The graph of the quadratic function f(x) = 0.5x² + x - 9 crosses the negative x-axis between the ordered pairs (-7,0) and (-6,0), and between (-2,0) and (-1,0).
Explanation:The graph of the quadratic function f(x) = 0.5x² + x - 9 crosses the negative x-axis at those x-values that make the function equal to zero. To find these, we solve for x in the equation 0.5x² + x - 9 = 0 using the quadratic formula x = -b ± √(b² - 4ac) / 2a.
Here, a = 0.5, b = 1 and c = -9. Substituting these into the formula gives x = -1 ± √(1 + 36) / 1 = -1 ± √(37) / 1. The two possible solutions are approximately -7.06 and +5.06. Therefore, the ranges of x-values crossing the negative x-axis are between the ordered pairs (-7,0) and (-6,0), as well as between (-2,0) and (-1,0).
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The function f(x) = one-halfx2 + x - 9 intersects the negative x-axis between the ordered pairs (-4, 0) and (-3, 0) and also between (-3, 0) and (-2, 0) when solved using the quadratic formula.
Explanation:The question concerned is a quadratic function, specifically, it wants to know where f(x) = one-halfx2 + x – 9 intersects with the negative x-axis. The x-axis is the line where y = 0, so we need to solve the equation 0.5x² + x - 9 = 0 to locate the roots. By applying the quadratic formula, x = [-b ± sqrt(b² - 4ac)] / (2a), we substitute our coefficients into the equation to get: x = [-1 ± sqrt((1)² - 4*0.5*(-9))] / (2*0.5). This will lead to two solutions, x = -2 and x = -3. Hence, the function f(x) = one-halfx2 + x – 9 intersects the negative x-axis between the ordered pairs (-4, 0) and (-3, 0) and also between (-3, 0) and (-2, 0).
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Givem the geometric sequence where à1=2 and the common ratio is 4, what is domain for N
The domain for N is All integers where n ≥ 1
Solution:
According to statement a1 = 2 and r = 4. This shows that r is greater than 1.
If r is greater than 1 than it includes integers greater than 1 or equal to 1. It does not include all the real numbers because real numbers include negative numbers also.
If starting value is 2, if we put n=0, then we get 2, but if we put a negative value than we would get a number which is not a part of our sequence.
Thus the domain of n is All integers where n greater than or equal to 1
what output is 4 more than twice the input 3
Answer:
10
Step-by-step explanation:
4 more than twice the input 3
more indicates addition, twice indicates multiplication
y = output value
x = input value
y=4+2x
y=4+2(3)
y=4+6
y=10
4 more than twice the input 3 is 10
Final answer:
To find the output that is 4 more than twice the input when the input is 3, we calculate 2(3) + 4, which equals 10.
Explanation:
The output that is 4 more than twice the input when the input is 3 can be found using a simple algebraic expression. If we let x represent the input and y the output, the expression can be written as y = 2x + 4. By substituting the input value of 3 into the equation, we have y = 2(3) + 4, which simplifies to y = 6 + 4, and further simplifies to y = 10. Therefore, the output is 10.
are the diagonals congruent justify your answer
Answer:
Sometimes
Step-by-step explanation:
If the shapes' sides are congruent? Using congurent triangles to prove
Drag each graph to show if the system of linear equations it represents will have no
solutions, one solution, or infinitely many solutions.
help please !
Answer:
The answer in the attached figure
Step-by-step explanation:
we know that
The solution of a system of linear equations is the intersection point both graphs.
If both graphs has one intersection point , then the system has only one solution
If both graphs have no intersection point, (parallel lines) then the system has no solution.
If both graphs are equal, (identical lines) then the system has infinitely solutions.
The answer in the attached figure
Mika placed $4200 in a savings account which compounds interest continuously at a rate of 2.3%. How much will she have in the account after 3 years? Round to the nearest dollar.
Mika placed $4200 in a savings account which compounds interest continuously at a rate of 2.3%. To find out how much she will have after 3 years, we use the formula for continuous compound interest and find that the total in the account, rounded to the nearest dollar, is $4513.
Explanation:The subject is continuous compound interest, which differs slightly from simple interest. In Mika's case, she placed $4200 in a savings account which compounds interest continuously at a rate of 2.3%. To calculate the total amount after 3 years, we use the formula A = P * e^(rt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), and t is the time in years.
So A = $4200 * e^(0.023 * 3). When we calculate this, we find that the total in the account, rounded to the nearest dollar, is $4513.
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how many times does 18 go into 40
Answer:
2 times
The drawing will help
PLEASE HELP QUICKLY!!!!
