Given:
[tex]y=-x^2+5x+14[/tex]
To find:
The interval on which the given function is positive.
Solution:
We have,
[tex]y=-x^2+5x+14[/tex]
Splitting the middle term, we get
[tex]y=-x^2+7x-2x+14[/tex]
[tex]y=-x(x-7)-2(x-7)[/tex]
[tex]y=(x-7)(-x-2)[/tex]
[tex]y=-(x-7)(x+2)[/tex]
Using zero product property, we get
[tex]x-7=0\text{ and }x+2=0[/tex]
[tex]x=7\text{ and }x=-2[/tex]
-2 and 7 divide the number line is three interval.
Interval Signs of [tex]y=-(x-7)(x+2)[/tex] Result
(-∞,-2) (-)(-)(-) Negative
(-2,7) (-)(-)(+) Positive
(7,∞) (-)(+)(+) Negative
So, the function is positive for the interval (-2,7), i.e., -2 < x < 7.
Therefore, the correct option is D.
Zena needs a salesperson. Salesperson A is offering his services for an initial $100 in addition to $5 per hour. Salesperson B is offering her services for $25 per hour. When will the two salespeople charge the same amount of money?
Answer:
Step-by-step explanation:
The correct question is
Zena needs a salesperson. Salesperson A is offering his services for an initial $50 in addition to $5 per hour. salesperson B is offering her services for an initial $40 in addition to $7 per hour. When will the two coaches charge the same amount of money?
Let
x ----> the number of hours
y ----> the total charge
we know that
Salesperson A
------> equation A
Salesperson B
------> equation B
To find out when the two coaches charge the same amount of money, equate equation A and equation B and solve for x
7x+40=5x+50
7x-5x=50-40
2x=10
x=5 hours i think just im not sure but i triedStep-by-step explanation:
a&b equals the same meaning five hours
Please help will mark brainliest
Answer:
A
Step-by-step explanation:
This is a hopeless question. The best anyone can do is guess.
The only one that is completely wrong is C. It says that the more you watch TV the less snacks you eat. Not what the premise says.
D oddly enough could be. You might reach a pinacle and not want anything more. I don't think it is the intended answer, but it is possible.
B is hard to eliminate as well. There might not be any relationship at all or a very weak one. I think it should be eliminated because it most resembles C.
The answer is A. I think this is what you are intended to answer.
(5.1 × 106) ÷ (2.4 × 103)
Answer:
2.1868932
Step-by-step explanation:
In one day Mr Henson spent $100 five times with his debit card how much money was deducted from his account
Answer:
now from the top make it drop thats a wop
Step-by-step explanation:
Which of the following is the solution to the inequality -2x-4 ≤ 11
Answer:
[tex]x\geq -\frac{15}{2}[/tex]
Step-by-step explanation:
add 4 on both sides
leaves you with 15 on the right side
you then divide by negative 2
since you divide by a negative you have to switch the sign
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x ≥ −15/2
Interval Notation:
[−15/2, ∞)
pls help with this problem!
Answer:
x interpret: (20,0)
y interpret: (0,8)
Step-by-step explanation:
To find the x-intercept, set y = 0
To find the y-intercept, set x = 0
Subtract -3x-8−3x−8 from 4x^2-7x-24x
2
−7x−2.
Answer:
20x² - 8x + 14
General Formulas and Concepts:
Algebra I
Combining like termsStep-by-step explanation:
Step 1: Define expression
4x² - 7x - 24x² - 7x - 2 - (-3x - 8 - 3x - 8)
Step 2: Simplify
Combine like terms (x²): -20x² - 7x - 7x - 2 - (-3x - 8 - 3x - 8)Combine like terms (x): -20x² - 14x - 2 - (-6x - 8 - 8)Combine like terms (Z): -20x² - 14x - 2 - (-6x - 16)Distribute negative: -20x² - 14x - 2 + 6x + 16Combine like terms (x): -20x² - 8x - 2 + 16Combine like terms (Z): -20x² - 8x + 14(Ignore the C that was answered I don’t think it’s correct)
Angelo wants to graph the quadratic function shown.
Answer:
c is actually correct lol
Step-by-step explanation:
g(x) = (x-4)(x+2)
set both (x-4) and (x+2) equal to zero
x-4=0
x=4
& bx+2=0
x=-2
c has 4 and -2 as x values
F (x)= 3x^2+4
G (x) = 2x^2 – 3x+1
H (x) = -4x^2 + 8x
Find G (x) H (x)
Show your work
Answer: -8x^4+28x^3-28x^2+8x
Here are some letters and what they represent. All costs are in dollars. m represents the cost of a main dish. n represents the number of side dishes. s represents the cost of a side dish. t represents the total cost of a meal. Discuss with a partner: What does each equation mean in this situation? a. M = 7.50
The given question is incomplete
Here are some letters and what they represent. All costs are in dollars.
m represents the cost of a main dish.
n represents the number of side dishes.
s represents the cost of a side dish.
t represents the total cost of a meal.
