The slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.
What is the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) as required in the task content?It follows from the task content that the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) be determined.
On this note, it follows from the slope formula that slope;
m = (y2 - y1)/(x2 - x1)
Therefore, the slope of the line segment joining the two points is;
m = (-1.5 - (-3))/(0 - (-6))
m = 1.5/6
m = 1/4.
Ultimately, the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.
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find all the roots of x^3-5x^2-7x+51 if one root is 4-i
Answer:
Hello,
Step-by-step explanation:
P(x)=x^3-5x^2-7x+51
Since the coefficients are all reals,
4+i (conjugate of 4-i) is also a root.
The polynomial est divisible by (x-4-i)(x-4+i)=(x-4)²+1=x²-8x+17
If we divide P(x) by x²-8x+17 we find the quotient (x+3) and the remainder 0
P(x)=(x+4)(x-4-i(x-4+i)
Roots are -4,4+i and 4-i
Answer:
All the roots are -3, 4-i and 4+i.
Step-by-step explanation:
If oine root is 4 - i then another one is 4 + i as complex roots occur as conjugate pairs.
(4 - i)(4 + i)
= 16 - i^2
= 17.
As the last term = 51 = 3 * 17
looks like the other root is 3 or -3.
By the Factor theorem
If x = 3 then f(3) = 0
f(3) = 27 - 5(3)^2 - 7(3) + 51
= 27 - 45 - 21 + 51 = 12 so 3 is not a root.
If x = -3:
f(-3) = -27 - 45 _ 21 + 51
= 0
So, x = -3 is a root.
Solve the equation. Check your solution.
2(x+4)=-5x-1
Due tomorrow pls help.
Answer:
-9/7
Step-by-step explanation:
Distribute
2x + 8 = -5x - 1
Get variables on left; constants on right
2x + 5x = -1 -8
Gather like terms and do the math
7x = -9
x = -9/7
A large container ship is moving at a constant velocity of (2i − 5j) mph.
a) Find its speed.
At t = 0, the ship has position vector (8i + 3j) miles, relative to a fixed origin O.
b) Find its position vector p at time t hours.
A lighthouse has position vector (20i − 50j) miles.
c) Find the time at which the ship is due north of the lighthouse.
d) Find the distance of the ship from the lighthouse at this point.
Using vectors, and the relation between velocity and position, it is found that:
a) The speed is given by: v(t) = 2i - 5j.
b) The position vector p at time t hours is: p(t) = (2t + 8)i + (-5t + 3)j.
c) The ship is due north of the lighthouse at a time of 6 seconds.
d) The ship is 23 miles from the lighthouse at this point.
What is the relation between velocity and position?The position function is the integral of the velocity function.
As stated in the problem, the velocity is constant, hence:
The speed is given by: v(t) = 2i - 5j.
The position is the integral of the velocity, hence, integrating each component.
[tex]p(t) = \int v(t) dt[/tex]
[tex]p(t) = \int (2i - 5j) dt[/tex]
p(t) = (2t + k1)i + (-5t + k2)j.
Considering the initial position, we have that:
k1 = 8, k2 = 3.
Hence:
The position vector p at time t hours is: p(t) = (2t + 8)i + (-5t + 3)j.
The ship is due north of the lighthouse(20i - 50j) when it has the same x-coordinate, hence:
2t + 8 = 20
2t = 12
t = 6.
Hence:
The ship is due north of the lighthouse at a time of 6 seconds.
The position of the ship at t = 6 seconds is:
(2(6) + 8)i + (-5(6) + 3)j = 20i -27j.
The distance is given by:
|-50 - (-27)| = |-23| = 23.
The ship is 23 miles from the lighthouse at this point.
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What is the reciprocal of each mixed number?
Answer:
No 1. 3/31
No 2. 3/8
No3. 3/16
Step-by-step explanation:
you mainly just turn it into an improper fraction and then turn it upside down
Brainiest, please :) tysm
Answer:
a) 3/31
b) 3/8
c) 3/16
Step-by-step explanation:
You take the mixed number, turn it into an improper fraction (to do that, you multiply the whole number with the denominator on the fraction, and then you take that number and add it to the numerator of the fraction), and then you flip that improper fraction.
Slove n+5>7 helppp pls
Answer: n > 2
Step-by-step explanation: n + 5 > 7
n > 7-5
n > 2
solve for |3x+9|=30
X=7
X = 1, -19
no solution
x = 7,-13
Answer:
x = 7
Hope this helps :)
Explanation and Check part below.
Step-by-step explanation:
1. Isolate variable by doing the inverse operation which is in this case subtracting 9 on both sides of the equation.
3x + 9 = 30
- 9 - 9
3x = 21
2. Divide both sides of the equation by 3 since this is the inverse operation.
3x = 21
--- ---- <-------- fraction bar, divide
3 3
x = 7
Check:
3(7) + 9 = 30
21 + 9 = 30
30 = 30 ✓
If x = −2 and y = −8, what is the value of 4x + 5y + 17?
Answer:
-31
Step-by-step explanation:
4(-2) + 5(-8) +17
=(-8) + (-40) + 17
=-31
Find the measure of missing angles
[tex]\angle g=112^{\circ}[/tex] (vertical angles)
[tex]\angle h=68^{\circ}[/tex] (linear pair)
[tex]\angle k=92^{\circ}[/tex] (vertical angles)
[tex]\angle m=88^{\circ}[/tex] (linear pair)
Alan is putting weed killer on a field to get it ready for planting. the directions on the container say to use of a quart for each acre of land. how much weed killer will alan need for two fields, one that is acres and one that is acres? a. quarts b. quarts c. quarts d. quarts
The required amount of weed killer is 48.6 quarts.
To find the amount of weed killer required, first we will find the total acres of land of two fields.
So, total area of land is -
Area of land = [tex]22\frac{1}{2} + 38\frac{1}{4}[/tex]
Converting mixed fraction to fraction
Area of land = ((2×22)+1)÷2 + ((4×38)+1)÷4
Solving the bracket -
Area of land = 45÷2 + 153÷4
Area of land = 22.5 + 38.25
Area of land = 60.75 acres
Now, for 1 acre of land the required amount of weed killer = 0.8 quarts
So, for 60.75 acres of land the required amount of weed killer = 0.8×60.75
Performing multiplication to find the amount of weed killer
Amount of weed killer required = 48.6 quarts
Hence, the amount of weed killer required is 48.6 quarts.
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The complete question is -
Alan is putting weed killer on a field to get it ready for planting. The directions on the container say to use 4/5 of a quart for each acre of land. How much weed killer will Alan need for two fields, one that is 22 1/2 acres and one that is 38 1/4 acres?
3. How could you adapt the rule for division by 3 to decide easily when
a number is divisible by 9?
A divisibility rule is a simple method for determining whether or not an integer is divisible by a fixed divisor without having to divide it by looking at its digits.
The three-digit divisibility rule asserts that if the sum of a whole number's digits is a multiple of three, the original number is also divisible by three.
The total of all the digits in 1377 is 1+3+7+7 = 18. Because 18 is divisible by three, 1377 is likewise divisible by three. The quotient is 1377 3 = 459, and the remainder is 0.
The divisibility rule of 9 asserts that if a number's sum of digits is divisible by 9, the number is divisible by 9 as well.
The three-digit divisibility rule and the nine-digit divisibility rule are quite similar. As previously stated, the divisibility rule for the divisibility test of 3 asserts that if a number's sum of all digits is divisible by 3, the number is also divisible by 3. The divisibility rule of 9 is similar to the divisibility rule of 3, in that a number is said to be divisible by 9 if the sum of all of its digits is divisible by 9.
Take 52884 for example. 52884 is divisible by three since the total of all digits is 5+2+8+8+4 = 27. The quotient is 52884 ÷ 3 = 17628, and the remainder is 0. It's worth noting that the sum of the digits is 27 is 2 + 7 = 9, which is likewise divisible by three.
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You start a lawn mowing company and charge $15 per lawn. If you need $200 to buy new airpods, how many lawns would you need to mow?
Point A is chosen at random on BE- . Find the probability of the following event.
P(A is on CD-)
The probability of the event P(A is on [tex]\bar{CD}[/tex]) is 6/13.
Probability:
The term probability defines the possibility of the favorable event across the total event.
Given,
Point A is chosen at random on [tex]\bar{BE}[/tex].
Here we need to find the the probability of the following event.
P(A is on [tex]\bar{CD}[/tex]).
Let us consider the following image, in order to solve this.
