A curve is given the equation xy=25 and the equation of a line y=mx+b.
i. Express m in terms of b given that the line and the curve have one and only one point of intersection.
ii. If the line intersects the curve in two distinct points, find the set of values of b, given m=-5
Answer:
Below in bold.
Step-by-step explanation:
i, This is a rectangular hyperbola with symmetry about the line y = -x
If it touches the graph at one point only then
y = 25/x
y = mx + b so
25/x = mx + b
mx^2 + bx + 25 = 0
Using the quadratic formula:
x = (-b + sqrt(b^2 - 25*4*m)) / 2m
Now there's only one value of x so
b^2 - 25*4*m = 0
b^2 = 100m
m = b^2/100.
m = +/-b/10.
ii In this case b^2 > 100m
If m = |-5|
b^2 > 500
b > +/-√500
So b > √500 or b < -√500.
What is the quotient of the fractions below? 3/5 divided by 2/3?
A. 2/5
B. 10/9
C. 9/10
D. 5/2
HUURRYYY!!!
Answer:
9/10
Step-by-step explanation:
WILL GIVE BRAINLIEST IF BOTH QUESTIONS ARE CORRECT!!!
Answer:
69824.21
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Step-by-step explanation:
Find the indicated side of the
triangle.
a
7.
30°
D
b = [ ? IV
serious answers only<3 i really need to get this done before i get grounded and i used to be good at math but during quarantine all of my skill just went away
Answer:
-3 1/2
Step-by-step explanation:
-4.5 + 1 = -3.5
You throw two dice. What is the probability of rolling a sum of 6 given that you rolled a sum that is greater than 4?Ill give BRAINLEST to best answer with explanation
Answer:
8/12
Step-by-step explanation:
if you have 2 dice and roll them t the same time you have 11 possible outcomes. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. If you roll something higher then a 4 then you get left with 5, 6, 7, 8, 9, 10, 11, 12. If you count them there is 8 different outcomes you can get out of the 2 dice since the highest you can roll is a 12.
A scale diagram of an Amoeba (a single celled organism) is 5cm wide, representing the real-life Amoeba's width of 0.1mm. Determine the scale factor of the scale diagram and select the best answer choice below. (note: there are 10 millimeters in 1 cm)
choose the correct vertical asymptote(s).
Glven the function, f(x) =
x+1
X-4
O x= -4, x= 4
O x= 4
O x= -2, x = 2
O x= 2
Tran is using a coordinate plane to design a treasure hunt for his students. The hunt begins at the flagpole at the origin. The first clue is hidden 5 units north of the flagpole. The second clue is located 6 units east of the flagpole. The final clue is located 5 units south of the flagpole. Plot the locations of the flagpole and the 3 clues on the coordinate plane and show the path students will follow from the flagpole to all three clues. . Each unit represents 50 feet. What is the shortest combined distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3?
Answer:
The shortest combined distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 is approximately 1,031.025 feet
Step-by-step explanation:
The given coordinates of the clues for the treasure hunt are
The location of the first clue = 5 units north of the flag pole
The coordinates is (0, 5)
The location of the second clue = 6 units east of the flag pole
The coordinates is (6, 0)
The location of the final clue = 5 units south of the flag pole
The coordinates is (0, -5)
The flagpole is at the origin
The coordinates of the flagpole is (0, 0)
Each unit on the graph = 50 feet
From the drawing of the treasure hunt created with Microsoft Excel, the shortest distances between the clues are as follows;
The shortest distance between 2 points is a straight line
Therefore
The shortest length from the flagpole to Clue 1 = 5 - 0 = 5 units
The actual distance from the flagpole to Clue 1 = 5 units × 50 feet/unit = 250 feet
The length from Clue 1 to Clue 2= √(6² + 5²) = √(61) units
The actual distance from Clue 1 to Clue 2 = √(61) units × 50 feet/unit = 50·√61 feet
By similarity, the actual distance from Clue 2 to Clue 3 = 50·√61
The combined shortest distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 = (250 + 50·√61 + 50·√61) feet ≈ 1,031.025 feet
John saved up enough money to buy a $20 can of shoe shine after paying for the $150 pair of Nikes. How much money did he save in all?
Answer:
170$
Step-by-step explanation:
150+20=170
Answer:
Step-by-step explanation:
170
Which of these expressions would be the best estimate of the quotient 15 1/2 ÷ 3 2/3?
A. 15÷3
B. 15÷4
C. 16÷3
D. 16÷4
Answer:
D
Step-by-step explanation:
Because 15 1/2 ÷ 3 2/3 equals 4.22727272727 and 15 divided by 3 is 5, 15 divided b 4 = 3.75 16 divided by 3 is 5.33333333333 and 16 divided by 4 equals 4 so thats the closest answer
Hope this helps
Please Help Me!! Will Give Brainliest!!!
What is the area of the trapezoid below
Answer:
[tex]Area: 29 cm^{2}[/tex]
Step-by-step explanation:
[tex]Aear=(8.5+6)(\frac{4}{5} )[/tex]
[tex]Area=14.5 (2)[/tex]
[tex]Area=29[/tex]
----------------------
hope it helps...
have a great day!!
Alice found the area of the figure by breaking apart it apart where the dashed line is drawn. Her work is shown below. area of rectangle = bh = 6(2) = 12 mm2 area of triangle = bh = 2(2) = 4 mm2 area of figure = 12 + 4 = 16 mm2 A figure can be broken into a rectangle and triangle. The rectangle has a base of 6 millimeters and height of 2 millimeters. The triangle has a base of 2 millimeters an height of 2 millimeters. What error did Alice make? She didn’t use the correct formula for area of a triangle. She didn’t use the correct formula for area of a rectangle. She didn’t find the height of the triangle correctly. She didn’t add the areas of the triangle and rectangle correctly.