13. Find the slope of each linear function.
The slope of Graph A is
The slope of Graph B is
The slope of Graph C is
The slope of Graph D is
Answer:
A= -4
B= 4
C= 1/4
D= -1/4
Step-by-step explanation:
I see u counted which is good. remember it's rise over run so for a u got up down 4 over 1. that's why the slope would be -4. You figure out the other ones the same way.
Doe the math equation y=6x -4 have a negative slope
Answer:
yes it does have a negative slope
Step-by-step explanation:
Final answer:
The equation y=6x - 4 does not have a negative slope; instead, it has a positive slope because the coefficient of x is positive, indicating that y increases as x increases.
Explanation:
The math equation given is y=6x - 4. To determine whether it has a negative slope or not, we look at the coefficient of x, which in this case is 6. A negative slope indicates that as x increases, y decreases, and vice versa. However, since the coefficient of x here is positive (6), this line has a positive slope, not a negative one. Therefore, it means that as x increases, y also increases, which is characteristic of a positive relationship between x and y.
It is important to note that a line with a negative slope would have a negative coefficient of x. The slope is the number that is multiplying the x variable, and it represents the rate of change of y with respect to x. Graphically, a line with a positive slope, such as this one, will rise as it moves from left to right on a graph.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
A.
y = 3x + 4
B.
c.
D.
y= 3x - 14
y= 3x - 4
y=3x + 12
Answer:
A: y = 3x + 4
Step-by-step explanation:
A slope of 3 is given, so the co-efficient of x must be three
If you are going through point (-3, -5), then you must have a starting point.
Adding 3 to the y coordinate for every x value gives us 4.
This means that the equation must be adding 4 to x.
So, the answer is y = 3x + 4, or A.
Nathaniel is saving money to buy a new graphics card for his computer that
costs $260.
If he is saving $18 a month and already has $134, in how many
more months will he have enough money for the graphics card?
Answer:
7 months
Step-by-step explanation:
Which ordered pair is a solution of the equation? X+7y=17
Answer Choices
A. Only (10,1)
B. Only (-4,3)
C. Both (10,1) and (-4,3)
Answer:
C. Both (10,1) and (-4,3)
Step-by-step explanation:
The equation is x + 7y = 17
Option A: x = 10, y = 1
Now, putting the value in the equation,
L.H.S.,
x + 7y
= 10 + 7*1
= 10 + 7
= 17
Therefore, L.H.S. = R.H.S.
The equation is correct.
Option B: x = -4, y = 3
Now, putting the value in the equation,
L.H.S.,
x + 7y
= -4 + 7*3
= -4 + 21
= 17
Therefore, L.H.S. = R.H.S.
The equation is also correct with this value.
As the option "A" and Option "B" shows the correct value, the answer is both A and B.
Answer:
C.) Both the answers are true
Step-by-step explanation:
Simply plug it in
(10, 1) = 10 + 7(1) = 17
10 + 7 = 17
17 = 17
So A.) is true, but let's check B.)
-4 + 7(3) = 17
-4 + 21 = 17
17 = 17
B.) is also true
Seth’s father is thinking of buying his son a six-month pass for $40. With the pass, matinees cost 1.00. If matinees are normally $3.50 each, how many times must Seth attend in order for it to benefit his father to buy the pass?
Seth must attend matinees at least 16 times for the six-month pass to be financially beneficial to his father.
Explanation:To determine how many times Seth must attend matinees for the six-month pass to be beneficial economically, we need to calculate the break-even point where the cost of the pass equals the savings from discounted ticket prices. The normal ticket cost for a matinee is $3.50, and with the pass, the cost is reduced to $1.00. Therefore, each time Seth attends a matinee with the pass, he saves $2.50 ($3.50 - $1.00).
Let's denote the number of times Seth needs to attend matinees to benefit from the pass as 'x'. The six-month pass costs $40, So, we need to set up the following equation to find the break-even point: $2.50 × x = $40.
Divide both sides of the equation by $2.50 to solve for 'x':
x = $40 ÷ $2.50
x = 16
Thus, Seth needs to attend matinees at least 16 times to make the purchase of the six-month pass worthwhile for his father.
b/5 -34<-41 what is B
Answer:
b<-35
Step-by-step explanation:
b/5-34<-41
b/5<-41+34
b/5<-7
b<-7*5
b<-35
Quadrilateral RSTU has vertices at R(2,-2), S(4, -3), T(4-6), and U(2, - 7). Which of the following statements is true?