Discuss with a partner: What does each equation mean in this situation? a. a. m = 7.50
b. m = s + 4.50
c . ns = 6
d. m + ns = t
2. Write a new equation that could be true in this situation.
Answer:
t = 3m -n(s+1)
Step-by-step explanation:
Using the information we can describe the value of each letters
using a and b
we have m = 7.50 and m = s + 4.507.50 = s + 4.50
s = 3
substitute s in c, we get
ns = 6n = 6/3 = 2using equation d we have
m + ns = t7.50 + 6 = tt = 13.50so we an equation using the above data
t +ns = 3m - n
t = 3m -n(s+1)
please help me asap will give brainliest
Answer:
Step-by-step explanations:
At noon, the minute and hour hands overlap. In how many hours will they overlap again?
24 hours
Because 24 hours equals 1 day or one rotation of the clock
Answer:
1 hour 5 9/20 minutes
Step-by-step explanation:
The equation of the line in this graph is y = ____x + ____.
Answer:
y=3/2x+3
Step-by-step explanation:
The equation is in y=mx+b format. m is the slope, or steepness of the line, while b is the y intercept (where the line crosses with the y axis).
The given line shows the y intercept; it's 3.
To find the slope, use this equation: y2-y1/x2-x1
Pick any two points and plug them into the equation. For example, use (0,3) (y intercept) and (-2, 0) (x intercept.)
now,
3-0/0-(-2)
3/2
the slope is 3/2.
Now, the line is
y=3/2x+3.
You are going to receive 420 boxes of clothing each box is 2 feet x 2 feet x 2 feet. Your storage room is 20 feet x 30 feet x 8 ft. Assuming is it ok to fill the entire room, can you fit all your boxes in ?
Solve for G. g+ (-5) = 27
g=
Answer:
G=32 I think,
Step-by-step explanation:
Hope it helps
Answer:
G = 32
Step-by-step explanation:
To do this problem, we first should rewrite the problem.
g + (-5) =27
Turns into
g - 5 = 27.
Then you can do the problem:
g - 5 = 27
+ 5 + 5
----------------
g = 32
Hope this helped!
Look carefully at the following equation:
2x +4= – 4 + 2x
Which of choices below holds true for this equation
A
One Solution
OB
No Solutions
с
Infinitely Many Solutions
Answer:
no solution
Step-by-step explanation:
25 points if you do it and favorite. On Saturday it rained 2 1/4 inches in 18 hours. Assume the rain fell at the same rate throughout the storm. How many inches of rain fell per hour?
Answer:
0.125 inches per hour
Step-by-step explanation:
2.25/18 = 0.125
0.125in per hour
What is the value of this expression when x = -1 and Y = 2?
4x^3 × y^2
Answer:
-16
Step-by-step explanation:
Replace x by -1, and y by 2. If you simplify it, you get -16
Answer:
-16Step-by-step explanation:
Given
4x^3 × y^2To find
The value of expression when x = -1 and y = 2Substituting values:
4(-1)^3*2^2 = -4*4 = -1615−21
Please help me
Answer:
The answer is -6
Can the sides of a triangle have lengths 1, 2, and 10?
Answer:
No
Step-by-step explanation:
According to the triangle inequality theorem, for it to be a triangle the sum of two sides must be greater than the third side, but it isn't so for
1 + 2 is less than 10
Define a variable, set up an inequality, and solve. Only algebraic solutions are accepted.
Ben wrestles in the 132 to 138-pound weight class. If he currently weighs 133 pounds, how much weight can he gain if he wishes to stay in the same class?
Answer:
X is less than or equal to 5
Step-by-step explanation:
I cant do the less than or equal to sign so I wrote it in words. Hope this helps :)
Answer:
5 pounds
Step-by-step explanation:
Let x represent Ben's weight gain.
[tex]138 \geq 133 + x\\[/tex]
Subtract 133 from both sides
[tex]5 \geq x[/tex]
Therefore, Ben can't gain more than 5 points if he wishes to stay in the same weight class.
Hurryyy !!! Lincoln Glass pays it workers overtime if they work on weekends or
holidays. Overtime is 1/2 times the usual hourly pay. If Tim was
earning $8.25 an hour, how much would he get for 1 hour of
overtime? For 8 hours of overtime?
Step-by-step explanation:
since overtime is 1/2 the usual pay which is 8.25 or 8 1/4 then its 8 1/4 (divided) by 1/2 which is equal to 4.125 or 4 1/8 so: in 1 hour the workers get paid 4 1/8 dollars and in 8 hours its 8 x 4 1/8 which is equal to 33
really hope this helps :) good luck
#Answer:
1 hour = $4.13 (rounded) . 1 hour = $4.125 (not rounded)
8 hours = $33.04 (rounded) 8 hours = $33 (not rounded)
Step-by-step explanation:
A table showing Number, Value, and Total Value. The first row shows Nickels, with the entries, n, 0.05, and 0.05 n. The second row shows Quarters, with the entries 36 minus n, 0.25, and 0.25 left-parenthesis 36 minus n right-parenthesis. The last row has Total, with the entries 36, blank, 6.
