Immediately, we can factor an x out of each term to simplify the polynomial.
x(x^2 + 2x - 24)
In doing this, we know the first zero will be x = 0.
Using the AC method, we can find the next two zeros.
x(x - 4)(x + 6)
The zeros, or x-intercepts of the polynomial, are 0, 4, and -6.The zeros of the polynomial function f(x) = x^3 + 2x^2 -24x are x = -6, 0, and 4.
Explanation:The question requires finding the zeros of the polynomial function f(x) = x^3 + 2x^2 -24x. The zeros of this function can be found by setting the function equal to zero and solving for x. So, we have 0 = x^3 + 2x^2 - 24x. All terms have an 'x', so we can factor out 'x' to give: 0 = x (x^2 + 2x - 24). The quadratic formula (which is used for expressions of the form ax^2 + bx + c = 0) to solve x^2 + 2x - 24 = 0, we get x = -6 and x = 4. Therefore, the zeros of the function are x = -6, 0, and 4.
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The table shows the temperature (in degrees) for eight consecutive days as well as the respective number of ice cream cones an ice cream shop sold on each of these days.
Temperature: 68, 77, 83, 85, 89, 94, 96, 99
number of cones: 403, 447, 457, 465, 489, 503, 543, 576
About how many ice cream cones woud you expect the shop to sell if the temperature one day is 106 degrees? Find a line of best fit for this data and use it to make your prediction.
A. 579
B. 585
C. 602
D. 617
Answer:
B. 585
Step-by-step explanation:
A graph of the scatter plot and line of best fit is attached.
The temperature in this problem will be the independent variable, or x. This is because we are assuming that the number of ice cream cones sold depends on the temperature; this means the number of ice cream cones will be the dependent variable, or y.
This means in our graphing calculator, we will enter temperature in the first list and the number of cones in the second.
After drawing the scatter plot, we run the linear regression; we get the values for a and b in our equation, y = ax+b:
a = 5.08
b = 46.59
This gives us the equation y = 5.08x + 46.59.
Entering our temperature, 106, in for x gives us
y = 5.08(106) + 46.59 = 585.07 ≈ 585
Answer:
B
Step-by-step explanation:
585 Just took the test. Reference above to see explanation.
What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?
y−1=4(x−3)
y+3=4(x+1)
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = 4 and the point (-1, -3). Substitute:
[tex]y-(-3)=4(x-(-1))\\\\\boxed{y+3=4(x+1)}[/tex]
Answer:
Step-by-step explanation:
About Point Slope Form:
Y- Y1 = m (x -X1)m is the slopeY1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineY - 3 = 4 (x - -1)
Write an equation of the line that is perpendicular to the line y = 2x + 8, and which passes through the point (6,-2).
A) y = 2x + 4
B) y = -2x + 1
C) y = - 1 /2 x - 4
D) y = - 1 /2 x + 1
Answer: D) y = - 1 /2 x + 1
Step-by-step explanation:
Got this right on USA test prep
The equation of the perpendicular line that passes through (6, -2) will be y = - (1/2)x + 1. Then the correct option is D.
What is the equation of a perpendicular line?If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line is given as,
y = 2x + 8
Then the slope of the line is 2, then the slope of the perpendicular line will be - 1/2. Then the equation is given as,
y = - (1/2)x + c
The equation of the line is passing through (6, -2). Then we have
- 2 = - (1/2)6 + c
- 2 = - 3 + c
c = 1
Then the equation of the line is given as,
y = - (1/2)x + 1
The equation of the perpendicular line that passes through (6, -2) will be y = - (1/2)x + 1. Then the correct option is D.
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write the equation of the line with x-intercept of -4 and y-intercept of 2. Hint:with those intercepts, (-4,0) and (0,2) are points on the line
Final answer:
The equation of the line with an x-intercept of -4 and a y-intercept of 2 is y = 0.5x + 2. We found this by calculating the slope using the two given points and then using the slope-intercept form to construct the equation.
Explanation:
To write the equation of the line with an x-intercept of -4 and a y-intercept of 2, we can use the two intercepts as points on the line: (-4,0) and (0,2). We can find the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line. For our points this would be:
m = (2 - 0) / (0 - (-4)) = 2 / 4 = 0.5
Once we have the slope, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since the y-intercept is given as 2, we can write:
y = 0.5x + 2
This is the equation of the line with the given intercepts.
