I’m not sure how to answer this in a Graph, Diagram, and Algebra(algebraic reasoning too) for a,b,c, and d. Can someone please help me?
Answers
The outline that that illustrate how k values change so that the solutions are the ones in the question are as follows
(a) The number line solution contains zero
Using algebra, we have;
The given quadratic inequality is; -x² + 4 ≥ x + k
The number line solution is the expression of the solution on the number line.
We have;
-x² + 4 ≥ x + k
-x² - x + 4 - k ≥ 0
Dividing by (-1), we get;
x² + x - 4 + k ≤ 0
When - 4 + k = -2
k = 2, we get;
x² + x - 4 + 2 ≤ 0
x² + x - 2 ≤ 0
(x - 1)·(x + 2) ≤ 0
Given that the result of the product is less than zero, we have;
((-3) - 1)·((-3) + 2) > 0
Therefore, the solution are;
x ≤ 1, or x ≥ -2
Which gives
-2 ≤ x ≤ 1
Using diagram;The solution of the above inequality includes 0 as shown in the attached number line
Graphically;The graph of the inequality is plotted using MS Excel, showing the solution set, of -2 ≤ x ≤ 1
(b) There are no solution to the inequality
In the present case, we have;
((-1)² - 4×(-1) × (4 - k) < 0
17 - 4·k < 0
[tex]k > \dfrac{17}{4}[/tex]
Let k = 5, we have;
-x² + 4 ≥ x + k
-x² - x + 4 - 5 ≥ 0
-x² - x -1 ≥ 0
The discriminant, is (1² - 4×(-1)×(-1)) = -3 < 0, therefore, there are no real
roots to inequality, and -x² - x -1 is not equal to zero.
GraphicallyPlease find attached the graph of the function, which does not intersect with the x-axis, and therefore, has no values at which y = 0
(c) The solution is a single number
-x² + 4 ≥ x + k
When k = x + 5, we have;
0 ≥ x² + 2·x + 1
0 ≥ (x + 1)²
Therefore;
The only solution is; x = -1
Using diagrams:
Please find attached the solution of the function on the number line
GraphicallyThe graph of the function showing only one intercept is attached
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https://brainly.com/question/11982012
Related Questions
PLEASE HELP I NEED HELP
Which verb of ser do I use?
Example: son, sois, somos, es, eres, soy
Ricardo y yo _____.
I WILL GIVE BRAINLIEST
Answers
Answer:
somos
Step-by-step explanation:
somos means us
Ricardo and us
YES I WILL MARK BRAINLIST:D
Sarah is going to the food truck with her friends. Hot dogs cost $2 and drinks cost $3. She has a total of $24 that she can spend. The equation 2x+3y=24 represents this scenario.
Determine the amount of hotdogs that can be purchased if Sarah orders 4 drinks.
Question 4 options:
4 hotdogs
7 hotdogs
6 hotdogs
5 hotdogs
Answers
Answer:
6 hotdogs
Step-by-step explanation:
:)
The Clark family bought 8 crates of eggs last week. Each crate had 12 eggs. Since then, they have eaten 28 of the eggs. How many eggs are left?
Answers
96 - 28
68
68 eggs are left.
Subtract 6 1/3 - 2 1/5
Answers
Answer:
4 2/15
Step-by-step explanation:
Convert both fractions to have the same denominator. Find the LCM of 3 and 5 and multiply by what you need to get there. 1x5=5, 3x5=15, so 1/3 becomes 5/15, and 1x3=3, 5x3=15, so 1/5 becomes 3/15. Finally, do normal subtraction, to get 4 2/15.
if angle d is 15 what is angle CED?
Answers
Answer:
135
Step-by-step explanation:
this seems like a continuation of the question which was answered previously
we know angle AEB=135, using vertical angle theorem, AEB and CED are congruent, so CED=135
Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 21 gallons of gasoline to travel 399 miles. How many miles can the car travel if it has 28 gallons of gasoline
Answers
Answer:
6 gallons of gasoline
Step-by-step explanation:
1 gallon = 24 miles
you need to get 144 miles
144 divided by 24 = 6
there fore you need 6 gallons
hope it helps
Solve -3(x-2)=2(x-7) and write a reason for each step
Answers
Answer:
4=x
Step-by-step explanation:
-3(x-2)=2(x-7)
Distribute -3 and 2.
-3x+6=2x-14
Add 3x to both sides of the equation.
