5. Find the equation of the line joining the points A(5, 7) and B(8, 12).
Given:
There are given that the two points:
[tex]A(5,7),and,B(8,12)[/tex]Explanation:
According to the question:
We need to find the equation of the line:
Then,
To find the equation of the line, first, we need to find the slope of the line.
So,
From the formula of the slope of the line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=5,y_1=7,x_2=8,y_2=12[/tex]Then,
Put all the values into the given formula:
So,
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{12-7}{8-5} \\ m=\frac{5}{3} \end{gathered}[/tex]Then,
From the formula of the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]Then,
Put the value of m into the above equation:
So,
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-7=\frac{5}{3}(x-5) \\ 3y-21=5(x-5) \\ 3y-21=5x-25 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3y-21=5x-25 \\ 3y-21+21=5x-25+21 \\ 3y=5x-4 \\ y=\frac{5}{3}x-\frac{4}{3} \end{gathered}[/tex]Final answer:
Hence, the equation of line is shown below:
[tex]y=\frac{5}{3}x-\frac{4}{3}[/tex]Find the measure of B
PLS HELPPPPP
PLS EXPLAIN
The values needed to complete the relative frequency table in the context of this problem are as follows:
a = 69.06%.b = 30.91%.c = 68.60%.d = 31.40%.What is a relative frequency?The relative frequency of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
To find the relative frequency for boys, we look at the frequency two-way table, and consider that out of 110 boys, 76 went to 4-year colleges and 34 went to two year colleges, hence the relative frequencies are found as follows:
a = 76/110 = 0.6909 = 69.09%.b = 34/110 = 0.3091 = 30.91%.For girls, we also look at the frequency two-way table, and consider that out of 121 girls, 83 went to 4-year colleges and 38 went to two year colleges, hence the relative frequencies are found as follows:
c = 83/121 = 0.6860 = 68.60%.d = 38/121 = 0.3140 = 31.40%.More can be learned about relative frequencies at https://brainly.com/question/1809498
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Please Help I'm soooo stuck
There are 40 fish in a pond. 12 of the fish are bream. Of the fish that are not bream, 1/4 are tench and the rest are carp.
What is the ratio of bream to tench to carp in the pond? Give your answer in its simplest form.
The ratio of bream to tench to carp is given by the expression; 12 : 7 : 21
What is a ratio of items?A ratio is a relationship between two or more items, that quantitatively expresses the number of times a unit item can be found within the quantity of each item in the set of items.
The given parameters are;
Number of fish in the pond = 40
The number of fish in the pond that are bream = 12
The number of fish that are tench = 1/4 of the fish that are not bream
The number of the fish that are carp = The rest of the fish that are not bream or carp
Required;
The ratio of bream to tench to carp of the fish in the pond.
Solution;
The number of fish that are either tench or carp = 40 - 12 = 28
The number of the fish that are tench = (1/4) × 28 = 7
Therefore;
The number of fish that are carp = 28 - 7 = 21
Which gives;
Number of bream in the pond = 12
Number of tench in the pond = 7
Number of carp in the pond = 21
The ratio of the number of bream to tench to carp in the pond is given by the expression;
[tex]\displaystyle{ \frac{12}{40}:\frac{7}{40}:\frac{21}{40}}[/tex]
Given that the expression for the ratio cannot be simplified further, we have;
The ratio of bream to tench to pond is 12 : 7 : 21
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How do to solve this problem? (The answer is 262 Hz) I don't need to know the question that it is asking. I just want to know how to solve the equation and its answer. I am a grade 10 student if this helps you.
Step-by-step explanation:
Given the formula below
[tex]undefined[/tex]Brickhouse is expected to pay a dividend of $3.30 and $2.52 over the next two years, respectively. after that, the company is expected to increase its annual dividend at 4.2 percent. what is the stock price today if the required return is 11.6 percent?
The company’s stock price today would be $33.46.
Dividend per share for the first 2 yearsDividend per share Year 1 (D1) = $3.30 per share
Dividend per share Year 2 (D2) = $2.52 per share
Calculation of Stock Price for the Year 2 (P2)Stock Price for the Year 2 (P2) = D2(1 + g) / (Ke – g)
= $2.52(1 + 0.042) / (0.1160 – 0.042)
= $2.63 / 0.0740
= $35.48 per share
The Stock Price todayThe company’s stock price is the Present Value of the future dividend payments and the present value the stock price for the year 2
The Stock Price = D1/(1 + r)1 + D2/(1 + r)2 + P2/(1 + r)2
= $3.30/(1 + 0.1160)1 + $2.52/(1 + 0.1160)2 + $35.48/(1 + 0.1160)2
= [$3.30 / 1.1160] + [$2.52 / 1.24546] + [$35.48 / 1.24546]
= $2.95 + $2.02 + $28.49
= $33.46 per share
Hence, the company’s stock price today would be $33.46.
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solve for z
6(x-h)=z
Answer: I hope these two answers help please mark me brainlist
Step-by-step explanation:
Simplifying
z = 6(x + -1h)
Reorder the terms:
z = 6(-1h + x)
z = (-1h * 6 + x * 6)
z = (-6h + 6x)
Solving
z = -6h + 6x
Solving for variable 'z'.
Move all terms containing z to the left, all other terms to the right.
Simplifying
z = -6h + 6x
or another answer
6(x-h)=z
Distribute 6 through the parentheses
6x-6h=z
Swap the sides of the equation
Z= 6x-6h
What is the solution set for -3x + 12 < 4x - 9
A) x > 21
B) x > 3
C) x < -3
D) x < -21
Answer:
C) x < -3
Step-by-step explanation:
-3x +12 < 4x - 9
-3x -4x < -12 - 9
-7x < -21
x > -3
an you guys help me with this one too
Amanda and Diana given right solution set.
The solution set of given graph of inequality is,
x < 4.
Now, The solution of given created inequality,
Amanda:- -3x + 5 > -7
=> -3x> -7 -5
=> - 3x > -12
=> 3x < 12
=> x < 4
So, it is correct
Briana:- 1/2 (2x - 4)> 2
=> 2x - 4 > 4
=> 2x > 8
=> x > 4
It is wrong
Courtney:- -7x+8 > -3x + 24
=> -7x + 3x > 24 - 8
=> -4x > 16
=> 4x < -16
=> x < -4
It is wrong
Diana:- 9x -6 < 3x + 18
=> 9x - 3x < 18 + 6
=> 6x < 24
=> x < 4
So, it is right
Hence, Amanda and Diana given right solution set.
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an empty swimming pool is in the shape of a rectangle meters long, meters wide and meters deep. a child starts to fill the pool using a saucepan with a circular base having a diameter of and a depth of . the child can fill the saucepan and empty it into the pool twice per minute. how many days would it take the child (working 24 hours per day) to fill the pool? don’t round to the nearest day.
the child would take 11.5 days (working 24 hours per day) to fill the swimming pool
an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep.
filling rate =2*10*π*(0.1)^2
or 0.002 π cubic meters per minute
or 0.12 cubic meters per hour
or 2.88 cubic meters per day
volume to fill = 100 cubic meters
how many days to fill ? × days= 2.88π × x=100
this implies x= 100/2.88π
x= 11.05
the complete question is
an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep. a child starts to fill the pool using a saucepan with a circular base having a diameter of 20cm and a depth of 10 cm. the child can fill the saucepan and empty it into the pool twice per minute. how many days would it take the child (working 24 hours per day) to fill the pool? don’t round to the nearest day.
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Solve three-fourths + two-sixths = ___.
five-tenths
five-twelfths
twelve-twelfths or 1
thirteen-twelfths or one and one-twelfth
The value of three-fourths + two-sixths is thirteen-twelfths or one and one-twelfth. Option D
What is a fraction?A fraction can be defined as a part of a whole set or element.
There are several types of fractions which includes;
Simple fractionsComplex fractionsMixed fractionsProper fractionsImproper fractionsExamples of simple fractions; 1/ 2, 1/6
Examples of proper fractions; 2/3, 4/7
Examples of improper fractions; 4/3, 3/2
Examples of mixed fractions; 2 1/ 4, 7 1/2
From the information given, we have that;
3/ 4 + 2/ 6
Find the lowest common multiple
9 + 4 /12
13/ 12
Hence, the value is 13/12
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need help having problems
Solve for b.49 = b 2b = = 1or
√49 = +/- 7
√16 = +/- 4 as you calculated
Congrats, you did it!
What is the purpose of carbon sequestering technology? To remove carbon from the air and put it into the ground To use respiration to remove carbon from the air To release carbon from the ocean and move it into the air To store carbon in glaciers and snow
Carbon sequestering technology has the main purpose of being used To remove carbon from the air and put it into the ground.
Find out more below.
What is carbon sequestering?Carbon Sequestering refers to various processes that are used to remove the carbon in the air. This carbon is then stored in various places such as the ground and the oceans.
Carbon Sequestering happens naturally such as the process of photosynthesis. Thanks to Carbon Sequestering technology however, humans are able to use the technology to reduce our carbon footprint on Earth.
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If x = 6 and y = 4, work out the value of the following:
4x + y
2y squared
( x - y ) squared
Step-by-step explanation:
If x = 6 and y = 4. Substitute x and y in the expression.
4x+y
4(6)+(4)
24+4
28
2y²
2(6)²
2(36)
72
( x - y )²
(6+4)²
(10)²
100
A) 35° B) 55° C) 70° D) 145° In the figure above, lines and m are parallel and lines s and t are parallel. If the measure of 21 is 35°, what is the measure of Z2?
If lines and m are parallel and lines s and t are parallel. If the measure of 21 is 35°, the measure of ∠2? is : D) 145°.
Parallel lineBased on the given figure ∠1 and ∠3 form a parallel line.
Now let determine the measure of ∠2
Hence,
∠1+∠3=180 °
35° +∠3= 180 °
∠3 = 180 ° - 35°
∠3 = 145 °
The corresponding angles is ∠4 = ∠3 = 145 °
∠ 2 an ∠ 4 are as well a corresponding angles
So,
∠2 = ∠4 = 145 °
Therefore the we can conclude that the correct option is D.
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The sum of two rational numbers is 4. If one of the numbers is 2/3, then what is the other number
Answer:
10/3
Step-by-step explanation:
Let x be the value of the second rational number. The first rational number is 2/3, and we are told that the sum of these numbers is 4:
x + 2/3 = 4
Therefore:
x + 2/3 = 4
x = 4 - 2/3
x = 12/3 - 2/3
x = (10/3)
Write the equation of the line in fully simplified slope-intercept form.
Answer:
Step-by-step explanation:
Choose two points on the graph: (-6,-7) and (6,-9)
The straight line equation is: y=mx+b
[tex]\displaystyle\\\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-6\ \ \ \ x_2=6\ \ \ \ \ y_1=-7\ \ \ \ y_2=-9\\\\m=\frac{-9-(-7)}{6-(-6)} \\\\m=\frac{-9+7}{6+6} \\\\m=\frac{-2}{12} \\\\m=-\frac{1}{6}\\\\Hence,\ y=-\frac{1}{6}x+b\ \ \ \ \ (1)[/tex]
To determine the coefficient b, take any of the two points,
for example (-6,-7), that is, x=-6 y=-7
Substitute these values into formula (1):
[tex]\displaystyle\\-7=-\frac{1}{6}(-6) +b\\\\-7=1+b\\\\-7-1=1+b-1\\\\-8=b\\\\Thus,\ b=-8\\\\The\ result\ is\ y=-\frac{1}{6}x-8[/tex]
5y/3 = 30 solve for y simplify your answer as much as possible
Answer: y= 18
Step-by-step explanation:
5y/3 = 30
First step: multiply 3 on both sides
5y/3 * 3 = 30*3
5y = 90
Second step: divide 5 on both sides (isolating variable)
5y/5 = 90/5
y = 18
Answer:
y = 18
Step-by-step explanation:
[tex]\frac{5y}{3}[/tex] = 30 ( multiply both sides by 3 to clear the fraction )
5y = 3 × 30 = 90 ( divide both sides by 5 )
y = 18
Jada drew triangle ABC. If angle B is a right angle, what are possible measures for the other two angles?
angle A:
The possible measures for the other two angles will be that the sum of that angle must be 90 degree.
A triangle is considered to be 3-sided polygon in some cases Each triangle has three sides and three angles, a few of which may be the same. The portion of the plane enclosed by the triangle is said the triangle interior, whereas the leftover portion is the exterior. Since we are given that one of the angles of the given is a right angle, according to one of the rules of the triangle the sum of all the interior angles of a triangle should be 180, for the triangle ABC,
=>A+B+C = 180
=>A+90+C= 180
=>A+C= 180-90
=>A+C=90
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Points A(8, 4) and B(−7, 4) are located on a coordinate plane. Graph the pair of points. Then find the distance between them and complete the explanation.
If the point A(8,4) and B(-7,4) are located one the coordinate plane. Then the graph has been plotted and the distance between the points is 15 units
The first point = A(8,4)
The second point = B(-7,4)
Plot the point on the coordinate plane
The distance between the two points d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where d is the distance between the two points
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The distance d = [tex]\sqrt{(-7-8)^2+(4-4)^2}[/tex]
= [tex]\sqrt{(-15)^2}[/tex]
= 15 units
Hence, If the point A(8,4) and B(-7,4) are located one the coordinate plane. Then the graph has been plotted and the distance between the points is 15 units
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4z+7 what is the value of z
Answer: it could literally be anything
Step-by-step explanation: if 4*z+7=15 then z=2
Can someone help me in this please
Angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.
What are supplementary angles?Two angles are considered to be supplementary if their sums total 180 degrees. If two angles in geometry add up to 180 degrees, they are said to be supplementary angles. For instance, A and B are referred to as supplementary angles if A + B = 180°. When combined, supplementary angles always make a straight angle (180 degrees).So, angles supplementary to ∠3:
∠1 is supplementary to ∠3 (Straight angle)∠2 is supplementary to ∠3 (Inversely opposite angle)∠4 is supplementary to ∠3 (Straight angle)∠5 is supplementary to ∠3 (Adjacent angles)∠6 is supplementary to ∠3 (Alternate angles)∠7 is supplementary to ∠3 (Corresponding angle)(Refer to the image attached below)
Therefore, angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.
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Missy rode her bicycle 16 miles in 1 1/4 hours. What was her average speed in miles per hour
Answer: 12.8 miles per hour
Step-by-step explanation:
divide 16 by 1.25 in order to get your answer
in these number grids two numbers are added to get th number below. example 13 +12=25.write the number in the grid to make it correct 4+?+9+?+?=35
Answer:
7+7+8
Step-by-step explanation:
9+4=13
35-13=22
22÷3 because they are three question mark
so 7 r 1
. .
. 4+7+9+7+8 =35
1. Technologies in the early 1800s not only
changed transportation but revolutionized what
as well?
a. black rights
b. the Constitution
c. women's rights
d. communication
The technologies that came in the early 1800s changed transportation and revolutionized D. Communication.
How did communication change in the 1800s?In the early 1800s, technology was making things better in the United States. The use of rail lines changed transportation by making many more areas accessible.
Thanks to this improvement in transportation, communication was also revolutionized. For instance, the rail lines made the Federal Postal Service better able to do its job. The Telegraph was also invented in the early 1800s (1844) and allowed for messages to travel much faster than ever before.
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4х-бу=-26
-2x+3y=13
find the solution of this system of equations2x+5y=-49-2x+8y=-68
Given the system of equations :
[tex]\begin{gathered} 2x+5y=-49 \\ -2x+8y=-68 \end{gathered}[/tex]Add the equations to eliminate x :
[tex]\begin{gathered} (2x+5y)+(-2x+8y)=-49+(-68) \\ 2x+5y-2x+8y=-117 \\ (2x-2x)+(5y+8y)=-117 \\ 13y=-117 \end{gathered}[/tex]divide both sides by 13 to find the value of y :
[tex]\begin{gathered} \frac{13y}{13}=\frac{-117}{13} \\ \\ y=-9 \end{gathered}[/tex]To find x , substitute with the value of y at the first equation :
[tex]\begin{gathered} 2x+5\cdot-9=-49 \\ 2x-45=-49 \\ 2x=-49+45 \\ 2x=-4 \\ \\ x=-\frac{4}{2} \\ \\ x=-2 \end{gathered}[/tex]So, the solution of the system is :
[tex]\begin{gathered} x=-2 \\ y=-9 \end{gathered}[/tex]The solution can be written as the order pair (x,y):
[tex](x,y)=(-2,-9)[/tex]A 150-pound person uses 5.2 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 240
calories?
Answer: 37.31 minutes
Step-by-step explanation:
HELP.
i want to know how to do all this "graph the slope equations" stuff. i need it as soon as you can, pls tell me the answer, how to do it, and tell me how it makes sense in SIMPLE FORM. I know its a lot but i need it. A piece of paper showing all the work would be nice too<3 <3 i will give brain points to the best answer.
9th grade Algebra 1
Answer:
y = 1/2x - 1
(fraction form)
or
y = 0.5x - 1
(decimal form)
Step-by-step explanation:
To graph:
Start at (0, 0), or the origin, which is in the center of the coordinate plane.Move over x units to the right or left. Then, move over y units up or down. Mark the point.If you're working with a linear equation, draw lines connecting points from left to right. For a quadratic equation, connect points with curved lines.Another suggestion, is to use Desmos Graphing Calculator (website) and just plug in the points to see where to graph.
Hope this helps! :)