Multiply. Express your answer in simplest form. 3 3/4 × 2 2/9
Answer:
The answer is 8 1/3.
The answer will be 8 1/3
The lunch special at Jimmy John’s costs $5.60. The math club has $50.40 in its treasury. How many lunch specials can the club buy? Write and solve an inequality. Show your work
They can afford 9. You work it out by dividing 50.40 / 5.60
The math club can buy at most 9 lunch specials from Jimmy John's with the money in its treasury.
To determine how many lunch specials the math club can buy, we need to divide the total amount of money in the treasury by the cost of one lunch special. Let's denote the number of lunch specials the club can buy as \( n \).
The cost of one lunch special is $5.60, which can be written as a fraction of dollars as[tex]\( \frac{560}{100} \)[/tex]to make the calculations easier. The total amount of money in the treasury is $50.40, which can similarly be written as [tex]\( \frac{5040}{100} \).[/tex]
Now, we set up the inequality to find the maximum number of lunch specials \( n \) that can be bought without exceeding the treasury's funds:
[tex]\[ \frac{560}{100}n \leq \frac{5040}{100} \][/tex]
To solve for \( n \), we divide both sides of the inequality by the cost of one lunch special:
[tex]\[ n \leq \frac{\frac{5040}{100}}{\frac{560}{100}} \][/tex]
[tex]\[ n \leq \frac{5040}{560} \][/tex]
[tex]\[ n \leq 9 \][/tex]
Since \( n \) must be an integer (you can't buy a fraction of a lunch special), the math club can buy 9 lunch specials at most. Any more than that, and they would not have enough money. Thus, the maximum number of lunch specials the club can buy is 9."
A calcium ion has 20 protons and 18 electrons. Each proton has a +1 charge and each electron has a -1 charge. What is the charge of the calcium ion?
Answer:
Ca^(2+) or the charge is 2 plus or just 2
Step-by-step explanation:
Charge on the calcium ion = 20*(+1) + 18*(-1) = 20 - 18 = 2
The charge on the calcium ion is +2
the graph shows the height of a gold ball driven from a tee box as a function of the horizontal distance that it travels
equation in intercept form
equation in vertex form
will give brainliest
Answer:
Intercept form y=-5/64 (x) (x-160)
Vertex form y = -5/64 (x-80)^2 + 500
Step-by-step explanation:
The equation for a parabola in intercept form is y =a(x-p) (x-q)
where p and q are the intercepts. We know that it intersects the x axis at 0 and 160, so we can substitute these in
y = a(x-0) (x-160)
y = a(x) (x-160)
We have to calculate the value of a.
Using the point (80, 500)
500 = a(80) (80-160)
500 = a (80) *(-80)
500 = a *-6400
Divide each side by -6400
a = -500/6400
a = -5/64
So the equation in intercept form is
y = -5/64 (x) (x-160)
The equation for a parabola in vertex form is
y = a(x-h)^2 +k
We know the vertex is (80,500)
y = a(x-80)^2 + 500
We need to pick a point to solve for a. (0,0)
0 = a(0-80)^2 + 500
Subtract 500 from each side.
-500 = a(-80)^2
-500 = a (6400)
Divide by 6400
-500/6400 = a
-5/64 = a ( Does this look familiar?)
y = -5/64 (x-80)^2 + 500
Simply 3(x-2)+5x Please
Answer:
2(4x - 3)
Step-by-step explanation:
Factor 3(x-2) + 5x
8x - 6
= 2(4x - 3)
A piece of steel pipe 12.5 feet long weighs 158 pounds. How much does a piece of the same steel pipe 18.75 feet long weigh?
Answer:
18.75 feet of steel pipe weighs 237 pounds
explanation:
find out how much 1 feet weighs than u can find out how much 18.75 feet.
by doing it like this
158÷ 12.5
=12.64
1 feet equals 12.64 pounds
12.64× 18.75
=237 pounds this is the answer
i do apologize if it wrong
Answer:
That new length would weight 237lbs
Step-by-step explanation:
To find this, we first need to find the weight per foot of the pipe. We can do this by taking the total weight and dividing by length.
158lbs/12.5ft = 12.64 pounds per feet.
