Answer:
[tex]-6 < k < 2[/tex]
Step-by-step explanation:
Given
[tex]y = x^2 - 2x[/tex]
[tex]y =kx -4[/tex]
Required
Possible values of k
The general quadratic equation is:
[tex]ax^2 + bx + c = 0[/tex]
Subtract [tex]y = x^2 - 2x[/tex] and [tex]y =kx -4[/tex]
[tex]y - y = x^2 - 2x - kx +4[/tex]
[tex]0 = x^2 - 2x - kx +4[/tex]
Factorize:
[tex]0 = x^2 +x(-2 - k) +4[/tex]
Rewrite as:
[tex]x^2 +x(-2 - k) +4=0[/tex]
Compare the above equation to: [tex]ax^2 + bx + c = 0[/tex]
[tex]a = 1[/tex]
[tex]b= -2-k[/tex]
[tex]c =4[/tex]
For the equation to have two distinct solution, the following must be true:
[tex]b^2 - 4ac > 0[/tex]
So, we have:
[tex](-2-k)^2 -4*1*4>0[/tex]
[tex](-2-k)^2 -16>0[/tex]
Expand
[tex]4 +4k+k^2-16>0[/tex]
Rewrite as:
[tex]k^2 + 4k - 16 + 4 >0[/tex]
[tex]k^2 + 4k - 12 >0[/tex]
Expand
[tex]k^2 + 6k-2k - 12 >0[/tex]
Factorize
[tex]k(k + 6)-2(k + 6) >0[/tex]
Factor out k + 6
[tex](k -2)(k + 6) >0[/tex]
Split:
[tex]k -2 > 0[/tex] or [tex]k + 6> 0[/tex]
So:
[tex]k > 2[/tex] or k [tex]> -6[/tex]
To make the above inequality true, we set:
[tex]k < 2[/tex] or [tex]k >-6[/tex]
So, the set of values of k is:
[tex]-6 < k < 2[/tex]
need help with this Q&A 3
Answer:
the second option
yes, because they are similar triangles
Step-by-step explanation:
the scaling factor is 3
3×3 = 9
3×7 = 21
so, the ratios of the sides remain the same, and the 90 degree angle remains the same. therefore, just one triangle is larger than the other, but the relative attributes and even the orientation are the same, so yes, since we don't know the absolute coordinates of the corners, indeed, the Hypotenuse of both triangles could be on the same line.
What is the average rate of change of f
over the interval (-5,0]?
Give an exact number.
Answer:
Average rate of change = 0.6
Step-by-step explanation:
Average rate of change of a function between x = a and x = b is given by,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
From the graph attached,
f(-5) = 0
f(0) = 3
Average rate of change of the graph between x = -5 and x = 0,
Average rate of change = [tex]\frac{3-0}{0-(-5)}[/tex]
= [tex]\frac{3}{5}[/tex]
= 0.6
Therefore, average rate of change of the given function between x = -5 and x = 0 is 0.6.
A squash ball is thrown from the top of a building and falls to the ground below. The height of the ball above the ground is approximated by the relation h=-6t^2+24t + 30, where h is the height above the ground in metres and t is the elapsed time in seconds. Determine the maximum height that is reached by the ball. Show all your work.
Step-by-step explanation:
the answer is 6 ft and all my workings are in the image above
Samuel places a ladder against his house. The base of the ladder is 6 feet from
the house and the ladder is 10 feet long. How high above the ground does the ladder
touch the wall of the house?
Answer: 60 ft
Step-by-step explanation: If you multiply 6 x 10 = 60 and there both in feet so the answer whould be 60ft
solutia reala a ecuatiei 4x la a doua = 6 intregi si 1/4 (dau coroana)
Answer:
x = + 5/4 or x = - 5/4
Step-by-step explanation:
[tex]4 x^2 = 6\frac{1}{4}\\\\4 x^2 = \frac{25}{4}\\\\x^2 =\frac{25}{16}\\\\x = \pm \frac{5}{4}[/tex]
use the diagram to find the value of x
Answer:
4
Step-by-step explanation:
18x = 12(x+2)
18x = 12x+24
18x-12x = 24
6x = 24
x = 4
What is the first step in solving quadratic equations by finding square roots? a. give the positive and negative answer c. square root both sides to isolate x b. isolate the x squared by using inverse operations d. none of these Please select the best answer from the choices provided A B C D
Answer:
C: isolate the x squared by using inverse operations
Step-by-step explanation:
This method of solving quadratic equation is used when there is only x² term and no x term. Thus;
For example, we have a quadratic equation;
x² - 1 = 80
To solve this by square root method, the first step we have to take is to isolate the x² term by inverse operation which is by addition of 1 to both sides to get rid of the -1 on the left side so that x² can be isolated.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Solve each equation. Leave the answer as an improper fraction.
