tan([tex]x^4[/tex])
d/dx [tex]tan(x^4)[/tex] = d/dx [tex]tan(x^4)[/tex] d/dx [tex]x^4[/tex]
d/dx [tex]tan(x^4)[/tex]= [tex]sec^2(x^4)\cdot(4x^3)[/tex]
d/dx [tex]tan(x^4)[/tex]= [tex]4x^3sec^2(x^4)[/tex]
Now putting the values of differentiation in equation 1
f'(x)= [tex]tan(x^4)\cdot9x^2[/tex] + [tex](3x^3+2)\cdot4x^3sec^2(x^4)[/tex]
f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]3x^3\cdot4x^3sec^2(x^4)+2\cdot4x^3sec^2(x^4)[/tex]
Simplifying
f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{3+3}sec^2(x^4)+8x^3sec^2(x^4)[/tex]
f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex]
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Spot Robin says, "I can find 6 x 9 by
multiplying 4 x 9 and doubling it." Does her statement
make sense? Justify your answer.
Answer:
No
Step-by-step explanation:
It does not make sense becuse 6x9=54
And 4x9(2)=72 so it would make no sense
If you borrow $28 000 to buy a car and repay it over 5 years with a fixed interest rate of 9.8% p.a., how much simple interest will you pay?
Answer:
$13,720.00
Step-by-step explanation:
Calculate simple interest using the equation A = P(1 + rt)
Convert 9.8% to a decimal for ease (0.098)Solve: A = 28000(1 + (0.098 × 5)) = $41720.00A = $41,720.00
Interest = total repayment - original cost
$41,720.00 - 28,000 = $13,720.00
A car traveled 120 miles in 2.5 hours the line represents that relationship between the distance travels and the time it took. The point 1,48 is on the line.
The ratio of boys to girls in a class is 2:3 if there are 48 pupils in the class.How many boy and girls are there?
tysm po
The graph of g(x) is the graph of f(x)=x−2reflected across the y-axis. Which equation describes function g?
The required equation of g(x) for reflection of f(x)=x-2 across the y-axis is g(x)=-x-2.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
Given that,
f(x)=x-2
To find the required equation for g(x) that is reflected across the y-axis, Use reflection property,
According to reflection property,
Reflection Across the y-axis, the x change in -x and the remaining part of the equation remains same.
The equation of f(x) changes in g(x) as g(x)=-x-2,
So, the equation of g(x)=-x-2 .
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The length of the segment is _____centimeters
The scale is __cm : __mm.
Answer:
I'm assuming it's just a conversion of mm into cm?? in that case it will be 2.4 cm
(1,y) and (x,−3).
6x+3y=15
The values of x and y are 4 and 3 respectively, this forms an ordered pair of (1,3) and (4,-3).
What are the the values of x and y?Given the equation and ordered pair the question;
6x + 3y = 15Point: ( 1,y)Point; (x,−3).To determine, the y-value, plug the x-value into the equation and solve for y.
6x + 3y = 15
Plug in x = 1
6(1) + 3y = 15
6 + 3y = 15
3y = 15 - 6
3y = 9
y = 9/3
y = 3
To determine, the x-value, plug the y-value into the equation and solve for x.
6x + 3y = 15
Plug in y = -3
6x + 3( -3 ) = 15
6x - 9 = 15
6x = 15 + 9
6x = 24
x = 24/6
x = 4
Therefore, the ordered pair are (1,3) and (4,−3).
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(ASAP Please)
Find the area of the sector. Use 3.14 for the value of pi. Round your answer to the nearest tenth.
A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.
The area of a circle is given as:
Area = πr²
The total sector of a circle is 360°
The area of the sector of 270° is 37.68 square meters.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.
The area of a circle is given as:
Area = πr²
We have,
The radius of the circle = 4 m
The total sector of a circle is 360°
The area of the sector with 270°.
= (270°/360°) x πr²
= 0.75 x πr²
= 0.75 x 3.14 x 4²
= 37.68
= 37.7 square meters
Thus,
The area of the sector of 270° is 37.68 square meters.
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solve the system of equations by the addition method
x-y= -2
x+y=4
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is }. (Type an ordered pair.)
B. There are infinitely many solutions. The solution set is {(x,y)}.
(Type an equation.)
C. There is no solution. The solution set is Ø.
Answer:
(x, y) = (1, 3)
Step-by-step explanation:
You want to solve the system of equations x-y= -2; x+y=4 by the addition method.
Addition methodThe addition method seeks to eliminate one of the variables by adding the equations with appropriate multipliers so that one of the coefficients becomes zero.