Now we can multiply the rate by the new length.
12.64 pounds per feet * 18.75ft = 237lbs
What is the proportional relationship of 15 mL to 3.75 L
To find the proportional relationship of 15 mL to 3.75 L, we first convert 3.75 L to milliliters, which is 3,750 mL. Then, we set up a proportion and solve for the unknown liter value. The proportional relationship of 15 mL to 3.75 L is 0.05625 L.
Explanation:The student is asking about the proportional relationship between two different units of liquid volume: milliliters (mL) and liters (L). To establish this relationship, a conversion is needed, since 1 liter is equivalent to 1,000 milliliters.
First, we need to convert 3.75 liters to milliliters:
Now, let's express the proportion:
48 POINTS! PLEASE HELP!
show your work
Answer:
c. y = 1.25
Step-by-step explanation:
The equation for direct variation is
y = kx,
where k is the constant of proportionality.
We can use the given values of x and y to find k for this case.
y = kx
-10 = k * 40
k = -10/40
k = -0.25
The equation for this case is
y = -0.25x
Now we let x = -5 and solve for y.
y = -0.25x
y = -0.25(-5)
y = 1.25
Answer: c. y = 1.25
Answer:
c y = 1.25
Step-by-step explanation:
The equation for direct variation is y= kx
If we know y and x we can solve for k
-10 = k*40
Divide each side by 40
-10/40 =k
-1/4 =k
The equation for this direct variation is
y =-1/4 x
Given that x =-5
y = -1/4 *-5
y = 5/4
y = 1.25
The ratio of boys and girls in a classroom is 15 to 12 what is the ratio of boys to total students
Hi There!
Answer:
15 to 27
Step-by-step explanation:
Boys: 15
Girls: 12
Total Students: 15 + 12 = 27
Boys to Total Students = 15 to 27
Hope This Helps :)
To find the ratio of boys to total students in a classroom, divide the number of boys by the total number of students. In this case, the ratio is 5/9.
Explanation:To find the ratio of boys to total students in a classroom, we need to know the total number of students in the classroom. Let's assume that there are 27 students in total.
The ratio of boys to girls is given as 15 to 12. This means that for every 15 boys, there are 12 girls. To find the ratio of boys to total students, we add up the number of boys and divide by the total number of students.
In this case, the number of boys is 15 and the total number of students is 27. So the ratio of boys to total students is 15/27. This can be simplified to 5/9.
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The total distance around Dave's rectangular-shaped bedroom is 220 feet. The width of the room is 50 feet. What is the area of Dave's bedroom in square feet?
The area of Dave's bedroom, which is a rectangle with a length of 60 feet and a width of 50 feet, is calculated to be 3000 square feet.
Explanation:The subject of this question is Mathematics, specifically geometrical calculations related to rectangles. The question provides the perimeter and one side length of a rectangle (Dave's bedroom) and asks for the area. First, remember that the perimeter of a rectangle is calculated by the formula 2(length + width). In the given problem, the total distance around the room (or the perimeter) is 220 feet and the width of the room is 50 feet. We can use the perimeter formula to find the length: 220 = 2(length + 50), so length = (220/2) - 50, which is 60 feet.
Now, the area of a rectangle is calculated by the formula length x width. In Dave's room, the length is 60 feet and the width is 50 feet. So Area = Length x Width = 60 feet x 50 feet = 3000 square feet. Thus, the area of Dave's bedroom is 3000 square feet.
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To find the area of Dave's rectangular-shaped bedroom, multiply the length by the width which is 6000 sq ft.
Explanation:To find the area of Dave's bedroom, we need to determine the length of the room.
Since the total distance around the room is 220 feet and the width is 50 feet, we can subtract twice the width from the total distance to find the length.
This gives us a length of 220 - 2(50) = 120 feet.
The area of a rectangle is found by multiplying the length by the width, so the area of Dave's bedroom is 120 * 50 = 6000 square feet.
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Account A and B each start out with $500. If Account A earns $50 each year and Account B earns 6% of its value each year, after how many years will Account B have more money than Account A? If necessary, round your answer to the nearest year.
Answer: After about years 27 Account B will have more money than Account A
Step-by-step explanation:
Account A: 27(50) + 500 = $1850
Account B: 500(1.05^27) = $1866.73
Hope this help
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What is the total number of students in Ms. perron class
Answer:
24 total students
Step-by-step explanation:
multiply 25 times 18 to get 450 then divide 450 by 75 then you get 6, which is the total amount of girls, so 6 + 18 = 24
x = number of students
75% of x = number of boys
(75/100)*x = 18
0.75x = 18
x = 18/0.75 <--- divide both sides by 0.75 to isolate x
x = 24
So there are 24 students in the class
Note how 18/24 = 3/4 = 0.75 = 75% represents the percentage of boys
Is 5x+y=7 linear or nonlinear
Answer:
Linear
Step-by-step explanation:
This can be written in slope intercept form (y=-5x+7) and there are no exponents.
Ham costs $3.40 a pound. How much is 1.2 pounds
Answer:$5.1
Step-by-step explanation: so since theres the 1 in 1.2 we know we have $3.40 right?, yeah so, half of $3.40 is 1.7 so jus add $1.7 to $3.40 wich is $5.1
The circumference of a circle can be found using the formula C = 2pi r. Which is an equivalent equation solved for r?
Answer:
[tex]\frac{C}{2\pi } =r[/tex]
Step-by-step explanation:
Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex]. Since we need r, we will use the second formula for circumference.
We start by solving for r in the Circumference formula. using inverse operations. We divide both sides (as the inverse of multiply) by 2pi.
[tex]C=2\pi r\\\frac{C}{2\pi } =r[/tex].
Answer: C
Step-by-step explanation:
The circumference of a particular circle is 18 cm. In square centimeters, what is the area of the circle? Express your answer as a common fraction in terms of pi.
Answer:
[tex]A=8.2 cm^2[/tex] or [tex]A=\frac{81}{\pi }[/tex]
Step-by-step explanation:
Since the the formula for the circumference of a circle is [tex]C=2\pi r[/tex] and C is 18, we can substitute and solve for r. After we solve for r, we substitute it into the area formula.
[tex]18=2\pi r\\\frac{18}{2\pi } =\frac{2\pi r}{2\pi }\\2.866=r[/tex]
The formula for the area is [tex]A=\pi r^{2} \\A=\pi 2.866^{2} \\A=8.2 cm^2[/tex]
As a fraction, we would not simplify to a decimal and the solution would be:
[tex]A=\pi r^{2} \\A=\pi (\frac{9}{\pi }) ^{2} \\A=\frac{81}{\pi }[/tex]
the quotient of 30 and the sum of 2 and 3
Answer:
30 divided by 2+3 is 6.
Step-by-step explanation:
The first thing you need to do is add 2 and 3, which is five, and then divide 30/5. The quotient is 6.
The quotient of 30 and the sum of 2 and 3 is 6.
Explanation:The quotient of 30 and the sum of 2 and 3 can be found by dividing 30 by the sum of 2 and 3.
Step 1: Calculate the sum of 2 and 3. 2 + 3 = 5.
Step 2: Divide 30 by 5. 30 ÷ 5 = 6.
Therefore, the quotient of 30 and the sum of 2 and 3 is 6.
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Please Help Me ASAP:
By what percent does the price change is the price was:
a. $100 and now it is $1250?
b.$160 and now it is $40?
Show your work!
First find the difference
160-40=120
Take the difference and divide it by the original number
120/160=0.75
Multiply by 100
75
Luke and Aiden go to the movie theater and purchase refreshments for their friends.
Luke spends a total of $30.50 on 8 bags of popcorn and 2 drinks.
Aiden spends a total of $49.00 on 7 bags of popcorn and 6 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer:
30.50 = 8p +2d
49= 7p +6d
The price of a bag of popcorn is $2.50
Step-by-step explanation:
p = price of popcorn
d = price of drinks
Luke costs:
30.50 = 8p +2d
Aiden
49= 7p +6d
I will multiply Lukes equation by -3 so I can use elimination on the d variable
-3 (30.50) =-3( 8p +2d)
-91.50 = -24p -6d
Now add the modified equation to Aidens equation
49 = 7p +6d
-91.50 = -24p -6d
-------------------------
-42.5 = -17p
Divide each side by -17
-42.50/-17 = -17p/-17
2.5 = p
Each popcorn costs 2.5
According to the table listing average daily expenses for a tourist by country based on high and medium categories, Brazil has a range from $12.25 to $18.33, and Greece has a range from $9.48 to $16.55. Which of the two countries has the larger difference between categories?
Answer:
Greece had a larger difference ($7.07)
Step-by-step explanation:
Brazil -
18.33 - 12.25 = 6.08
Greece-
16.55 - 9.48 = 7.07
Answer:
Greece has the larger difference between categories
Step-by-step explanation:
Difference in categories of Brazil
[tex]= 18.33 - 12.25\\= 6.08\\[/tex]
Difference in categories of Greece
[tex]= 16.55 - 9.48\\= 7.07\\[/tex]
Thus, Greece has the larger difference between categories
Which statement about a right triangle is true? The length of each leg equals 12 of the hypotenuse.
The square of the hypotenuse is equal to the sum of the squares of the legs.
One leg is always longer than the hypotenuse.
A right triangle can have only one obtuse angle.
Answer:
I didn’t know you could have more than 2 answers that’s pretty cool
Step-by-step explanation:
Help with #7 please I don’t understand
Answer:
A
Step-by-step explanation:
(2x^2 + 3x - 4) (x + 4)
FOIL.
2x^2 times x = 2x^3
3x times x is 3x^2
-4 times x = -4x
2x^2 times 4 = 8x^2
3x times 4 = 12 x
-4 times 4 = -16
Combine like terms to get 2x^3 + 11x^2 + 8x - 16.
Can someone check and see if I got the right answer on these problems
(1) is correct. [tex]\mathbf u\cdot\mathbf v=(-14)(0)+(8)(11)=0+88=88[/tex]
(2) is correct. I assume you just computed the dot product as above, but another way to do it is to notice that [tex]\mathbf v\cdot\mathbf v=\|\mathbf v\|^2[/tex] (that is, the dot product of a vector with itself is the square of its magnitude). Then since [tex]\|\mathbf v\|=\sqrt{1^2+2^2}=\sqrt5[/tex], we have [tex]\mathbf v\cdot\mathbf v=\|\mathbf v\|^2=5[/tex].
(3) is not correct. Since [tex]\mathbf u\cdot\mathbf u=\|\mathbf u\|^2=\sqrt{45}[/tex], we have [tex]\|\mathbf u\|=\sqrt{\sqrt{45}}[/tex].
(4) is correct.
[tex]2\mathbf u\cdot\mathbf v=2(\mathbf u\cdot\mathbf v)=2((-3)(1)+(6)(2))=2(-3+12)=2(9)=18[/tex]
Helppppppppppp me pleaseeeeeee
Need help with 5-8, will give brainliest to best and most accurate answer
Answer:
#5: 80mm, #6: 50yd, #7: 36m, #8: 32ft
Step-by-step explanation:
For #5:
The ratio between the two shapes is 24/15 = 8/5, based on the corresponding sides.
So, multiplying 8/5 with the smaller shape's perimeter of 50 would give you 80mm, which is the bigger shape's perimeter.
For #6:
The ratio between the two shapes is 15/9 = 5/3, based on the corresponding sides.
So, multiplying 5/3 with the smaller shape's perimeter of 30 would give you 50yd, which is the bigger shape's perimeter.
For #7:
The ratio between the two shapes is 12/4 = 3, based on the corresponding sides (You can also check this with 15/5).
So, multiplying 3 with the smaller shape's perimeter of 12 would give you 36m, which is the bigger shape's perimeter.
For #8:
The ratio between the two shapes is 12/21 = 4/7, based on the corresponding sides.
So, multiplying 4/7 with the bigger shape's perimeter of 56 would give you 32ft, which is the smaller shape's perimeter.
Hope this helps! Have a nice day!
Please help! 50 POINTS!!!
Answer:
f(x) = 2/3 x +3
Step-by-step explanation:
We know the y intercept ( where it crosses the y axis) is 3
We can calculate the slope from 2 points (-3,1) and (0,3)
Slope = (y2-y1)/(x2-x1)
= (3-1)/(0--3)
= (3-1)/(0+3)
= (2/3)
The slope is 2/3
Since we know the slope and the y intercept, we can use the slope intercept form
y= mx+b
y = 2/3 x+3
f(x) = 2/3 x +3