Find the slope and y intercept of the line through the point (9,10) that cuts off the least area from the first quadrant
The slope of the line is -10/9 and the value of y-intercept of the line is 50/3.
Slope of the line:
A slope of a line is the change in y coordinate with respect to the change in x coordinate.
Given,
The point (9,10) that cuts off the least area from the first quadrant
Here we need to find the slope and y intercept of the line.
A line is passing through a point (9,10) cuts off least area in first quadrant.
The equation of the line passing through point (9,10) and has slope m can be expressed as,
=> y - 10 = m (x - 9)
=> y = m(x - 9) + 10
=> y - mx = - 9m + 10
Divide the terms by - 9m + 10, then we get,
=> (y/- 9m+10) - (mx/ - 9m+10) = 1
=> (mx/9m+10) - (y/9m+10) = 1
It can be rewritten as,
[tex]\implies\frac{x}{\frac{9m-10}{m}} -\frac{y}{10-9m}[/tex]
We know that,
The equation of straight line in intercept form is
=> x/a + y/b = 1
So, the intercept made by the line on x-axis i.e. a and on y-axis i.e. b are:
a = 9m-10/m
b = 10 - 9m
The area of the triangle made by the line in first quadrant can be expressed as,
=> A = 1/2 x (9m-10/m) x (10 - 9m)
=> A = -1/2 (9m-10)²/m-----------------------(1)
Differentiate the equation (1) with respect to m.
[tex]\frac{dA}{dm}=-\frac{1}{2}[\frac{2m(9m-10).9-(9m-10)^2}{m^2}][/tex]
[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[2m.9-(9m-10)][/tex]
[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[18m-9m-10)][/tex]
when we simplify it,
=> dA/dm = -(9m-10)/2m² [9m-10]
Let dA/dm = 0, then
=> 0 = -1/2m² (9m-10)(9m-10)
=> 0 = 1/m² (10-9m)(9m-10)
=> 0 = (10 - 9m) (9m -10)
Therefore, the value of m is,
=> 10 - 9m = 0
=> -9m = -10
=> m = 10/9
And
=> 9m - 10 =0
=> 9m = 10
=> m = 10/9
The line will be in first quadrant and forms a triangle with axes if the slope is negative.
Substitute m = -10/9
Then, b = 10-9m
Then,
=> y = 10 - 6(-10/9)
=> y = 10 + 20/3
=> y = 50/3
So, the slope of the line is -10/9 and the value of y-intercept of the line is 50/3.
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In a triangle the measure of the first angle is 24 degrees more than the second angle. the measure of the third angle is four times the measure of the second angle. if the total number of degrees in a triangle is 180 what is the measure of the largest angle?
The greatest angle in the given triangle is 104 degrees.
What is a triangle?The polygon with 3 sides, three vertices, and three angles is known as a triangle. A triangle's overall number of degrees is always 180 degrees.Given:
Let, the second angle has a measurement of x degrees.The first angle's measurement is 24 degrees greater than the second angle's measurement. As a result, the first angle is (24+x) degrees.The third angle is four times as large as the second. As a result, the third angle has a measure of 4x.So,
(24 + x) + x + 4x = 1806x = 124 - 486x = 156x = 156/6x = 26As a result, the second angle has a measurement of 26 degrees.
The first angle's measurement is now 24 degrees greater than the second angle's measurement.
Now,
= 24 + 26= 50As a result, the first angle has a measure of 50 degrees.
The third angle is now four times the size of the second angle.
So,
4 × 26 = 104Therefore, the greatest angle in the given triangle is 104 degrees.
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Directions: Determine whether each relation is a function. Explain your answer.
7) No, y has two different values when x = -1.
8) Yes, each value of x maps onto only one value of y.
9) Yes, each value of x maps onto only one value of y.
EASY PLEASE HELP I NEED ANSWER TO SEVEN
Answer: a, 9x10^9, largest number 900000000
Answer: greatest is A.
Step-by-step explanation:
Find the value of x using the diagram below.
Given x is Complimentary angle
Also, line1 is parallel to line2
Thus,
x [tex]+[/tex] 139° [tex]=[/tex] 132° [Alternate angle]
x [tex]=[/tex] 132°[tex]_[/tex][tex]_[/tex]- 139°
x[tex]=[/tex] -7°
What is Complimentary angle?