A. The diagonals are the same length, which is greater than 5.
B. The diagonals are the same length, which is less than 5.
The length of diagonal RT is greater than that of diagonal US
D. The length of diagonal RT is less than that of diagonal
Answer:
The answer is B
Step-by-step explanation:
Edge 2022
Solve the equation 6 = -9 – 6x for x.
A. -5/2
B. -2/5
C. 2/5
D. 5/2
Answer:
a. -5/2
Step-by-step explanation:
To solve the equation 6 = -9 - 6x for x, add 9 to both sides, then divide by -6, resulting in x = -2.5 or -5/2.
To solve the equation 6 = -9
- 6x for x, you first want to isolate the variable x on one side of the equation. Start by adding 9 to both sides to move the constant term from the right side to the left side:
6 + 9 = -9 + 9 - 6x
15 = -6x
Next, divide both sides by -6 to solve for x:
15 / -6 = (-6x) / -6
x = -15 / 6
When you simplify -15 / 6, you get:
x = -2.5 which is the same as -5/2
Therefore, the solution to the equation is x = -5/2.
There was a plate of cookies on the table. Amanda was hungry because she hadn't had breakfast, so she
ate half the cookies. Then Beth came along and noticed the cookies. She thought they looked good, so she
ate a third of what was left on the
plate. Christine came by and decided to take a fourth of the remaining cookies with
her to her next class. Then Daniel came dashing up and took a cookie to munch on.
When Eva looked at the plate, she saw that there were two cookies left. She wondered how many cookies
were on the plate to begin with?
Answer:
10 2/3
Step-by-step explanation:
So in order to figure this out you have to work backwards. First, Daniel came and took a cookie. So when he took 1 there were 3 cookies available. Next Christine took one fourth of the cookies, meaning that the 3 available cookies are the remaining 3/4's. When she got there she took 1. Then Beth came and took 1/3. For it to be 3/3 there has to be 1 and 1/3 more cookies. Now there are 5 and 1/3 cookies. Amanda came and ate half of the cookies meaning that the amount of cookies we have now is the other half that she didnt eat. 5 and 1/3 plus 5 and 1/3 is 10 and 2/3. I hope this is correct.
m=-4, passes through the point (5,-3)
Answer:
y+3=-4(x-5)
Step-by-step explanation:
m=-4
y-(-3)=-4(x-5)
y+3=-4(x-5)
I need help for 8 and 9 plz help and thank you
Answer:
8) 0 + t = t ------- Identity Property of Addition
(2+b) * 0 = 0 ------- Zero Property of Multiplication
9) n * 0 = 0 ------- Zero Property of Multiplication
1m = m --------- Identity Property of Multiplication
Hope this helps
-Amelia
Answer:
8) Identity Property of Addition
9) Zero Property of Multiplication
I have no idea how to do this. My teacher just threw it on us, please help. <3
Answer:
(25 1/3)/76
15.5/2
Step-by-step explanation:
I'll do the first two for you, and you can use that to do the rest. Essentially, what we have to do is match up the functions so that they have the same numerator/denominator, and use that to figure out the missing part. For the first one, we have to match up 12 and 76. We can do this by obtaining the result of 76/12, which is 6 1/3. To match it up, we can multiply 12 by 6 1/3 or divide 76 by 6 1/3. As we want to match up to 76 because the missing number is on the 76 side, we must multiply both 4 and 12 by 6 1/3, resulting in our answer being (25 1/3)/76 for the first one. Similarly, for the second one, we can divide 8 by 2 to get 4. Since the missing number is on the 2 side, we divide the 8 side by 4 to get 15.5/2. Good luck, and feel free to ask if you need help!
find the quotient -33.615 and 4.98
Answer:
3.75 or 3 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
just divide
Need Help with these problems can so,e some explain and give me the answers.
Answer:
there you go all the answers
Patty has 20 to spend on gifts for her friends her mother gives her 5 more. If each gift costs 5 how many gifts can she buy
Answer:
5
Step-by-step explanation:
You have $20, and your mom gives you $5. You have $25 on total. If you divide 25 by 5, you get 5. So the answer is 5.
Answer: you have $20 mom gives you $5 you now have $25 each gift costs $5 25 divided by 5 is 5
Step-by-step explanation:
4 siblings split their inheritance in the ratio of 2:4:6:8. the inheritance is $40,000. how much does each sibling receive for his share
Answer:
First Sibling gets $4000
Second Sibling gets $8000
Third Sibling gets $12,000
Fourth Sibling gets $16,000
Step-by-step explanation:
A ratio of 2:4:6:8 means that
First sibling gets 2 parts of total
Second sibling gets 4 parts of total
Third sibling gets 6 parts of total
Fourth sibling gets 8 parts of total
Now, how many parts are there??
