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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Related Questions
3y-8=3y
solve for y
help asap
step by step please
Answers
Answer:
y=4/3
Step-by-step explanation:
3y-8=3y
3y+3y=8
6y=8
y=8/6=4/3
Hi I really need help with this please 25POINTS!!!
What is the Point of Maximum Growth of this function?
f(x)=(7)/(1+5e^(-0.9x)
Select the correct answer:
(0,7/6)
(0.39,3.5)
(-1.79,3.5)
(1.79,3.5)
Answers
Answer:
(0,7/6)
Step-by-step explanation:
Write
3^2 × 3√3 as a single power of 3.
Answers
Answer:
27√3
Step-by-step explanation:
what times what equals 48 and adds to -16
Answers
Answer:
-4 and -12
Step-by-step explanation:
For what times what equals 48:
-4(-12) = 48
-4 - 12 = -16
Answer:
x= -4 and y= -12
Step-by-step explanation:
x*y=48
x+y=-16
solve one equation for x
y=-16-x
then plug that y into the other equation
x(-16-x)=48
-16x-x^2=48
multiply by -1
x^2+16x=-48
complete the square
x^2+16x+64=-48+64
(x+8)^2=16
solve for x
x+8=sqrt(16)
x+8=4
x=4-8
x=-4
plug x back into original equation
x+y=-16
-4+y=-16
y=-16+4
y=-12
so your answers are x=-4 and y=-12
Find the lowest common multiple (LCM) of 18 and 21.
Answers
LMC (18,21) = 126
ok done. Thank to me :>
variables combining like terms
16. x+3
17. 5y+3
18. x+5y-5
Answers
Answer:
16.3x
17. 8y
18.x+y
I thing these are the answers of these equations
mike deposited a sum of rs 64000 in a post office for 4 years, compound annually at 4% per annum. What amount will he get on maturity
Answers
Answer:
79507
Step-by-step explanation:
because 64000(1+15/200)^3= 79507
us
What is the dividend yield on Stock A that sells at
15 $/share, when Company A pays a quarterly
dividend of $0.15 per share?
dividend yield = [?] %
Give your answer as a percent rounded to the
nearest tenth.
Fnter
Answers
Answer:4
Step-by-step explanation: $0.15 x 4 = 0.6
0.60 divide by 0.15
= 4.
El siguiente cuerpo es CUARTA PARTE de un cilindro. ¿Cuál es el volumen? r = 6 cm; h = 9 cm
Answers
Answer:
es 54 espero que esto ayude adiós!
Step-by-step explanation:
El volumen de un cilindro con un radio de 6 cm y una altura de 9 cm es 1018 cm³
Un cilindro es una forma tridimensional con dos bases paralelas unidas por una trayectoria curva a una distancia constante.
El volumen de un cilindro es:
Volumen = πr²h
Given that: r = 6 cm; h = 9 cm;
Volumen = πr²h = π(6)²(9) = 1018 cm³
El volumen de un cilindro con un radio de 6 cm y una altura de 9 cm es 1018 cm³
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A rectangular room has an area of 120 square feet. a. The length of the room is 15 feet. Find the perimeter of the room. The perimeter of the room is feet.
Answers
120/15 = 8
To find the perimeter, we use the following formula
2l + 2w = P
2 (15) + 2 (8) = 46 ft
what does the slope of jessicas function represent?
tyia
Answers
Answer:
The slope represents the rate of change of earnings in a week for every unitary change in number of doors knocked. For Jessica's function, her earnings change by +7 units for every unit of door she knocks.
Step-by-step explanation:
So, when comparing this to the meaning of slope stated above, we can say that the slope of Jessica's function represents the rate of change of earnings in a week for every unitary change in number of doors knocked.
- 2x + 4y = 17
3x - 10y = -3
Answers
-2x+4y-17=0
2x-4y+17=0
———————
2)3x-10y=-3
3x-10y+3=-3+3
3x-10y+3=0
Answer:
1.-2x+4y=17
if you want me to solve for x : x=-17/2 +2y
If you want me to solve for y: y=17/4+x/2
2. If you want me to solve for x: x=-1+10y/3
If you want me to solve for y: y=3/10+3x/10
3. If you want me to do it all together it would be:
x=-79/4, y=-45/8
Step-by-step explanation:
Someone plz help me :(
Answers
Answer:
I think it's D
Step-by-step explanation:
Their talking about "the difference", and since we all know difference with numbers mean subtraction. So it is 150-99 I'm sure.
The final grade on your math exam was determined by the function f(x) = 100 − 2x. Which statements are correct?
A) 100 is the maximum grade.
B) y equals your final grade.
C) This is an exponential function.
D) 2 is what each question is worth.
E) x is the number of correct problems.
Answers
Answer:
A. True
B. True
C. False
D. True
E. False
Step-by-step explanation:
A. True, you cannot get higher than 100 on this test , as you cannot get a negative amount of questions wrongs
B. True, as y = f(x)
C. False, as there is no exponents
D. True, as if x=1, you lose 2 points
E. False, as x is the number of wrong problems
kinyua spent
[tex] \frac{1}{4} [/tex]
of his net January salary on school fees
Answers
Answeby-step explanation:
zdssadads
simplify this addition 2m+(-2m)+4m
Answers
[tex]\\ \sf\longmapsto 2m+(-2m)+4m[/tex]
[tex]\\ \sf\longmapsto 2m-2m+4m[/tex]
[tex]\\ \sf\longmapsto (2-2)m+4m[/tex]
[tex]\\ \sf\longmapsto 0+4m[/tex]
[tex]\\ \sf\longmapsto 4m[/tex]
Answer:
4m
Step-by-step explanation:
2m+(-2m)+4m = 2m-2m+4m
= 4m
Hope it helps!!
What 5,727 dived by 83
Answers
Answer:
415
____
727
Step-by-step explanation:
Answer:
69
Step-by-step explanation:
what is the value of m in the figure below?
Answers
==========================================================
Explanation:
First we'll need the length of segment BD, which I'll call x for now. The similar triangles allow us to set up the proportion below to solve for x
AD/BD = BD/DC
13/x = x/4
13*4 = x^2
52 = x^2
x^2 = 52
x = sqrt(52)
Segment BD is exactly sqrt(52) units long.
------------
Now focus your attention on triangle BDC. We'll use the pythagorean theorem to find BC
(BD)^2 + (DC)^2 = (BC)^2
( sqrt(52) )^2 + ( 4 )^2 = ( m )^2
52 + 16 = m^2
68 = m^2
m^2 = 68
m = sqrt(68)
m = 8.2462 approximately
m = 8.2
JE VOUDRAI CONNAITRE LE RESULTA DE
5√200
Answers
What's (7 x 100) + (4 x /100) + (8 x 1/1000) in standard form?
Answers
Answer:
(7*100) can be written as 7*10^2
4 * / 100 i don’t know
if it was 4 * 100 then it’s 4*10^2
if it was divided then it’s 4*10^-2
8* 1/1000 = 8/1000 = 8*10^-3
add together to get 1.100008 * 10^3 (if it was 4*100)
or 7.00048 * 10^2 ( if it was 4/100)
464.93 to the nearest millions
Answers
Answer:
It can not be rounded to the nearest millionths bc there is not millionths place in the decimal
Step-by-step explanation:
3. Kyle and Michael a rup a lap around a track. Kyle gets a 50 a meter head start and runs 3 meters
per
second. Michael runs at a speed of 4 meters per second. How long will it take for Michael
to reach Kyle?
Answers
Answer:
50 second
Step-by-step explanation:
let the distance between Michael and kyle (s)
s= 50 m
we want to know how long it takes for Michael(speed 4 m/s ) to reach kyle(3m/s)
v = s/t
t = s/v
Vm = speed of Micheal
Vk = speed of kyle
v = ( Vm - Vk )
t = 50/(4-3) = 50 second
A local business donated 40,782 marbles to distribute equally
among 42 sixth grade classes in the district. How many marbles
did each class receive?
Answers
Answer:
971
Step-by-step explanation:
40782/42=971
Answer: 971 marbles per class
Step-by-step explanation:
40,782 marbles divided by 42 classes =
971 marbles per class
Check
971 x 42= 40782
Suppose the population of a town is 100,000 in 2014. The population increases at a rate of 4.5 percent every year. What will the population of the town be in 2020? Round your answer to the nearest whole number.
Answers
Answer:
127,000 people by 2020
Step-by-step explanation:
4.5% per year
We have 6 years since 2020-2014=6 years
4.5 • 6 = 27% of 100,000 = 27,000
To find our total population, it would be 100,000+27,000=127,000 people would live there in 2020
This is assuming the birth rate is consistent
Brainliest please :)
knife is 3 times cost of spoon
9 spoons and 12 knifes is £82.80
what is 1 knife
Answers
Answer:
The cost of spoon is £1.84 and therefore the cost of one knife is £5.52.
Given :
A knife is 3 times the cost of the spoon. 9 spoons and 12 knives costs £82.80.Solution :
This question is solve by creating a linear equation and linear equations are nothing but yet another subset of "equations". Linear calculations that requires more than one variable can be done with the help of linear equations. The standard form of a linear equation in one variable is ax + b = 0.Now let x be the cost of spoon. Than the cost knife is 3x. It is given that 9 spoons and 12 knives costs £82.80.
[tex]9x + 12 x (3x) = 82.809x + 36x = 82.8045x = 82.80x = 1.84[/tex]
Therefore the cost of 1 knife = 5.52
Step-by-step explanation: [tex]1.84 x 3 = 5.52[/tex]
Solve 2x + 3(x+ 10) = 60.
O A. x = 6
O B. x = 5
O C. x= 3
O D. x = 7
Answers
Answer:
A. x = 6
Step-by-step explanation:
2x+3(x+10)=60
Use the distributive property to multiply 3 by x+10.
2x+3x+30=60
Combine 2x and 3x to get 5x.
5x+30=60
Subtract 30 from both sides.
5x=60−30
Subtract 30 from 60 to get 30.
5x=30
Divide both sides by 5.
x=
5
30
Divide 30 by 5 to get 6.
x=6
find the sum of an arithmetic sequence 9, 15, 21, 27,…,183?
Answers
Answer:
It Jumps by six every number, so six would be my guess
Paetan pays $10.73 for 3.7 pounds of cherries. What is the cost for 1 pound of cherries?
Answers
Answer:
$2.9
Step-by-step explanation:
can anyone help me if so Ty no file answers please.
Answers
Answer:
I think the error in Cynthia's answer is when she multiplied
Step-by-step explanation:
-2x(x^2 - 3) here
It should be = -2x^2 + 4x^2 - 2
Which expression does not belong with the other three? Explain your reasoning.
2(x+2) 5(x-8) 4+(x•4) 8(9-x)
Which one does not belong:
Explain your reasoning:
Answers
Answer:
3. 4 + (x · 4)Step-by-step explanation:
Given expressions:
2(x + 2) 5(x - 8) 4 + (x • 4) 8(9 - x)Three of them in the form of:
a(b + c)One of them in the form of:
a + (bc)Number 3 doesn't belong