Here, we observe that the coefficient of y in one equation is the opposite of that in the other equation. This means adding the two equations will cancel the y-terms:
(x -y) +(x +y) = (-2) +(4)
2x = 2 . . . . . . . . . . . . . . . . simplify; y-term is eliminated
x = 1 . . . . . . divide by 2
1 +y = 4 . . . . . . . substitute for x in the second equation
y = 3 . . . . . . . . . subtract 1
The solution is (x, y) = (1, 3).
What is the product of the complex numbers below? 7-i / 3+i
Answer: 2-i
Step-by-step explanation:
multiply the fraction by 3-i/3-i
convert 7 yards per minute to feet per second. (3 feet=1 yard)
please help fast!! my life is in risk!
Answer:
The answer you are looking for is 0.35 foot per second.
Step-by-step explanation:
Formula = divide the speed by 20
(Or in this case 7 divided by 20).
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
The area of the rectangle shown is 44 m².
Work out the missing length x.
Answer:
x = 12 m
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × width
here A = 44 , then
x × 3 [tex]\frac{3}{4}[/tex] = 44 ( change mixed number to improper fraction )
x × [tex]\frac{11}{3}[/tex] = 44 ( multiply both sides by 3 to clear the fraction )
11x = 132 ( divide both sides by 11 )
x = 12 m
A triangle has a base of 8 inches and a height of 12 inches. What is the area?
Helpful conversion fact: A=1/2b•h
96 inches
96 square inches
48 inches
48 square inches
Answer:
48 square inches
Step-by-step explanation:
A=1/2 bh
A=(1/2)(8)(12)
A=(4)(12)
A=48 square inches
you can also multiply 8 x 12 then divide by 1/2 or 2 which is still 48. either way is correct but since the formula is half of the base times height that is the step i followed. Also area is always whatever measurement used (in this case inches) squared.
how to interpret data from a frequency distribution
Answer:
The first column is usually for the categories of the data set and the second or third column is usually for the frequency of each category.
The number written on the right of each category is its frequency
Step-by-step explanation:
3. Plumbers deal with measurements in inches and common fractions of an inch, while surveyors use feet and decimal
fractions of a foot. Often one trade needs to interpret the measurements of the other.
(a) A drain has a run of 52 ft at a grade of 1/8 in./in. The high end of the drain has an elevation of 126.30 ft. What is the elevation at the low end?
(b) The elevation at one end of a lot is 84.12 ft, and the elevation at the other end is 94.67 ft. Express the difference in elevation in feet and inches and rounded to the nearest 1/8 in
The elevation at the lower end of a drain is 119.8 feet. For the second drain difference in feet will be 10.55 feet and in inches will be 126.6 inch.
What is elevation?The height above or below a fixed reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. A vertical surface is depicted in an elevation when viewed from a point perpendicular to the viewer's picture plane. You are looking at the front elevation, for instance, if you are standing directly in front of a building and viewing its front. The height between a point and a horizontal surface is known as HEIGHT. The height of a point above (or below) sea level is known as its ELEVATION.
Here,
a. The length of drain= 52 feet
the gradual decrease=0.125 ft
elevation at high end=126.30 feet
elevation at low end,
=126.3-(52*0.125)
=126.3-6.5
=119.8 feet
b. The elevation at one end=94.67 feet
The elevation at other end=84.12 feet
The difference in elevation,
=94.67-84.12
=10.55 feet
=10.55*12
=126.6 inches
The elevation of a drain's lower end is 119.8 feet. The second drain will differ by 10.55 feet in feet and 126.6 inches in inches.
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#3 a. Complete the table for f(x) = 2x
#3b Use the coordinate points from the table to graph f(x) = 2^x
The complete table of values of the function is
x | f(x)
0 | 1
1 | 2
2 | 4
3 | 8
The ordered pairs are (x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)
How to make a table of values for the following equation?The equation of the function is given as
f(x) = 2ˣ
On the incomplete table of values, we have the following x values
x = 0, 1, 2, 3
Next, we substitute x = 0, 1, 2, 3 in the equation f(x) = 2ˣ
So, we have:
f(0) = 2⁰ = 1
f(1) = 2¹ = 2
f(2) = 2² = 4
f(2) = 2³ = 8
So, the complete table is
x | f(x)
0 | 1
1 | 2
2 | 4
3 | 8
When represented as ordered pairs, we have
(x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)
See attachment for the graph
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Eva says you can use the conversion for 60 km into
miles to convert 600 km into miles. Use Eva's
method to convert 600 km into miles.
300
miles
After using conversion of measurements , the answer is
60 km = 37.28 miles and 600km = 372.83 miles.
What is conversion of measurements?
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet. We must convert between different units in order to have accuracy and prevent measurement confusion.
Here the given we need to convert them km into miles.
To convert km to miles we need to divide the value by 1.609 .
=> 60 km
=> 60/1.609
=> 37.28 miles.
Now ,
=> 600 km
=> 600/1.609
=> 372.83 miles.
Therefore after conversion of measurement answer is
60 km = 37.28 miles and 600km = 372.83 miles.
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AGES Pedro, Sebastian, and Manuel Martinez are each one year apart in age.
The sum of their ages is greater than the age of their father, who is 60.
a. Write an inequality to represent this situation, where x is the age of the youngest brother.
b. Solve the inequality.
c. How old can the oldest brother be? Explain your reasoning.
a) The inequality is
P + S + M > 60
b) The solution of the inequality is:
P > 19
Where P is Pedro's age.
c) The oldest brother has more than 21 years-
How to write the inequality?Let's define the variables:
p = Pedro's age.
S = Sebastian's ae
M = Manuel's age
We know that the sums of their ages is more than 60, then:
P + S + M > 60
This is the inequality.
b) We know that the brother are one year apart, then:
S = P + 1
M = P + 2
replacing that we get:
P + P + 1 + P + 2 > 60
3P + 3 > 60
3P > 60 - 3
3P > 57
P > 57/3 = 19
P > 19
So Pedro has more than 19
c) The oldest brother is 2 years older than Pedro, then:
M > 19 + 2
M > 21
Manuel is more than 21 years old.
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Which number has a 6 whose value is
10 times greater than the value of the
6 in 237,629?
A. 328,564
B. 426,579
C. 519,638
D. 618,402
Answer: B
Step-by-step explanation:
For 237,629 the 6 is located in the hundreds section so its value is approx. 600.
Now when you multiply 600 by 10 you get 6000
So the number of 6 should be located in the 6,000 range which is only in answer B 426,579
Answer:
B- 426,579
Step-by-step explanation:
The value of 6 in 237,629 is 600
600×10=6,000
Which answer has 6,000 as the value of 6?
- Answer B: 426,579
Micheal wants to buy an efficient smart car that according to the latest EPA standards gets 33 mpg in the city and 40 mpg on the highway. The car that Micheal picked out costs $16,100. His dad agreed to purchase the car if Michael would pay it off in equal monthly payments for the next 70 months. The equation y= -230x+16,100 represents the amount, Y (in dollars), that Michael owes his father after X months.
A) How much does Michael owe his dad after six months?
B) determine the slope of the line and interpret its meaning in the context of this problem.
1) Micheal owes his father $[ ] after 6 months.
2) The slope is [ ]
3) The amount Michael owes his father [choose one] by $[ ] per month.
$17690 is the amount Michael owed his dad .
What is linear equation ?Equations and equations of maximum degree 1 are also called "linear equations". The linear equation formula can be written as Y = mx + b. where m is the slope of the line, b is the y-intercept, and x and y are the variables. Slope indicates the direction and slope of the line. . This is because (0,y) is the point where the line intersects the y-axis.
CalculationThe amount Michael owes is given by :
y = - 290x +18,560
x = number of months ; y = amount owed
Amount owed after 3 months :
Put x = 3 in the equation :
y= - 290(3) +18,560
y = - 870 + 18560
y = 17690
According to the general form of a linear equation :
y = mx + c
Where, m = slope ; c = intercept
The slope = - 290 ; Intercept = 18560
Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month
The intercept shows that the original amount borrowed is 18560
Amount Michael owes his father decreases by 290 per month.
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If you draw two cards from a standard deck of 52 cards without replacement, find
P (Queen ⋂ Queen).
The probability of drawing two queens without replacement from ths standard deck is 1/221.
What is probability?Probability is the likelihood that an event will occur.
In a standard deck of cards, the total number of cards is 52.
There are 4 queens, the probability of drawing the first queen is 4/52.
After the first draw, there'll be 3 queens left and 52 cards. Therefore, the probability will be:
= 4/52 × 3/51
= 1/13 × 1/17
= 1/221
The probability is 1/221.
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What is the slope of a line that is parallel to the line
−
7
x
−
5
y
=
−
6
? Write your answer as an integer or fraction.
The slope of the line that is parallel to the line -7x-5y=-6 is -7/5
What is the slope of a line?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass.
Any two unique places along the line may be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the vertical change to the horizontal change in each case. We shall comprehend how to discover the slope in this piece, along with some of its uses.
Given, line is -7x-5y=-6
We have to write the given line in slope-intercept form
Then, y= (-7/5)x+(6/5)
The slope-intercept form is y= mx +c
By using the slope-intercept form,
Slope=(-7/5)
The lines that are parallel to y= (-7/5)x+(6/5) have the same slope of -7/5
Therefore, the slope of the line that is parallel to the line -7x-5y=-6 is -7/5
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