Alexandra has 36 coins valued at $6.00. She has only nickels and quarters. Which equation can be used to solve for the number of nickels, n?
0.05n + 0.25(36 – n) = 6
0.05n + 0.25(36 – n) = 36
n + 0.05 = 0.05n
n + (36 – n) = 36
Answer:
a- 0.05n + 0.25(36 – n) = 6
Step-by-step explanation:
i just did it on edg
The value of each coin (Nickels and Quarters) determines their number in a money sum
The correct option that gives the equation that can be used to solve for the number of nickels, n, is option;
0.05·n + 0.25·(36 - n) = 6
Reason:
The given equation can be presented as follows;
[tex]\begin{array}{|c|c|c|c|}&\mathbf{Number}&\mathbf{Value}&\mathbf{Total \ value}\\&&&\\Nickels&n&0.05&0.05 \cdot n\\Quarters&36 - n&0.25 & 0.25 \cdot(36 - n)\\&&&\\\mathbf{Total}&36&&6\end{array}\right][/tex]
From the above table, we have;
0.05·n + 0.25·(36 - n) = 6
Solving the above equation gives;
0.05·n + 9 - 0.25·n = 6
-0.2·n = 6 - 9 = -3
[tex]n = \dfrac{3}{0.2} = 15[/tex]
Therefore;
The equation that can be used to solve for the number of nickels, n, is; 0.05·n + 0.25·(36 - n) = 6
Learn more here:
https://brainly.com/question/21612865
In 56 years, Kevin will be 9 times as old as he is right now.
Answer – 7 years old
SOLVINGS
Let Kevin’s present age be ‘x’
In 56 years, Kevin’s age will be x + 56
In 56 years, Kevin’s age will be 9x
Therefore, x + 56 = 9x
Solving for x
x + 56 = 9x
9x – x = 56
8x = 56
x = 56/8
x = 7
Kevin is 7 years old right now.
Calculate Total Wage: Hours Worked 38; Rate $15.70
PLEASE HELP URGENT
what is the slope of the line below
Answer:
m=1/2
Step-by-step explanation:
When finding the slope of a line on a graph, I like to count the steps up/down and to the side between two of the line's points. For this line, we can see that it has points at (2,-1) and (4,0). To get from (2,-1) to (4,0), you need to count
"up 1, over 2"
1/2
Therefore, the slope is 1/2.
HTH :)
Step-by-step explanation:
the process is shown in the above picture .
hope it helps
Solve the system of equations.
2.5y + 3x = 27
5x – 2.5y = 5
What equation is the result of adding the two equations?
What is the solution to the system?
Answer:
8x = 32
x = 4
y = 6
Step-by-step explanation:
2.5y + 3x = 27
5x – 2.5y = 5
_____________
8x = 32 (equation obtained after adding the two equations)
x = 32/8
x = 4
Plug x = 4 in 2.5y + 3x = 27
2.5y + 3*4 = 27
2.5y + 12 = 27
2.5y = 27 - 12
2.y5= 15
y = 15/2.5
y = 6
The equation results of adding the two equations is 8x = 32.
The solution to the system is (4, 6).
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
Given, A system of linear equations in variables 'x' and 'y'.
2.5y + 3x = 27...(i) and 5x - 2.5y = 5...(ii)'
Reaaranging eqn(i) we have
3x + 2.5y = 27...(iii)
Adding (ii) and (ii) we have,
8x = 32. (As + 2.5y and - 2.5y cancels)
x = 32/8.
x = 4.
Putting the value of 'x' in eqn(i) we have,
2.5y + 12 = 27.
2.5y = 15.
y = 6.
So, The solution to the system is (4, 6).
learn more about linear equations here :
https://brainly.com/question/11897796
#SPJ5
Please help asap!! Will mark the brainliest
Answer:
have you wacth a video yet please do it will help you alot
Step-by-step explanation:
What is the slope of the line that passes through the points shown in the table?
Answer:
The slope is 2
Step-by-step explanation:
Every time the x unit goes up one the y unit is going up 2
Help! I'm a little stumped when it comes to variables in matrices. An explanation would be super rad!
What is the determinant of A = [ -2 2 b 0 3 a 0 0 -5 ]
Answer:
30
Step-by-step explanation:
To find the determinant of a 3x3 matrix, you can use this method. (See picture.)
Start with the first number in the top row, and block off the row and column. A 2x2 matrix will be left. Find the determinant of this 2x2 matrix, and multiply it by the number in the top row.
Repeat for the other two numbers in the top row. Add the first result, subtract the second, and add the third.
det A = -2 [(3)(-5) − (a)(0)] − 2 [(0)(-5) − (a)(0)] + b [(0)(0) − (3)(0)]
det A = -2 (3)(-5) − 0 + 0
det A = 30