16x2 = 49
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Answer:
Given : isosceles right triangle hypotenuse = 8 cm
To find : leg of isosceles right triangle
Solution
isosceles right triangle
Hence Perpendicular = base
Both legs are of Equal length
Applying Pythagoras theorem
Perpendicular² + base² = Hypotenuse²
Hypotenuse = 8 cm given
=> Perpendicular² + base² = 8²
Perpendicular = base = x
=> x² + x² = 64
=> 2x² = 64
=> x² = 32
=> x = 4√2
legs of isosceles right triangle whose hypotenuse is 8 cm
are 4√2 cm
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
I was doing my khan and i got stuck
6=2(y+2)
Answer:
[tex]y=1[/tex]
Step-by-step explanation:
Given:
[tex]6=2(y+2)[/tex]
Distribute the parenthesis
[tex]6=2y+4[/tex]
Subtract both sides by 4
[tex]2=2y[/tex]
Divide both sides by 2 to get [tex]y[/tex] alone
[tex]1=y[/tex]
Hope this is helpful
Find the exact value of x.
Answer:
24
Step-by-step explanation:
4 times 4
8 times 8
Subtract the 2 #'s
Then divide your answer by 2.
Step-by-step explanation:
use Pythagoras theorem
hypotenuse² = base² + height²
8²=base²+4²
64-16=B²
√48=B
√2×3×2×2×2=B
2×2√3
4√3 = B
hope it helps
Which quadratic is written in graphing formRequired to answer. Single choice.
(10 Points)
f(x ) = 2x+4x^2+10
f(x ) = (x+2)^2+4
f(x) = (x+5)(x+4)
f(x) = 3x +7
Answer:
option B
Step-by-step explanation:
Option B is in vertex (or graphing ) form.
recall the equation for graphing form of a quadratic is
[tex]y = (x - h)^{2} + k[/tex]
Please help 50 points
Simplify the expression
Answer:
c
Step-by-step explanation:
A hat contains slips of paper with the names of the 26 other students in Eduardo’s class on them, 10 of whom are boys. To determine his partners for the group project, Eduardo has to pull two names out of the hat without replacing them.
What is the probability that both of Eduardo’s partners for the group project will not be boys?
StartFraction 9 Over 65 EndFraction
StartFraction 24 Over 65 EndFraction
StartFraction 64 Over 169 EndFraction
StartFraction 128 Over 325 EndFraction
Answer:
24/65
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
edge 2023
1. Convert the quinary number 42 into binary number.
Answer:
42 in binary number is 101010.
2. What is the mode for the data set 13, 11, 10, 12, 14, 9,
11, 8, 11?
A.10
B. 11
C. 12
D. none of the above
Answer:
11
Step-by-step explanation:
mode is the number that is most frequent
11
Answer:
11
Step-by-step explanation:
Mode means the highest repeated observation in the data set,
Therefore Mode = 11, as 11 has repeated 3 times, the most in the data set
Maria rode her bicycle at an average speed of 18 mph on level roads and then slowed down to 10mph on the hilly roads of the trip. The entire trip covered 98 miles. How long did the entire trip take if traveling the level roads took the same time as traveling the hilly roads? {Remember, d = r·t }
Let the time = X
Distance = Rate times time
Level roads = 18x
Hills = 10x
Total is 98 miles
18x+10x = 98
Add:
28x = 98
Divide both sides by 28:
x = 3.5
She spent 3.5 hours on each part
Total time = 3.5 + 3.5 = 7 hours
What is the equation of the following line written in general form? (The y-intercept is 7.)
y
(-2.1)
Answer:
[tex]{ \tt{slope = \frac{7 - 1}{0 - ( - 2)} = 3 }} \\ \\ { \tt{y = mx + c}} \\ { \boxed{ \bf{y = 3x + 7}}}[/tex]
Justin was asked to write equations based on the triangle below. So far he has come up with the following equations: Which of the following would be another correct equation?
Answer:
C: tan 60 = √3
Step-by-step explanation:
Let the adjacent part of the triangle be x and let the opposite side be y.