6=5x-14
Add 14 to both sides of the equation.
20=5x
Divide 5 from both sides of the equation.
4=x
Hope this helps :)
Answer:
x=5
Step-by-step explanation:
Our equation is
-3(x-2)=2(x-7)
First we will distribute -3 and 2, because in math when we have a number being multiplied into parenthesis we multiply both things inside of it
Our equation is now
-3x+6=2x-14
Next we subtract 6 from both sides because we want x to be on only one side
-3x=2x-20
Next we subtract 2x from both sides because we want x to equal something exactly
-5x=-20
Now we divide -5 from both sides because we only want x
x=5
Brainliest please :)
What's the circumference of a
circle with a radius of 2 inches?
Use 3.14 for t.
C = [? ] inches
Answers
Answer:
C = 12.57 inches
:) have a good day
Find an equation of the line parallel to y=2x+1 and that passes through the point (5,1)
Answers
Answer:
y = 2x - 9
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x + 1 ← is in slope- intercept form
with slope m = 2
Parallel lines have equal slopes , then
y = 2x + c ← is the partial equation
To find c substitute (5, 1 ) into the partial equation
1 = 10 + c ⇒ c = 1 - 10 = - 9
y = 2x - 9 ← equation of parallel line
plus $5 per day. The fee for the game booth is $50 plus $7 per day.
Write an expression for how much both booths will cost for the same number of days.
Answers
Question:
A company sets up a food booth and a game booth at the county fair. The fee for the food booth is $100 plus $5 per day. The fee for the game both is $50 plus $7 per day. Write an expression for how much both will cost for the same number of days.
Answer:
105 times 15= 1575
57 times 20= 1140
1140+1575= 2715
(2715)(d)= x
I don’t even know the answer to this one plz help me
Answers
Answer:
You would multiply -11 by 9/4
This is because they are on opposite sides of the equation, and 9/4 is connected to a variable.
How would a child use addition to find 8 X 2?
Answers
Answer:
16
Step-by-step explanation:
They would do 8+8 to get their answer
how fast is a skater traveling in meters per second if they are moving at a rate of 5.6 mile per hour
2.51m/s
0.25 m/s
14.24 m/s
25.09 m/s
Answers
Answer:
2.51
step by step explanation:2.51 meters per second is the speed of skater traveling if they are moving at a rate of 5.6 mile per hour.
To convert from miles per hour (mph) to meters per second (m/s), we will need to use the following conversion factors:
1 mile = 1609.34 meters
1 hour = 60 × 60 = 3600 seconds
Given the skater's rate of 5.6 mph:
Speed in m/s
= (5.6 mph) × (1609.34 m/mile) / (3600 s/hour)
≈ 2.51 m/s
So, the skater is traveling at a rate of approximately 2.51 meters per second.
Learn more about speed here:
https://brainly.com/question/5082291
#SPJ3
What is a real number.
Answers
Answer:
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
Which of these is not the net of a cube?
Answers
Answer:
B
I think it b hops it will help
How do I write 1/2y=2x-3 in standard form?
Answers
Answer: x−2y=6
hope this helps
What is the vertex and p-value of this parabola?
Answers
Answer:
vertex: (-7, 5)p = 2Step-by-step explanation:
The vertex is halfway between the focus and the directrix:
((-7, 7) +(-7, 3))/2 = (-14, 10)/2 = (-7, 5) . . . . vertex coordinates
The value of p is the distance from the focus to the vertex:
7 -5 = 2 = p
In vertex form, the equation of the parabola is ...
y = 1/(4p)(x -h)^2 +k . . . . . . vertex (h, k)
y = 1/8(x +7)^2 +5
A company rents out 16 food booths and 20 game booths at the county fair. The fee for a food booth is $200 plus $9 per day. The fee for a game booth is $95 plus $6 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
Answers
Answer:
20(95+6d)+16(200+9d)
Step-by-step explanation:
I'm not so sure about this question since I'm also learning about algebra right now.
But we know there's 20 game booths that costs 95$ and 6$ for d days
if so first we need to know how much 1 booth cost, which is $95 plus $6 per day and as an expression: 95+6d. Then there's 20 booths so we multiply it, and we need to add parentheses according to the priority rule. So it should be 20(95+6d)?
then food booths are 16(200+9d)
then we add them so
20(95+6d)+16(200+9d)
Will give brainliest! Is these answers correct?