When two angles are added together, complementary angles are defined. When the total of the two angles is 90 degrees, we get a pair of complimentary angles. In other terms, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.
If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complimentary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.
60° + 30° in the illustration below equals 90°. These two angles are therefore complimentary according to the "Definition of Complementary Angles." The term "complement" refers to each angle that is one of the complimentary angles. Here,
The opposite of 30° is 60°.
The opposite of 60° is 30°.
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j^² - 5k for j = -4 and k = -1
Answer:
21
Step-by-step explanation:
Hello!
Substitute the values of j and k and evaluate.
Evaluate[tex]j^2 - 5k[/tex][tex](-4)^2 - 5(-1)[/tex][tex]16 + 5[/tex][tex]21\\[/tex]The evaluated value is 21.
Consider this solution to a problem. what is the number of the step where the mistake is made? question 4 options: step 1 step 2 step 3 step 4
In step 1 mistake has been made because negative multiplication gives a positive result but is written negative.
What is the equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.
Given that,
−4(6−y) + 4 = −4
By using distribution property
-24 + 4y + 4 = -4
But in the question +4y is written as -4y which is wrong.
Hence In step 1 negative multiplication gives a positive result but is written negative so in step 1 mistake has been made".
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The given question is not complete.
Consider this solution to a problem.
Problem: −4(6−y)+4=−4
Step 1: −24−4y+4=−4
Step 2: −20−4y=−4
Step 3: −4y=16
Step 4: y=−4
In the first response box, enter the number of the step where the mistake is made.
Complete the standard form equation representing the quadratic relationship displayed above, where a,b, and c are consonants.
Answer:
y = - 2x² + 8x + 5
Step-by-step explanation:
the equation of a quadratic function in standard form is
y = ax² + bx + c ( a ≠ 0 )
to find a, b and c use ordered pairs from the table
(0, 5 )
5 = a(0)² + b(0) + c = 0 + 0 + c = 5 ⇒ c = 5 , then
y = ax² + bx + 5
(1, 11 )
11 = a(1)² + b(1) + 5 = a + b + 5 ( subtract 5 from both sides )
a + b = 6 → (1)
(2, 13 )
13 = a(2)² + b(2) + 5 = 4a + 2b + 5 ( subtract 5 from both sides )
4a + 2b = 8 → (2)
solve the 2 equations simultaneously to find a and b
multiplying (1) by - 2 and adding to (2) will eliminate b
- 2a - 2b = - 12 → (3)
add (2) and (3) term by term to eliminate b
2a + 0 = - 4
2a = - 4 ( divide both sides by 2 )
a = - 2
substitute a = - 2 into (1) and solve for b
- 2 + b = 6 ( add 2 to both sides )
b = 8
then a = - 2, b = 8 and c = 5 gives the standard quadratic function
y = - 2x² + 8x + 5
Step-by-step explanation:
standard equation would be
y = ax² + bx + c
out of that we know already from (0, 5) that c = 5, as
a×0² + b×0 + c = 5.
because of (-1, -5) we see
-5 = a×1 + b×-1 + 5 = a - b + 5
-10 = a - b
or
a = b - 10
because of (1, 11) we see
11 = a×1 + b×1 + 5 = a + b + 5
6 = a + b
now we use the previous equation :
6 = (b - 10) + b = 2b - 10
16 = 2b
b = 8
.
a = b - 10 = 8 - 10 = -2
so, our standard equation is
y = -2x² + 8x + 5
It took 5 hours to drive to Durham to Birmingham. The average speed was 48mph. What was the distance from Durham to Birmingham?
I need the explanation
Answer:
240 miles
Step-by-step explanation:
Because it took 5 hours going 48 miles per hour, therefore 5 x 48 =240
How do i write the value of this underlined digit 2.439 and 1.987 and 6.175 0.618
The value of the underlined digit 2.439 , 1.987 , 6.175 , and 0.618 is equal to tenth, thousandth, Ones and tenth.
As given in the question,
Given number = 2.439 , 1.987 , 6.175 , and 0.618
Value of underlined digit :
2.439 = Tenth or 4 / 10
1.987 = Thousandth or 7/1000
6.175 = Ones or 6
0.618 = Hundredth or 1/100
Therefore, the value of the underlined digit 2.439 , 1.987 , 6.175 , and 0.618 is equal to tenth, thousandth, Ones and tenth.