Based on the image we have identified that the probability of the event P(A is on [tex]\bar{CD}[/tex]) is calculated by dividing the length of CD by the length of BE.
So, the probability of the event P(A is on [tex]\bar{CD}[/tex]) is,
P(A is on [tex]\bar{CD}[/tex]) = (length of CD) / (length of BE)
Apply the values then we get,
P(A is on [tex]\bar{CD}[/tex]) = 12 / ( 5 + 12 + 9)
P(A is on [tex]\bar{CD}[/tex]) = 12 / 26
And it can be simplified as,
P(A is on [tex]\bar{CD}[/tex]) = 6/13
Therefore, the probability of the event P(A is on [tex]\bar{CD}[/tex]) is 6/13.
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Find the value of the variable and the measure of each labeled angle.
Answer:
x=2
angle 1= 27°
angle 2= 27°
Step-by-step explanation:
(x+6) =( 3x -36)
2x=42
x=21
Graph the following function by moving
the green and blue dots (if necessary).
Answer:
Reflect back on a time when you did something you later were at least somewhat uncomfortable with. Maybe it was something you said or did, but upon reflection you knew it wasn't the right thing to do. If you can't think of a real situation, you can create a hypothetical one.
[tex]\pink{ \rule{2pt}{99999pt}}[/tex]
Trigonometry Question pls help
Answer:
Hello,
Step-by-step explanation:
In the triangle ABG, using law of sin
[tex]\dfrac{sin(121^o)}{7} =\dfrac{sin(41^o)}{AG} =\dfrac{sin(18^o)}{BG} \\\\AG=\dfrac{sin(41^o)*7}{sin(121^o)} =5.358(km)\\\\BG=\dfrac{sin(18^o)*7}{sin(121^o)} =2.526(km)\\\\CG=5+BG=7.526(km)\\\\GD=CG*sin(31^o)=3.875(km)\\\\AD=AG+GD=9.233(km)\\\\CD=CG*cos(31^o)=6.451(km)\\\\AC=\sqrt{AD^2+CD^2} =11.263(km)\\[/tex]
A single ticket to a magic show costs m dollars, but there is a discount of 25% per ticket
if a group buys 20 or more tickets. The expression 20m - 20(0.25m) describes the
total cost of buying 20 tickets for a group.
Part A
Match each amount with the expression that represents it.
Total discount for 20 group tickets
Amount of discount per ticket
Number of tickets
Cost of buying 20 single ticket
The expression for Total discount for 20 group tickets is 5 m, Amount of discount per ticket is 0.25 m, Number of tickets is 20 and Cost of buying 20 single ticket is 20 m.
We have:
a discount of 25% per ticket if a group buys 20 or more tickets.
The expression 20 m - 20 (0.25 m) describes the total cost of buying 20 tickets for a group.
Total discount for 20 group tickets will be:
Total discount = 20 × 0.25 m = 5 m
Amount of discount per ticket = 5 m / 20 = 0.25 m
Number of tickets = 20
Cost of buying 20 single ticket = 20 m
where m = cost of buying 1 ticket.
Therefore, the expression for Total discount for 20 group tickets is 5 m, Amount of discount per ticket is 0.25 m, Number of tickets is 20 and Cost of buying 20 single ticket is 20 m.
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Find the measures of numbered angle.
a. ∠ 2
Measure of angle 2 i.e. m∠2 = 130°
What is measurement of an angle ?The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.
How to find angle measurement ?As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.
In the question,
Let given angle is ∠8.
Given, ∠8 = 50°
Now, according to vertical angle property
∠5 = ∠8
therefore, ∠5 = 50°
Also, ∠5 = ∠4 = 50° (alternate interior angles)
As, ∠4 and ∠2 are supplementary angles
Hence, ∠4 + ∠2 = 180°
50° + ∠2 = 180°
∠2 = 130°
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The complete question is :
Find measure m∠2
Um yea anyone want to answer this for me
Answer: 2
Step-by-step explanation:
120/72 = 5/3 or 1.6666
5/3 tutors needed however you cannot have a portion of a tutor so the academy actually needs 2 tutors.
Answer: 10 tutors
Step-by-step explanation: to simplify the numbers a bit we will do 72 students divided by 6 tutors to get 12 (72/6=12). This means we need 1 tutor for every 12 students. Therefore we can take the 120 students and divide that by 12 to get 10 (120/12=10) meaning we need 10 tutors for 120 students.
Find the HCF of : 484 and 628
Answer:
4
Step-by-step explanation:
The factors of 484 are: 1, 2, 4, 11, 22, 44, 121, 242, 484
The factors of 628 are: 1, 2, 4, 157, 314, 628
Then the greatest common factor is 4.
Solve each system by elimination.
5x - 2y = -19 , 2x + 3y = 0
By elimination, the solution of the system of equations, 5x - 2y = -19 and 2x + 3y = 0, is (-3 , 2).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
First, multiply the first equation by 3 and the second equation by 2.
5x - 2y = -19 ⇒ 15x - 6y = -57 (equation 1)
2x + 3y = 0 ⇒ 4x + 6y = 0 (equation 2)
Adding the two equations will eliminate the variable y.
15x - 6y = -57 (equation 1)
4x + 6y = 0 (equation 2)
19x = -57
x = -3
Substitute the value of x to any of the two equation and solve for y.
2x + 3y = 0 (equation 2)
2(-3) + 3y = 0
3y = 6
y = 2
Hence, the solution of the system of equations is (-3 , 2).
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Give the equation of the line passing through the point
(28,2) that is perpendicular to y= -7
The equation of the line passing throigh the given points is given by y = x/7 + 3.
Define slope of a line.The slope of a line indicates its steepness and direction.
The slope of a line can be calculated using any two distinct points on it. The slope of a line formula calculates the ratio of "vertical change" to "horizontal change" between two distinct points on a line.
Given: Point (28,7)
An equation of perpendicular line y = -7x.
We know if fwo lines are perpendicular then their slopes are negative inverse of each other.
i.e., [tex]m_{1} = \frac{1}{m_{2} }[/tex]
Therefore, y = -7x
Slope, [tex]m_{1}[/tex] = - 7x
Slope of other line will by be [tex]$\frac{1}{m_1}$[/tex].
[tex]$$m_2=\frac{+1}{7}$$[/tex]
Slope of required equation = 1/7
Substitute [tex]\left(x_1, y_1\right)[/tex] = (28,7), m=1/7 in
(y-[tex]y_1[/tex]) = m (x-[tex]x_1[/tex])
(y -7) = 1/7 (x - 28)
(y - 7) = x/7 - 4
y = x/7 + 3
This is the required equation of line.
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HELP FIND THE AVERAGE RATE OF CHANGE
Answer:
(a): 26.1
(b): 27.9
Please see below for the steps.
Step-by-step explanation:
(a):
Use points (0,0) and (3, 78.3)
Use slope formula. The slope formula is also used to find average rate of change (just so you know).
y2-y1/x2-x1
78.3-0/3-0=78.3/3=26.1
Answer for (a) is 26.1
(b):
Use points (4, 147.6) and (9, 287.1)
Use slope formula.
y2-y1/x2-x1
287.1-147.6/9-4=139.5/5=27.9
The answer for (b) is 27.9
Hope this helps!
Please mark as brainliest if correct!
Have a great day!
You can choose between two tennis courts at two university campuses to learn how to play tennis. One campus charges 25 per hour. The other campus charges 20 per hour plus a one-time registration fee of 10 .
a. Write a system of equations to represent the cost c for h hours of court use at each campus
The system of equations to represent the cost c for h hours of court use at each campus; c = 25h and c = 20h + 3.3.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
WE have been given that we can choose between two tennis courts at two university campuses to learn how to play tennis.
The system of equations to represent the cost c for h hours of court use at each campus;
The first campus charges 25 per hour.
c = 25h
Similarly The other campus charges 20 per hour plus a one-time registration fee of 10 .
c = 20h + 1/3(10)
c = 20h + 3.3
Therefore, the system of equations to represent the cost c for h hours of court use at each campus; c = 25h and c = 20h + 3.3.
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a candle is 16 inches tall after burning for 3 hours. after 5 hours , it is 15.5 inches tall.write a linear equation to model the relationship between height h of the candel and time t. predict how tall the candel will be after burning 2 hours
The height of the candle after burning for 2 hours is 16.25 inches.
Given that, a candle is 16 inches tall after burning for 3 hours. after 5 hours, it is 15.5 inches tall.
We need to write a linear equation to model the relationship between the height h of the candle and time t.
What is a linear equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent of more than 1. The graph of a linear equation always forms a straight line.
Let t be the time in hours and h be the height in inches.
Now, the ordered pair of the given situation is A(3, 16) and B(5, 15.5).
Find the slope m of the linear equation between points A and B
We know that the formula to calculate the slope between two points is equal to m=(y2-y1)/(x2-x1)
=(15.5-16)/(5-3)=-0.5/2
=-1/4
We know that the equation of the line in the point-slope form is (y-y1)=m(x-x1)
⇒y-16=(-1/4)(x-3
⇒4y-64=-x+3
⇒4y=-x+3+64
⇒4y=-x+67
We need to find how tall the candle will be after burning for 2 hours.
That is, put x=2
4y=-2+67
⇒4y=65
⇒y=16.25 inches
Therefore, the height of the candle after burning for 2 hours is 16.25 inches.
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when you have a quadratic in the form of 2(x+1)(x+4), do you distribute the 2 to both parentheses, or just the first one {(x+1)}?
Answer:
2x²+10x+8
Step-by-step explanation:
you have to multiply the brackets first the multiply the 2 in
2(x+1)(x+4)
2(x²+4x+x+4)
2(x²+5x+4)
2x²+10x+8
5. A group of hikers walked 540 kilometers at a rate of 30 kilometers each day. How many days did they
hike for?
Answer: 18 Days
Step-by-step explanation: 30x18=540
Solve for d in the proportion.
804/d = 6/4
Work Shown:
804/d = 6/4
804*4 = 6d
3216 = 6d
6d = 3216
d = 3216/6
d = 536
Choose the letter of the word or phrase that best completes each statement.
a. ratio
b. proportion
c. means
d. extremes
e. similar
f. scale factor
g. AA Similarity Post.
h. SSS Similarity Theorem
i. SAS Similarity Theorem
j. midsegment
k. dilation
I. enlargement
m . reduction
A(n) ___?____ is an equation stating that two ratios are equivalent.
A proportion is an equation stating that two ratios are equivalent.
Ratio is defined as the comparison of two quantities. The ratio between quantities a and b can be expressed as a : b or a/b.
example:
There are 3 girls for every 5 boys in a class. Then, the ratio of girls to boys is 3 : 5 or 3/5.
On the other hand, proportion is defined as the equality between two or more ratios.
a : b = c : d
Two ratios are equivalent if their cross-products are equal. Cross products are the products of the extremes and means.
If a : b = c : d, then ad = bc.
example:
2 : 3 = 6 : 9 is proportion since 2(9) = 3(6) ⇒ 18 = 18
3 : 5 and 4 : 6 is not a proportion since 3(6) ≠ 5(4) ⇒ 18 ≠ 20
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Jessie baked p cupcakes on Saturday. She baked (p + 3) more cupcakes on Sunday than on Saturday. She baked 30 cupcakes altogether. How many cupcakes did Jessie bake on Saturday?
Answer:
9 cupcakes on Saturday
Step-by-step explanation:
(p + 3) more than p is p + p + 3 = 2p + 3
on Saturday she baked p
on Sunday she baked 2p + 3 , then
p + 2p + 3 = 30
3p + 3 = 30 ( subtract 3 from both sides )
3p = 27 ( divide both sides by 3 )
p = 9
She baked 9 on Saturday and 21 on Sunday
Use the following image to answer questions
1.) 12a =
2.) 12b =
3.) 12c =
Answer:
:D
Step-by-step explanation:
1.) One ticket out of eighty can be represented by a fractions, 1/80. To find the percentage, you can change 80 to 100 proportionally and then the difference (multiply/divide) to the 1 to find the percentage. You can also cross multiply to find the answer ("a")
[tex]\frac{1}{80} =\frac{x}{100}[/tex]
0.0125 is the chance of getting the ticket, and multiply by 100 to get percentage.
a = 1.25%
2.)
Same thing as #1, different equation :)
[tex]\frac{5}{80} =\frac{x}{100}[/tex]
x = 6.25%
3.)
Same thing as #2, but now, on the bottom is not 80, but instead 70.
[tex]\frac{5}{70} =\frac{m}{100}[/tex]
m = 7.14285714286%
m = 7.14%
Answer:
12a) 1/80=0.0125 = 1.25%
12b) 5/80=0.0625 = 6.25%
12c) 5/70=0.07142 = 7.14%
Step-by-step explanation:
