The slope of equation y = -5/6 x + 4 is -5/6 and the slope-intercept form of -5/6x+4 is y = -5/6 x + 4
The slope of a function y = f(x) is given by a formula
slope = y2-y1 / x2- x1
where ( x1 , y1) and (x2, y2) are coordinates of any two points on the line of graph representing y = f(x)
Or we can simply use the slope-intercept form
y = mx+ c
where m is the slope of the given equation and c is the constant
so, in the given equation y = -5/6 x + 4
slope of the equation is -5/6
Hence, The slope of equation y = -5/6 x + 4 simply is -5/6 and the slope intercept form of -5/6x+4 is y = -5/6 x + 4
When you know the slope of the line to be investigated and the point given is also the y intercept, you can utilize the slope intercept formula y = mx + b. (0, b). The y value of the y intercept point is represented by b in the formula.
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Damian is building a display case to hold
75 model cars. The case will have fewer
than 10 shelves, and each shelf will hold
no more than 15 cars. If Damian wants
each shelf to have the same number of
cars, how many shelves should he put in
the display case?
please solve this question step by step
Answer:
Step-by-step explanation: The given question is wrong. To be a valid question, there must be "-9" in place of "-7" in the second given matrix.
Solve for x and write your answer in simplest form.
x-3(2/3x+3)=3(-3/2x+1)-3/2x
Answer:
x= -6
Step-by-step explanation:
[tex]x-3(\frac{2}{3}x+3)=3(\frac{-3}{2}+1)-\frac{3}{2}\\\\x-2x-9=\frac{-9}{2}+3-\frac{3}{2}\\\\clear fraction\\\\2x-4x-18=-9+6-3\\\\-2x-18=-6\\\\-2x=12\\\\x=-6[/tex]
Write 6.42 as a mixed number in simplest form.
6.42=
Answer:
6 [tex]\frac{21}{50}[/tex]
The figure shows two triangles on a coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A′B′C′? (1 point)
a
A 180 degree counterclockwise rotation about the origin followed by a translation 5 units up
b
A 270 degree counterclockwise rotation about the origin followed by a translation 5 units up
c
A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin
d
A translation 5 units to the left followed by a 270 degree counterclockwise rotation about the origin
The set of transformations that is performed on triangle ABC to form triangle A′B′C′ is C. A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin.
What is a translation?A translation is a geometric transformation when each point in a figure, shape, or space is moved in a specific direction by the same amount. A translation can also be thought of as moving the coordinate system's origin or as adding a constant vector to each point.
In this case, it can be seen that the shape was rotated counterclockwise twice. That's 90° × 2 = 180°
Therefore, the transformation that is performed on triangle ABC to form triangle A′B′C′ is a translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin.
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What is the area, in square meters, of the shape below? Express your answer as a fraction in simplest form.
Area = 5/12 m².
For image see the attachment below-
Area of Triangle - A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. The above figure is a triangle denoted as △ABC. Some real-life examples of triangles include sandwiches, traffic signs, cloth hangers, and a rack in billiards.
The basic formula to find the area of a triangle is,
Area of triangle = 1/2 (b × h);
where b = base and
h = height of the triangle.
Now , we have been given that -
Base =5/3 m
Height = 1/2 m
Find out area of the triangle .
The area of a triangle = 1/2 x base x height
Put the values in formula
area of a triangle = 1/2 x 5/3 x 1/2
area of a triangle = (1x5x1)/ (2x3x2)
area of a triangle = 5/12 m².
Hence, the area in square meters of the given shape is 5/12 .
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Find the distance between the two points on the graph.
Answer:
[tex]3 \sqrt{5} [/tex]
Step-by-step explanation:
See attached for details. Basically finding the distance between 2 points requires creating a right angle triangle. And we are looking for the hypotenuse.
The pythagorean theorem is used.
Can anyone pleases solve this?
By rationalization and algebra properties, the irrational expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) is equivalent to the integer 1.
How to simplify a subtraction of irrational fractions
In this question we find a composite irrational expression formed by a irrational fraction being subtracted by other two irrational fraction. Eliminating the irrational denominators by transforming it into rational numbers is an important step for this question, this can be done by means of rationalization, along with algebra properties.
The complete procedure of this exercise is shown below:
7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2)
[7√3 · (√10 - √3)] / [(√10 + √3) · (√10 - √3)] - [2√5 · (√6 - √5)] / [(√6 + √5) · (√6 - √5)] - [3√2 · (√15 - 3√2)] / [(√15 + 3√2) · (√15 - 3√2)]
(7√30 - 21) / 7 - (2√30 - 10) - (3√30 - 18) / (- 3)
(7√30 - 21) / 7 + (10 - 2√30) + (3√30 - 18) / 3
(7√30 - 21 + 70 - 14√30) / 7 + (3√30 - 18) / 3
(49 - 7√30) / 7 + (3√30 - 18) / 3
(147 - 21√30 + 21√30 - 126) / 21
21 / 21
1
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a quarry needs to ship a marble block weighing 10000 pounds. if the cost of shipping is 110 per ton, how much will shipping cost?
The cost of shipping the marble block is 550.
The total weight of the marble block is 10,000 pounds.We need to convert the weight from pounds to tons.Unit conversion is the process of converting various units of measurement for the same amount, often using multiplicative conversion factors that modify the measured quantity value without affecting its effects.1 ton equals 2000 pounds.The total weight of the marble block in tons is 10000/2000.The total weight of the marble block is 5 tons.The cost of shipping is 110 per ton.The total cost of shipping the marble block = 5 * 110.The total cost of shipping the marble block is 550.To learn more about unit conversion, visit :
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2. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate
The additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
How to state the additional information required?The congruence postulate is given as:
SSS Triangle Congruence Postulate
The above means that the three sides of the triangles are congruent.
From the figure, the following side lengths are said to be congruent
UV and FV
TV and TV
For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent
This is represented as:
UT = T F
Hence, the additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
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russell runs 9/10 miles in 5 minutes. at this rate how many miles can he run in one mintue?
Answer:
1.8 miles
Step-by-step explanation:
4x100+7x10+6x1+6x(1/10)+3x(1/100)+7x(1/1000)
Please help
Vishal came up with an answer of 41 square units for the area of this square.
How long is each side of the tilted square?
_____ units
The length of each side of the given tilted square is √41 units.
What is the length of the side of the square?
The formula to find the area of a square is;
Area = x²
Where x is the side length of the square.
Thus;
x = √41
Now, since all sides of a square are always equal, we can easily say that the length of each side of the given tilted square is √41 units.
Thus, our conclusion is that the length of each side of the given tilted square is √41 units.
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Write and solve a system of equations for each problem situation. Interpret the solution in terms of context.
Pedro has 97 athlete cards. In his collection, he has 39 more baseball player cards than football player cards. How many of each type of card does Pedro have?
Number of each type of cards after solving system of equations for given situation of Pedro cards are 29 and68.
Interpretation is Pedro collected 29 football cards and 68 baseball cards.
As given,
Total number of cards=97
Let y=football cards
x=baseball cards
System of equations are
x + y=97 __(1)
x=y +39 __(2)
Substitute (2) in (1)
y+ 39 +y=97
⇒2y=58
⇒y=29
Substitute y=29 in (2),
x=29 +39
=68
Therefore, number of each type of cards after solving system of equations are football cards 29 and baseball cards 68.
Interpretation is Pedro collected 29 football cards and 68 baseball cards.
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a sailmaker is designing a mainsail for a newly constructed sailboat. the mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 52° angle at the head with the leach.
So, Part A:
By employing the sines law,
SinA/10 = SinB/13SinA/10 = Sin50/13A = 36.10C = 180-(180-36.10)C = 93.90So,
Sin36.10 / a = Sin50/ b = Sin93.90/cSin36.10 / 10 = Sin50/ 13 = Sin93.90/cc = Sin93.90 × 13 ÷ Sin50c = 16.93 ftNow, Part B:
Area of the mainsail:
= 1/2 × abSinC= 1/2 × 10 × 13 × Sin93.90= 64.85Therefore, the answers to both parts are:
(A) The mainsail foot is 13 feet long, the luff is 10 feet long, the leach is 6.93 feet long, and the mainsail area is 64.85 ft².(B) The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff forms a 50° angle with the leach at the head, requiring the length of the leach and the area of the mainsail.Know more about sines law here:
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The complete question is given below:
A sailmaker is designing a mainsail for a newly constructed sailboat. The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 50° angle at the head with the leach.
Part A: Determine the length of the leach.
Part B: Find the area of the mainsail.
PLS HELP :) 50 POINTS!!!
heidi was able to walk 2/3 of a mile in 12 minutes how far could heidi walk in 1 hour
Heidi is able to walk 10/3 miles in 1 hour (60 min).
What is described as unitary method?It is a method for determining the value of a single unit by subtracting the value of multiple units and subtracting the value of multiple units from of the value of a single unit.
The value of many items is given in the unitary method, and we must either determine the worth of more or fewer items. To do so, we must first determine the value of one item by division and then determine the value of more as well as fewer items by multiplication.Now, for the given question;
It takes Heidi 12 minutes to walk 2/3 miles.
Applying the unitary method.
Then, for in 1 minutes Heidi will walk = 2/(3×12).
For walking in 1 hour or 60 min = (2×60)/(3×12).
Further simplifying;
In 1 hour = 10/3 miles.
Therefore, Heidi would be be able to walk 10/3 miles in 1 hour.
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Can someone please help I will be giving Brainliest to whoever can answer :)
Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)
1. A = {(x, y): y > x^2}
2. B = {(x, y): y ≥ x^2+ 3}
3. C = {(x, y): y ≤ 3x^2 + 2}
4. D = {(x, y): y ≥ 2x^2- 5x + 1}
5. E = {(x, y): 16 ≤ x^2+ y^2 ≤ 25}
6. x^2- 3x ≥ 0
7. x^2- 3x + 2 ≤ 0
8. {(x, y): y ≤ 1 - x^2} and {(x, y): y ≥ -1}
The questions are matched with the graphs that are labeled A-H. (
1. A = {(x, y): y > x^2} Matching answer D2. B = {(x, y): y ≥ x^2+ 3} Matching answer G3. C = {(x, y): y ≤ 3x^2 + 2} Matching answer C4. D = {(x, y): y ≥ 2x^2- 5x + 1} Matching answer A5. E = {(x, y): 16 ≤ x^2+ y^2 ≤ 25} Matching answer F6. x^2- 3x ≥ 0 Matching answer J (the curve should be solid line)7. x^2- 3x + 2 ≤ 0 Matching answer E8. {(x, y): y ≤ 1 - x^2} and {(x, y): y ≥ -1} Matching answer BHow to find the matching graphThe graph has some rules for matching them to the equation some of the rules are:
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You are swimming each 25-yard length of a swimming pool 3 seconds
faster than your personal best. What integer represents your change in
time of your personal best after 200 yards?
24 seconds faster time of your personal best after 200 yards.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Suppose the number of laps = m
According to the question, each lap of 25 yards is covered 3 seconds faster than the previous one, so the series become
x , x-3 , x-6 , x-9, ............................
25 * m = 200
m = 200/25
m = 8
As m is the number of laps, and each lap is 3 second faster.
So 8 laps will be 8*3 = 24 seconds faster.
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WILL GIVE YOU BRAINILEST or however you spell it
BIRDHOUSES Ebony can build 0.7 birdhouse in 1 day. How many birdhouses can she build in 10 weeks?
Step-by-step explanation:
0.7 birdhouses in 1 day.
how many in 10 weeks ?
for that we need to know how many days are in 10 weeks.
1 week = 7 days
assuming that she is working on the birdhouses also on weekends, that means 10 weeks = 10×7 = 70 days.
and that means she can build
0.7 × 70 = 49 birdhouses in 10 weeks.
now, if she works only Monday to Friday on the birdhouses, then that means
1 week = 5 days
and 10 weeks = 10×5 = 50 days.
and that means she can build
0.7 × 50 = 35 birdhouses in 10 weeks.
if there is really no other information about that, I would use the usual 7 days per week and the first solution (49).
Two ways to group 26 students
. The oxygen saturation of a lake is found by dividing the
amount of dissolved oxygen the lake water currently has
per liter by the dissolved oxygen capacity per liter of the
water, and then converting that number into a percent.
If the lake currently has 6.4 milligrams of dissolved oxy-
gen per liter of water and the dissolved oxygen capacity
is 9.5 milligrams per liter, what is the oxygen saturation
level of the lake, to the nearest percent?
A. 64%
B. 67%
C. 70%
D. 89%
E. 95%
Answer:
70% i think
Step-by-step explanation:
George was solving the equation (2x-1)(x+3)=4 and he got the solution x=1/2 and x=-3. Jeffrey came along and said, "You made a big mistake! You set each factor equal to zero, but it's not equal to zero, it's equal to 4. So you have to set each factor equal to 4 and then solve." Who is correct? Show George and Jeffrey how to solve this equation. To be sure that you are correct, check your solutions.
The solution to the system of equation is -7/2 and 1
Solving linear equationAn algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.
Given the quadratic equation below;
(2x-1)(x+3)=4
Expand
2x^2+6x-x-3 = 4
2x^2+5x-3-4=0
2x^2+5x-7=0
2x^2-2x+7x-7=0
2x(x-1)+7(x-1) = 0
2x+7 = 0 and x - 1 = 0
x = -7/2 and x = 1
Hence the solution to the system of equation is -7/2 and 1
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Is ✓225 + ✓196 a rational or irrational number?
Answer:
yes
Step-by-step explanation:
√225 + √196
15 + 14
29
29 can be written as 29/1 thus 29 is a rational number
Can someone help me out
Answer:
I believe its graph 4 (not sure though, you can plug in some values to make sure)
Step-by-step explanation:
Please answer these two questions!
Answer:
The answer to your first question would be B. The answer to the second is C.
Step-by-step explanation:
Hope it helps! =D
Can someone help me
Answer: well look you can fid live tutors
Step-by-step explanation:
n vcxvbnm
There are 26 kids who have either black or red pencils.
15 of them have red
21 of them have black
How many kids have both
Answer:
this doesn't make sense cuz 15 have red 21 have black and that's 36 kids but the title says there is 21 kids in all ?
Step-by-step explanation:
Which algebraic expression represents each verbal expression?
a. the product of five and a number, decreased by eleven
b. the sum of a number and five less than eleven
c. five times a number fewer than eleven
d. the quantity of a number minus eleven, multiplied by five
Answer:
A) 5n − 11
B) 11 − (n + 5)
C) 11 − 5n
D) 5(n − 11)
Your Welcome ;)
The required verbal algebraic expressions are given as ,
(a) 5x - 11 (b) (x + 5) - 11
(c) 5x - 11 (d) (x - 11)×5
What is an algebraic expression?The algebraic expression consists of constants and variables. eg x, y, z etc.
Here,
Let the number x,
a. The product of five and a number, decreased by eleven
⇒ 5x - 11
b. The sum of a number and five less than eleven
⇒ (x + 5) - 11
c. Five times a number fewer than eleven
⇒5x - 11
d. The quantity of a number minus eleven, multiplied by five
⇒(x - 11)×5
Thus, the required expression is shown above
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Evaluate.
2/5 exponent 2
Answer: 4/25
Step-by-step explanation:
[tex](\frac{2}{5}) ^2=\frac{2}{5}\times\frac{2}{5}=\large\boxed{\frac{4}{25} }[/tex]
Say you are given the graph of the line y = -x. Write the equation of the line that is perpendicular to the given line and goes through the point (-8, 2).
Linear equations are often organized in slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptTo find a linear equation, we often first solve for the slope, and then solve for the y-intercept algebraically.
To find the slope of a perpendicular line, we must find the negative reciprocal of the slope of the reference line.
Solving the Question
We're given:
Reference line is [tex]y=-x[/tex]Perpendicular line passes through [tex](-8,2)[/tex]1) Find the slope of the reference line
We can rewrite the reference line to be clearer in slope-intercept form:
[tex]y=-1x+0[/tex]
This means that -1 is the slope.
2) Find the slope of the perpendicular line
The negative reciprocal of -1 is 1. Therefore, the slope of the perpendicular line is 1. Plug this into slope-intercept form:
[tex]y=x+b[/tex]
3) Solve for the y-intercept of the perpendicular line
[tex]y=x+b[/tex]
Plug in the given point (-8,2) and solve for b:
[tex]2=-8+b\\b=2+8\\b=10[/tex]
Therefore, the y-intercept of the perpendicular line is 10. Plug this back into our original equation:
[tex]y=x+10[/tex]
Answer[tex]y=x+10[/tex]