The complete question is :
How do i write the value of this underlined digit 2.439 , 1.987 , 6.175 , and 0.618 ?
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what is the graph
picture below
pls helppppp for brainlest
Answer:
B
Step-by-step explanation:
5x + 4y >= 2
4y >= -5x + 2
y >= -5/4x + 1/2
Since the equation is >=, everything on or above the line y = -5/4x + 1/2 should be shaded.
whats the answer for 5x5/2
William paid $50 to his credit card and divided the rest of his paycheck evenly into a savings account, a checking account, and cash to spend for the week. he has $100 to spend for the week. write an equation to represent the situation. then solve.
The equation can be summarized as; p = $50 + 3($100 ). Hence William was paid $350.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
Let p represents the paycheck.
William paid her parents $50 for rent. After paying the rent he evenly divided the rest of the amount into three parts.
He puts $ 100 into her savings account. It means that he also puts $100 into checking account and $ 100 into retirement fund
If we put the parts together, the equation we get is;
p = $50 +$100 +$100 +$100
The equation can be summarized as;
p = $50 + 3($100 )
Now we can easily find how much was William paid;
p = $50 + 3($100)
p = $50 +$300
p = $350
Hence William was paid $350.
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I need help fast please and thank you
Answer:
Option a 340 cm²
Area= bxh
20x17=340 cm²
Select all of the terms that are "like."
x^2
2x^2y
-xy
1/2 xy
xy^2
2xy
The like terms are -xy, 1/2xy and 2xy
How to select all of the terms that are "like."?Like terms are expressions that have the same variable factor
Take for instance, 2x and 5x are like terms because their variable factors are x
Also, 5x and 2xy are not like terms
Using the above as a guide, the like terms are -xy, 1/2xy and 2xy
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PLSSSS HELPPPPPP IM STUCK ON THIS
Answer:
1. 15.17ft 2. 18.57ft 3. 22.41%
Step-by-step explanation:
1. What was the length of one side of the garage originally?
Area of a square = s × s which is also equal to s²
s means one side of the square, as it is a square, all sides are equal.
so
230 = s²
s = √230 = 15.17
2. What is the length of one side of the garage now?
The original area of the garage was 230ft²
But now, the area has increased by 50%
Increased Area = 230 × 50% = 115ft²
Total Area = 230 + 115 = 345ft²
In the question, they are saying that after the area is increased, the garage is still a square which means that the side lengths have equal values.
Area = s²
345 = s²
s = √345 = 18.57
3. What was the percentage increase of the length of one side?
Length : Percentage
15.17 : 100
18.57 : x
When the length of one side was 15.17, the percentage was 100% as that is what the original length was, we can use ratio and proportion to find what the percentage will be when the length is 18.57.
Now cross multiply
18.57 × 100 = 15.17x
1857 = 15.17x
1857/15.17 = x
x = 122. 41
The new percentage is 122.41%
The difference between both percentages is:
122.41 - 100 = 22.41
And 22.41 is the percentage increase.
Write an absolute value inequality for the graph below.
Use x for your variable.
Answer:
The absolute value inequality will be |x| ≥ -2.
Step-by-step explanation:
solve the similtaneous equations
y=9-x
y=2x^2+4x+6
The solution of the given equation are (1/2 , 17/2) and (-3 , 12)
The two equation that we have been given are :
y = 9 – x (1)
y = 2x² + 4x + 6 (2)
We will solve this simultaneously, from equation (1) we will equate the value of y in equation (2) we get
9 – x = 2x² + 4x + 6
3 = 2x² + 5x
2x² + 5x – 3 = 0
Now to find the factors of the value x we will use quadratic formula.
x = (-b±√b² – 4ac)/2a
x = [ -5 ± √25 + 24 ]/4
x = [ -5 ± 7 ]/4
x = (-5 + 7)/4 and x = (-5 – 7)/4
x = 1/2 and x= -3
putting the required value of x in equation (1) we get
y = 9 – 1/2 and y = 9 – (-3)
y = 17/2 and y = 12
Hence the solution of the equation is (1/2 , 17/2) and (-3 , 12)
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Which graph represents the function h (x) = -√x+2?
Answer:
Step-by-step explanation:
See the attached file below it will help to understand this problem and it will improve your grade and score.