Answers
Answer:
Yep, they are all correct
Both the answers are correct
Simplify: 7.2 x10^4/3.0 x 10^2
Answers
Answer:
240
Step-by-step explanation:
x-8/2=-14
solve for x
Answers
Answer:
-20
Step-by-step explanation:
-14 x 2 = -28
-28 + 8 = -20
There you go :D
Answer:
-10
Step-by-step explanation:
first Solve for the fraction
-8/2= -4
x-4= -14
next add the negative 4 to 14
x=-10
and there's you're answer!
a^4 divided by a^-2
please help
Answers
Answer:
hope this helps
Step-by-step explanation:
[tex]a^{6\\}[/tex]
to do this you factor the numerator and denominator and then you cancel the common factors
What’s the gradient and y intercept for c and e and could u explain pls thx
Answers
Step-by-step explanation:
if you are given an equation of a form y=kx+b, k is gradient and b is y-intercept
in c you can write this equation as y=(2x/3)-2,so gradient = 2/3 and y-intercept =-2
in e:6y=2x+3
y=x/3+1/2,gradient = 1/3, y-intercept=1/2
The gradient or Slope in a linear equation is simply the value "a" in this equation : y = ax + b
And the y-intercept is simply the value b.
so for example, what is the slope of y = 5x + 3 ? What is the y-intercept ? Well the gradient (or slope) is 5, and the y-intercept is 3.
So, for a.
y = -1/2x + 8
it's pretty simple : gradient = -1/2
y intercept = 8
Now for c.
[tex]y=\frac{2x-6}{3}[/tex]
[tex]y=\frac{2}{3}x-\frac{6}{3}[/tex]
[tex]y=\frac{2}{3}x-2[/tex]
So the gradient is 2/3 and the y intercept is -2 (and not +2, be careful there is a negative sign :) )
e.
-2x + 6y - 3 = 0
6y = 2x + 3
y = (2/6)*x + (3/6)
y = (1/3)*x + (1/2)
so the gradient is 1/3
and the y-intercept is 1/2
Good luck, your the best :)
An item on the sale rack at a local supermarket was marked $3.42. The original price
of the item was $4.75.
What was the percent of the discount?
Answers
Answer:
The real answer would be 28%
Step-by-step explanation:
It's true!
Preston's vegetable patch is 7 yards wide and 17 yards long. Preston wants to build a fence around the vegetable patch. The fencing material costs $2.00 per yard. How much would it cost in total to build the fence
Answers
Answer: 238$
Step-by-step explanation: 7 x 17 = 119 mutiply this x 2.00 = 238
HELPPPPPPPPPPPPPPPPPP
Answers
help me with this please and thank you
Answers
Answer:
a. 2x +5
b. Pic attached
c. f(4) = 2•4 +5
f(4) = 8 +5
f(4) = 13
d. Domain: all the real numbers
Range: all the real numbers
Find the cost per roll if a bag of five lunch rolls is $2.50.
Answers
2. How many tens are in 9 hundreds?
Answers
Answer:90
Step-by-step explanation:
900/10 = 90
Answer: 90
Step-by-step explanation:
+
What is the quotient when (16x4 + 40x3 - 24x2) is divided by 8x??
OA.
2x + 5x-3
OB. 2x + 3x-5
OC. 2x - 5x+5
D. 2x3 + 5X-3
+
Relat
Next
Answers
Answer: [tex]2x^{2} + 5x -3[/tex]
Step-by-step explanation:
Find the quotient of [tex]\frac{16x^4+40x^3-24x^2}{8x^2}[/tex]
Step 1: Break down the polynomial equation
[tex]\frac{16x^4}{8x^2}[/tex] + [tex]\frac{40x^3}{8x^2}[/tex] - [tex]\frac{24x^2}{8x^2}[/tex]
Step 2: Divide each piece by dividing the coeffients and subtracting the variables.
16 ÷ 8 = 2
[tex]x^{4}[/tex] - [tex]x^{2}[/tex] = [tex]x^{2}[/tex] → 2[tex]x^{2}[/tex]
40 ÷ 8 = 5
[tex]x^{3}[/tex] - [tex]x^{2}[/tex] = [tex]x[/tex] → 5[tex]x[/tex]
- 24 ÷ 8 = - 3
[tex]x^{2}[/tex] - [tex]x^{2}[/tex] = 1 → - 3
Step 3: Put the polynomial together
2[tex]x^{2}[/tex] + 5[tex]x[/tex] - 3