Thus, from trigonometric ratios;
x/10 = cos 60
We are given cos 60 = ½
Thus;
x/10 = ½
x = ½ × 10
x = 5
Similarly;
y/10 = sin 60
Now,from trigonometric relationship we know that; sin 60 = cos 30. Thus;
y/10 = cos 30
We are given cos 30 = (√3)/2
Thus;
y/10 = (√3)/2
y = 10 × (√3)/2
y = 5√3
Since it is a right angle triangle with one angle being 60°, it means the other one is 30° since sum of angles in a triangle is 180°.
Thus;
5/(5√3) = tan 30°
1/√3 = tan 30
Similarly;
5/10 = sin 60°
sin 60° = ½
Also;
tan 60 = (5√3)/5
tan 60 = √3
Also;
sin 30 = 5/10
sin 30 = ½
Looking at the options, the only correct one is Option C
Help me pls look at this PHTOo Bc I don’t know how to explain
Answer:
42.1
Step-by-step explanation:
15.2% = 0.152
277 * 0.152 = 42.104
42.1 megabytes have been downloaded.
Hope this is helpful.
Answer:
42.1
Step-by-step explanation:
thanks for the pts
✌️❤️✌️
if( 1 ,2 )and( 3 - 2)
are the two end point of a diameter of circle find the coordinates of the centre
Answer:
(2,0)
x-value: [1+3]/2 = 4/2 = 2
y-value: [2+-2]/2 = 0/2 = 0
Step-by-step explanation:
Which of the following is NOT an example of a contract?
lease
credit card
borrowing lunch money
rental
help asap please thanks
-pi/4 is the same thing as 7pi/4.
The sine function will get us the y-value we need.
Keep in mind that our y-value will be negative (based on the position of the line), and pi/4 and 3pi/4 will both have positive y-values.
Therefore, the correct expression is sin(7pi/4).
Hope this helps!! :)
The area of Ray’s rectangular living room, in square feet, can be found by using the expression 4(3x+3y). Use the distributive property to write an equivalent expression for the area of Ray’s living room. Equivalent Expression Use your equivalent expression to find the area of Ray’s living room, in square feet, if x = 2 and y = 4. Write answer here: square feet Show work
Answer:
Area = 72 square feet
Step-by-step explanation:
[tex]4(3x+3y)[/tex]
Multiply the four to the values inside the parentheses to find the "equivalent expression"
[tex]12x +12y[/tex]
Using the "equivalent expression" we found above, we now want to find the area of Ray's living room, in square feet if [tex]x=2[/tex] and [tex]y = 4[/tex]
[tex]12(2) + 12(4)[/tex]
[tex]= 24 +48[/tex]
[tex]= 72[/tex]
Which number is the EXPONENT? 4^2 = 16 *
Answer: 4
Step-by-step explanation:
The exponent in the given number [tex]4^{2}=16[/tex] is 2.
What is exponent?
An exponent refers to the number of times a number is multiplied by itself.
For example, [tex]3^{4}[/tex] means we are multiplying 3 four times. Here the base is 3 and exponent is 4.
According to the question
We have a number
[tex]4^{2} =16[/tex]
Here, we are multiplying 4 two times. So, the base is 4 and the exponent is 2.
Hence, the exponent in the given number [tex]4^{2}=16[/tex] is 2.
Learn more about the exponent here:
https://brainly.com/question/5497425
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The mean age of 5 peoplein a room is
36 years
A person enters the room.
The mean age is now 36
What is the age of the person who
entered the room?
A cafe stores ice cream in a large hemisphere-shaped bowl with a diameter of 36 cm.
The ice cream has a density of 0.87 g/cm3.
The cafe sells the ice cream for £2.10 for a portion of 160 g.
If the bowl is filled to the top, what is the maximum amount of money the cafe can make by selling whole portions of ice cream?
Answer:
1115.8
Step-by-step explanation:
Graph 8x-2y=1 and 4x+y=3
Answer:
no thanks i dont feel like doing all that work to help u. i apologize my dear friend bahahahahahahahahahahhahaha
Step-by-step explanation:
state wether the product of √3 and √9 is rational or irrational. explain your answer
√9 is rational and √3 irrational number
1. Which two points fail the VLT here in this graph?
PLEASE HELP!!!!
A roll of nickels is worth $2.00. Write and
solve an equation to determine the number
of nickels in a roll.
Answer: 20 nickels to make $2.00
Step-by-step explanation:
Answer:
5x = 200
x=40
Step-by-step explanation:
