Answer: a) [tex]x=\dfrac{-9 \pm\sqrt{113} }{8}[/tex]
b) x₁ = - 14; x₂ = 6.
Step-by-step explanation:
a) 4x² + 9x - 2 = 0
[tex]x=\dfrac{-b \pm \sqrt{b^{2}-4ac } }{2a} \\\\a=4; \: \: b=9; \: \: c=-2\\x =\dfrac{-9 \pm \sqrt{9^{2}-4 \cdot 4 \cdot (-2) } }{2 \cdot 4} =\dfrac{-9 \pm\sqrt{113} }{8}[/tex]
b) x² + 8x - 84 = 0
[tex]x=\dfrac{-b \pm \sqrt{b^{2}-4ac } }{2a} \\\\a=1; \: \: b=8; \: \: c=-84\\\\x =\dfrac{-8 \pm \sqrt{8^{2}-4 \cdot 1 \cdot (-84) } }{2 \cdot 1} =\dfrac{-8 \pm\sqrt{400} }{2}=\dfrac{-8 \pm 20}{2} =-4 \pm 10\\\\x_{1} =-14\\x_{2} =6[/tex]
Greg and Carl work at neighborhood car wash facilities and are paid daily. Greg is paid $25 a day plus $7 for each car he washes. Carl earns the same amount per car washed, but his total earnings in a day are always $6 more than Greg's. Which equation expresses the total amount, t, that Carl earns, as a function of the cars he washes, c?
A)t=19+7c
B)t=25+7c
C)t=31+7c
D)t=25+13c
Answer:
Answer: It's easy, compare the same answers.
Step-by-step explanation:
A. 19+7= 16
B. 25+7= 32
C. 31+7= 38
D. 25+13= 38
Helpeoepeoeoeo show work
IMPORTANT THIGNS TO REMEMBER:
Has 20 lb. dog food!Gives dog 1 3/5 everyday!Find how much eaten after 2 days!Find how much is left!ANSWER:
Dog has eaten 3 1/5 after 2 days!
There is 16 4/5 left in bag!
EXPLANATION:
Since she gives 1 3/5 to her dog everyday and their asking for 2 days you would multiply 1 3/5 × 2 OR add 1 3/5 + 1 3/5
Which would give you 3 1/5
So, the dog has eaten 3 1/5 lb. of dog food in 2 days.
However then, you would subtract 20 lb. - 3 1/5 lb. because there is 20 lb. dog food in all and the dog has eaten 3 1/5 of it. This would give you 16 4/5 lb.
Meaning there is 16 4/5 lb. left in the bag of dog food!
Determine which function(s) are exponential. Select all that apply.
Answer:
option B and option C represent an exponential function.
Step-by-step explanation:
We know that following are some of the properties of different functions.
Linear Function:
The constant change in x and y
Quadratic Function:
The constant change in x
The constant 2nd differences in y
Exponential Function:
The constant change in x
The constant ratio in y
Determining the nature of the exponential function
Option A)
x 0 1 2 3 4
y 0 1 4 9 16
Here:
There is a constant change in x:
1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1
BUT, there is NO CONSTANT ratio, as
1/0 = ∞, 4/1 = 4, 9/4 ; 16/9
Thus,
Table A DOES NOT represents an exponential function.
Option B)
x 0 1 2 3 4
y 1/3 1 3 9 27
Here:
There is a constant change in x:
1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1
There is also a constant ratio, as
1/[1/3] = 3, 3/1 = 3, 9/3 = 3; 27/9 = 3
As there is constant change in x as well a constant ratio.
Thus,
Table B REPRESENTS an exponential function.
Option C)
x 0 1 2 3 4
y 5 5/2 5/4 5/8 5/16
Here:
There is a constant change in x:
1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1
There is also a constant ratio, as
[5/2]/5= 1/2,
[5/4]/[5/2] = 1/2
[5/8]/[5/4] = 1/2
[5/16]/[5/8] = 1/2
As there is constant change in x as well a constant ratio.
Thus,
Table C REPRESENTS an exponential function.
Option D)
x 0 1 2 3 4
y 4.5 4 3.5 3 2.5
Here:
There is a constant change in x:
1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1
BUT, there is NO CONSTANT ratio, as
4/4.5 = 4/[45/10] = 40/45 = 8/9
3.5/4 = [35/10]/4 = 35/40 = 7/8
3/3.5 = 3/[35/10] = 30/35 = 6/7
2.5/3 = [25/10]/3 = 25/30 = 5/6
Table D DOES NOT represent an exponential function.
Conclusion:
Therefore, option B and option C represent an exponential function.
The functions that are exponential would be:
B). [tex]x[/tex] 0 1 2 3 4
[tex]y[/tex] 1/3 1 3 9 27
C). [tex]x[/tex] 0 1 2 3 4
[tex]y[/tex] 5 5/2 5/4 5/8 5/16
What are Exponential Functions?
B). Given that,
[tex]x[/tex] 0 1 2 3 4
[tex]y[/tex] 1/3 1 3 9 27
As we see,
The value of [tex]x[/tex] undergoes a constant change of 1
[tex]1 - 0 = 1; \\2 - 1 = 1; \\3 - 2 = 1; \\4 - 3 = 1[/tex]
The ratio also remains constant
[tex]1/[1/3] = 3, \\3/1 = 3, \\9/3 = 3; \\27/9 = 3[/tex]
Thus, it exemplifies an exponential function.
Similarly,
C). [tex]x[/tex] 0 1 2 3 4
[tex]y[/tex] 5 5/2 5/4 5/8 5/16
As we see,
The value of [tex]x[/tex] undergoes a constant change of 1
[tex]1 - 0 = 1; \\2 - 1 = 1; \\3 - 2 = 1; \\4 - 3 = 1[/tex]
The ratio also remains constant
[tex][5/2]/5= 1/2\\\\[5/4]/[5/2] = 1/2\\\\[5/8]/[5/4] = 1/2\\\\[5/16]/[5/8] = 1/2[/tex]
Thus, it exemplifies an exponential function.
Thus, options B and C are the correct answers as the other two have a constant change but not a constant ratio.
Learn more about "exponential function" here:
brainly.com/question/15352175
converting slope-intercept form into standard form, i’m so confused
Answer:
7x+2y=(-6)
Step-by-step explanation:
help pleaseeee!!!!!! 30 points
Answer:
Pen = y
25.00 + y
Step-by-step explanation:
expressions do not have equal signs.
25 more than the pen is 25 + y
the expression would be
25 + y
Answer:
we will say that x stands for the pen
x + $25 = cost of the pencil
Step-by-step explanation:
Which of the following is a central angle?
A
LEGD
B
LEAD
ZCOB
D
LCDA
10,295 - 3,429 = N
N = ?
Answer:
The Answer is 6,866
HELP ME ASAPPP
Write the standard equation of a circle with center (2, 1) and radius 8.
Answer:
C
=
(
a
,
b
)
the center coordinates of circle
a
=
2
,
b
=
−
1
,
r
=
8
Step-by-step explanation:
how do I do this problem I'm doing test corrections and I have no idea how to do it
Answer:
i think its 3 but dont quote me
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
9 can help in completing square formula
find the area cirlcle if the circle has a radius of 11 centimeters.
Answer:
380.133
Step-by-step explanation:
A = πr²
Hope this helps!
Pls 5 stars <3
A+B=44
A : B is equvililent to 13 :8
Please solve
Step-by-step explanation:
13:8A=13x. B=8x13x + 8x = 44 21x=44 x=2.095The first person to answer correctly I will give them a brainlies, 5 stars, and a thank you!
Which process in photosynthesis uses energy from the sun?(1 point)
1. splitting water into hydrogen and oxygen
2. combining carbon dioxide and hydrogen
3. absorbing carbon dioxide
4. releasing oxygen
Answer:
1. splitting water into hydrogen and oxygen
Step-by-step explanation:
Answer:
Photosynthesis takes place in two stages: the light-dependent reactions and the Calvin cycle. In the light-dependent reactions, which take place at the thylakoid membrane, chlorophyll absorbs energy from sunlight and then converts it into chemical energy with the use of water.
Step-by-step explanation:
can u pls go answer my question? Thank you and have a nice day :)
https://brainly.com/question/21589806
What is the equation of the function that is graphed as line a?
Answer:
b
Step-by-step explanation:
4) Justin had 32 coins in nickels and quarters. He had 8 more quarters than nickels. How many of
each type of coin did he have?
if in a parallelogram diagonals bisect each other at right angle and are equal then it is a ___________
PLSSSSSSS HELP ILY TYSM
Answer:
5. k=−3
6. x=4
7. n=−108
Step-by-step explanation:
5. -14k+29=71
Subtract 29 from both sides
-14k+29-29=71-29
Simplify
-14k=42
Divide both sides by -11
-14k/-14=42/-14
6. -33=19-13x
Subtract 29 from both sides
-14k+29-29=71-29
Simplify
-14k=42
Divide both sides by -14
-14k/-14=42/-14
Simplify
k=-3
7. 8+n/25=-4
Multiply both sides by 25
25(8+n)/25 = 25 (-4)
Simplify
8+n=-100
Subtract 8 from both sides
8+n-8=-100-8
Simplify
n=-108
What is the area of the trapezoid?
6 m
4 m
5 m
3 m
square meters
Pls help I don’t get it
Answer:
Rotation 90 degrees counter clockwise, dilation of 6, translation down
Step-by-step explanation:
A cylinder has a height of 14 centimeters and a radius of 17 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Volume = [tex] \sf{\pi r^2 h} [/tex]
[tex] = \sf{3.14 \times {17}^{2} \times 14 } = \sf{12704.45~cm^3} [/tex]
find the solution for X
3x - 5 = 7x + 11
Answer:
x=-4
Step-by-step explanation:
3x-5=7x+11 Add like terms
+5 +5
3x=7x+16 Do it again...
-7x -7x
-4x=16 Now divide
x=-4
Answer:
The answer is x=-4
Step-by-step explanation:
3x-5=7x+11
1) you have to move the number that has a variable with it onto one side(3x and +7x) and the numbers that do not have a variable move them onto the other side (-5 and +11),but if you move them you have to change the sign like the underlined numbers below
3x-7x=5+11
2) you have to subtract 3x and-7x which it equals -4x and then you have to add 5 and 11 which it equals 16
Equation now -4x=16
3) you have to divide -4x into -4x and also divide -4x into 16 which you will get x=-4
Hope it helps out! :)
What is the radius of this circle?
Answer:
9in
Step-by-step explanation:
radius is half the diameter
18/2 is 9 so the radius is 9in
14. Shawn usually sells umbrellas for $20. On rainy days, he sells them for
30% more. What is the cost on a rainy day of buying a new umbrella? *
$14
$26
O $6
O $30
Answer:
$26
Step-by-step explanation:
Triangle EFG is dilated with a scale factor of 1/2 to create triangle E'F'G'.
The measure of angle G is 42 degrees. What is the measure of angle G'? *
a)21
b)42
c)84
d)148
The blue line is the graph of y = –4x + 5. Use the sliders to make the orange line represent y = –2x + 3. Examine the graph. What is the solution of the system of these two equations?
(0, 5)
(1, 1)
(2, 2)
(3, 0)
Answer:
1,1
Step-by-step explanation:
MAY YOU PLEASE HELP ME
Answer: y=20x+10
Step-by-step explanation:mark me brainlest please
j – 18 = 43 what's the answer guys
Answer:
61
Step-by-step explanation:
We know from the equation 43 is 18 less then j. Therefore, if we add 18 to 43, we will get the value of j.
43 + 18 = 61
The price paid for
a $15 shirt after a
45% discount is
applied
Answer:
BStep-by-step explanation:
Trust mey=-2/3x+1
how do you find the slope and y intercept
Answer:
The slope is -2/3 and the y intercept is 1
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -2/3 x+1
The slope is -2/3 and the y intercept is 1
A recipe uses 5 cups of flour for every 2 cups of sugar. How much sugar is used for 1 cup of flour? Exact answers only
Answer:
0.4
Step-by-step explanation:
Hopefully this can help
HELP!!
Question 4 (1 point)
How likely is it for the spinner to land on a 3?
Impossible
Unlikely
Likely
Certain
Answer:
likely
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