(PLS HURRY ASAP 100 POINTS)
(Theoretical Probability MC)
The tree diagram represents the sample space for the repeated experiment of a coin being tossed 4 times.
Determine P(at least 3 tails).
A: 0.025
B: 0.0625
C: 0.125
D: 0.3125
Answer:
D) 0.3125====================
Total number of outcomes is 16, count of all outcomes.
Number of outcomes with 3 or more tiles is 5:
HTTT, THTT, TTHT, TTTH, TTTTThe probability is:
P = favorable outcomes / total outcomesP(at least 3 tails) = 5/16 = 0.3125Correct choice is D.
helppppppppppppppppppp
Answer:
19
Step-by-step explanation:
5w+3°=98°
5w=98°-3°
5w=95°
therefore w=95/5=19
m Ixl math...............
Answer:
baby help you with what? All i can do is pray for you,
Step-by-step explanation:
matter of fact bow yo head..............Amen
A 7-year-old boy was struck by a car while riding his bicycle. his bp is 60/40 mm hg, pulse is 160 beats/min, and respirations are 34 breaths/min. how much iv fluid should you administer per bolus?
If the boy is riding a bicycle and gets stuck or got accident by a car, 440ml of IV fluid will be administered.
What should be done to provide first assistance in the event of an accident?To avoid further injury, place the victim on the ground very gently and slowly without handling vigorously. In one direction, tilt the sufferer. Dress loosely around the waist, chest, and neck. So that the tongue can fall forward and allow blood and vomit to drain out, tilt your head back and slightly downward. When you come across an accident victim, the first thing you need to determine is whether the victim's body has sustained any physical wounds. Depending on how severe the collision was, you might not be able to see any inside injuries, but you will see a few exterior ones.
In a car accident, spine injuries and head trauma are common. Therefore, be aware that rough handling of the sufferer will result in additional injuries while opting to assist the victim in moving to a safer location on the road. Therefore, request any onlookers to carefully assist in moving the sufferer to a location near the road where it will be safer.
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Write each equation in function notation. y=12+3/4x
Step-by-step explanation:
y = f(x)
this has the same meaning. y is just the variable for the functional result value. while x is usually used as variable for the input value.
so (I recommend to use the brackets to make sure that people understand it is meant that x gets multilevel by 3 in the numerator, and not by 4 in the denominator),
y = 12 + (3/4)x
is the same as
f(x) = 12 + (3/4)x
you could also write it as
f(x) = 12 + 3x/4
don't skip things, always think about the rules of the sequence of the operations in an expression, and how a reader could understand it. always be as precise, complete and consistent as possible.
PLS HELP A LITTLE LOST Sally is 3 years younger than Sue. The sum of their ages is 27. How old is Sally?
Answer:
Sally is 12 years old.
Step-by-step explanation:
[tex]2x+3=27\\2x+3-3=27-3\\2x=24\\\frac{2x}{2}=\frac{24}{2}\\x=12[/tex]
A huge 52-foot subway sandwich is cut into 7 pieces. There are five pieces one length, and the other two pieces are five feet longer. What is the length of the larger pieces?
Based on the length of the subway sandwich, the length of the larger pieces is 11 feet.
How long are the larger pieces?Assume that the length of the shorter pieces is x.
The length of the larger pieces is therefore 5 + x.
The relevant equation to find the length is:
52 = x + x + x + x +x + 5 + x + 5 + x
52 = 7x + 10
x = (52 - 10) / 7
= 6 foot
The length of the larger pieces is:
= 5 + x
= 5 + 6
= 11 foot
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find the value of x ?
The value of x from the given diagram is 64 degrees
Lines and anglesA line is defined as the shortest distance between two points. From the given diagram, we have that the line AB bisects FAB, hence;
<FAB = <CAB = 58 degrees
Also since the sum of angles on a straight line is 180 degrees, hence;
58 + 58 + x = 180
116 + x = 180
x = 180 - 116
x = 64 degrees
Hence the value of x from the given diagram is 64 degrees
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Kofi is 5years older than Ama now. Two years ago, Kofi was twice as old as Ama. Find their ages now.
Answer:
Ama is an elephant so she is 2 years old
Step-by-step explanation:
find the midpoint of each line segment. WILL GIVE BRAINLIEST!!
one on right is 2,-2 and one on left is -1,1
Scatter plots are used to visualize association in samples of paired data (x, y). group starts
a. true
b. false