Answer:
She didn’t use the correct formula for area of a triangle.
Step-by-step explanation:
edg 2021 Sorry for the late answer.
F(x)=400-4/5x find the function and intercepts
Answer:
The x-intercept is (500, 0); the y-intercept is (0, 400).
Step-by-step explanation:
F(x)=400-4/5x is already a function: a function of x.
To find the y-intercept, set x = 0 and calculate F(0):
F(0) = 400 - 0 = 400; the y-intercept is (0, 400).
To find the x-intercept, set F(x) = y = 0 and solve for x:
0 = F(x) = 400 - (4/5)x, or (4/5)x = 400. To isolate x, multiply both
sides by (5/4): x = (5/4)(400) = 500. The x-intercept is (500, 0).
what is this help me out pls
Answer:
That would be -2n - 1.
Answer:
-2n - 1
Step-by-step explanation:
You have to combine like term which would be 4n,n,and 7n.
Since n doesn't have a variable just add a one in front. So now the equation would be
1n+4n-7n That equation equals -2n
Now just add the remaining number
So that makes the answer -2n -1
Which two consecutive integers does -√138 lie between?
A:11 and 12
B:12 and 13
C:-11 and -12
D:-12 and -13
Answer:
C:-11 and -12
[tex] - \sqrt{138} \\ = - 11.747 \\ - 11 < x < - 12[/tex]
which set of side lengths will form a right triangle 8,15,17
7,24,26
6,8,11
10,24,25
1-point free throw 2-point field goal he made 35 shots he scored 62 points how many of each shot does he make in 1 minute write the two equations for the problem
Answer:
x + y = 35 equation 1
x + 2y = 62 equation 2
He made 8 1 point free throw
He made 27 2 point field goal
Step-by-step explanation:
let x = 1 point free throw
y = 2 point field goal
two equations can be derived from the question
x + y = 35 equation 1
x + 2y = 62 equation 2
Subtract equation 1 from 2
y = 27
Substitute for x in equation 1
x = 35 - 27 = 8
He made 8 1 point free throw
He made 27 2 point field goal
Help plz i will give brainliest!!
SOMEONE PLS HELP ME FIND THE AREA OF THIS COMPOSITE FIGURE. ILL GIVE BRAINLIEST!
Help me please !!!!!!
Answer:
The y-int represents the base price of $200 for airfare from NYC
The slope represents a cost of 30 cents per mile traveled
If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y=50+0.30x
If the cost per mile changed to 50 cents, the new equation would be y=200+0.50x
what is the height of a rectangular prism that has a volume of 2880 cubic inches and a base of 240 inches
Answer:
h = 12 in
Step-by-step explanation:
To find the height, divide the volume by the base:
2880 in^3
height: ------------------ = 12 in
240 in
help please i don’t get it
The ratio of the areas of two smaller similar quadrilaterals is 81/16. The perimeter of the smaller is 32 centimeters. What is the perimeter of larger quadilaterals
A rectangular tank with length 50 cm and width 30 cm contains 36 litres of water. Find the depth of the water.
Answer:
24cm
Step-by-step explanation:
Given data
Length=50cm
Width= 30cm
Volume = 36liters
=36000cm^3
We know that the expression for volume is
V= L*W*H
substitute
36000=50*30*H
36000= 1500*H
H= 36000/1500
H= 24cm
Hence the height is 24cm
Kaylee read 19 1/2 pages in 3/4 of an hour. If she continues reading at the same rate,
how many pages will she read in an hour?
Answer: The answer is 26.
Step-by-step explanation:
Simple, find the unit rate. That's 19.5 / 0.75 = 26.
or using fractions:
19 2/4 divided by 3/4
78/4 divided by 3/4
78 / 3 = 26
4 / 4 = 1
Unit rate = 26books/1 hour
a line is reflected. Which of these could be the result? Pls help
Answer:
A
Step-by-step explanation:
Answer:
The answer is A.
Step-by-step explanation:
AP EX
Type the correct answer in each box. Use numerals instead of words.
Consider the quadratic equation x² + 10x + 27 = 0.
Completing the square leads to the equivalent equation (x + ___)² = ___.
.
Answer:
(x + 5)² = 2 ==> x² + 10x + 27 = 0
Completing the square of the given quadratic equation leads to the equivalent equation (x + 5)² = -2.
What are Quadratic Equations?Quadratic equations are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given quadratic equation is,
x² + 10x + 27 = 0
We have the algebraic identity that,
(a + b)² = a² + 2ab + b²
The given quadratic equation is in the form of a² + 2ab + b², where a = x.
So, 2xb = 10x
⇒ b = 5
Now, b² = 25.
So, the given can be written as,
(x² + 10x + 25) + 2 = 0
(x + 5)² = -2
Hence the equivalent form is (x + 5)² = -2.
Learn more about Quadratic Equations here :
https://brainly.com/question/12014272
#SPJ7
plzz help if right i give brainliest
Answer:
b. (x+6)(x-6)
Step-by-step explanation:
x^2-36 So to get to this answer you can do two things
1. Guess and check
2. Factor it out (which is what I like to do)
In order to get x^2 you need 2xs that are positive which knocks out c and d
Then to get to -36, you need to multiply a positive 6 and a negative 6
(This was poorly explained but if you need anymore help just lmk)