2 + 4 + 6 + 8 = 20 parts
Now, we divide the total inheritance ($40,000) in 20 parts, so each part is worth:
40,000/20 = $2000
Hence,
First Sibling gets = 2000 * 2 = $4000
Second Sibling gets = 2000 * 4 = $8000
Third Sibling gets = 2000 * 6 = $12,000
Fourth Sibling gets = 2000 * 8 = $16,000
Solving a word problem using a two-step med
equally
Espaho
Jim wants to rent a boat and spend at most $34. The boat costs $6 per hour, and Jim has a discount coupon for $8 off. What are the possible numbers of hours
Jim could rent the boat?
User for the number of hours.
Write your answer as an inequality solved for t
Inequality is 6t ≤ 44 and Jim can rent a boat for 7.33 hrs or less
Solution:
Given that
Maximum amount Jim can spend to rent a boat = $34
Rental cost of boat for 1 hour = $6
Also Jim has a discount coupon for $8 off.
Need to determine possible number of hours Jim could rent a boat.
Let’s assume possible number of hours Jim could rent a boat be represented by variable "t"
Cost of renting boat for 1 hour = 6
So Cost of renting a boat for t hours = t x renting boat for 1 hour = t x 6 = 6t
Also Maximum amount Jim can spend to rent a boat = $34
As Jim has a discount coupon for $8 off, so Total amount Jim can spend to rent a boat = $ 34 + $ 8 = $ 44
So cost of renting a boat for t hours must be less that of equal to Total amount Jim can spend to rent a boat
=> 6t ≤ 44
On solving above equality for "t" we get ,
[tex]\begin{array}{l}{t \leq \frac{44}{6}} \\\\ {=>\mathrm{t} \leq 7.3333 \mathrm{hrs}}\end{array}[/tex]
Hence inequality is 6t ≤ 44 and Jim can rent a boat for 7.33 hrs or less.
10x+5y=25 in standard form
Answer:
10x=20
Step-by-step explanation:
Determine whether each relationship represented by the ordered pairs is a function. Explain.. Please answer both problems. 8. (2,2), (3,1), (5,7), (8,0), (9,1)... 9. (0,4), (5,1), (2,8), (6,3), (5,9)
Answer:
8.) Not a function
9.) Is a function
Step-by-step explanation:
In order for a set of coordinates to be a function, the y cannot be repeated.
In number 8, there is (3,1) and (9,1)
Not a function
In number 9, each coordinate is unique and doesn't repeat the y.
Is a function
A jet travels 550 miles in 5 hours.At this rate, how far could the jet fly in 14 hours? What is the rate of speed of the jet?
Answer:
The jet travels 1,540 miles in 14 hours going at about 110 mph
Answer:
I think its 1540 miles.
Step-by-step explanation:
r=550/5
You get 110.
110 times 14= 1540.
1540 miles!
There are between 24 and 40 students in the class
the ratio for boys to girls is 4:7
how many students are in the class
Answer:
33 students
Step-by-step explanation:
Without any other data to go by, guess and check is the only method we can use. Staying in a 4:7 ratio, only one combination gives a total student number between 24 and 40, with 12 boys and 21 girls.
4 + 7 = 11
8 + 14 = 22
12 + 21 = 33
16 + 28 = 44
2. Name a combination of coins that is 130% of the value of a dollar.
I need a simple answer
Answer:
Step-by-step explanation:
5 quarters, 1 nickel
Answer:
The required combination of coins will be 5 quarters and 1 nickel.
Step-by-step explanation:
The required combination should be such that the resultant will be 130% of 1 dollar or 1.3 dollar.
Now, the value of 1 quarter is $0.25 and the value of 1 nickel is 5 cent or $0.05.
So, the combination of 5 quarters and 1 nickel will be,
[tex]5\times \$0.25+1\times \$ 0.05=\$1.25+\$0.05\\=\$1.30[/tex]
The above value is equal to 130% of a dollar.
Therefore, the required combination of coins will be 5 quarters and 1 nickel.
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Which of the following number lines represents the solution to
+5 = 7?
- 10
-8
-6
-4
2
0
2
4
6
8
10
- 10
-8
6
4
2
0
2
4
6
8
10
-10
-8
6
4
2
0
2
4
6
8
10
10
8
6
4
2
6 2
4
6
8
10
Answer:
-8 , 5
Step-by-step explanation: