Answer:
(See explanation for further details).
Step-by-step explanation:
The sign does not affect the domain, as second-order polynomials are continuous functions. Nonetheless, the sign affect the range of function in the sense that elements can be lesser and equal to zero (a < 0) or greater and equal to zero (a > 0).
The sign of 'a' in the function f(x) = ax2 affects the direction the parabola opens, influencing the range of the function, either [0, ∞) for a positive 'a' or (-∞, 0] for a negative 'a'. The domain, which is always (-∞, ∞), isn't affected by 'a's sign.
Explanation:In mathematics, the function f(x) = ax2 is a quadratic function where 'a' is the coefficient of x2. The sign of 'a' determines whether the parabola opens upward or downward. When 'a' is positive, the parabola opens upward hence making the range of the function [0, ∞) because the lowest point (vertex) is on the x-axis and it extends to positive infinity. If 'a' is negative, the parabola opens downward, and the range becomes (-∞, 0] as the highest point is on the x-axis and it extends to negative infinity.
The domain of f(x) = ax2 does not depend on the 'a' value; it is always all real numbers because x can be any real number regardless of the value of 'a'. Therefore, the domain is always (-∞, ∞).
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Vera ordered a soup, salad, and sandwich to share with her friends. The probabilities of each item being ready first are as follows:P(Soup ready first)=
5
1
start text, P, left parenthesis, S, o, u, p, space, r, e, a, d, y, space, f, i, r, s, t, end text, right parenthesis, equals, start fraction, 1, divided by, 5, end fraction
P(Salad ready first)=0.45\text{P(Salad ready first}) = 0.45
P(Salad ready first)=0.45
start text, P, left parenthesis, S, a, l, a, d, space, r, e, a, d, y, space, f, i, r, s, t, end text, right parenthesis, equals, 0, point, 45
P(Sandwich ready first)=35%\text{P(Sandwich ready first}) = 35\%
P(Sandwich ready first)=35%
start text, P, left parenthesis, S, a, n, d, w, i, c, h, space, r, e, a, d, y, space, f, i, r, s, t, end text, right parenthesis, equals, 35, percent
Put the following events in order from least to most likely.
Salad ready first\text{Salad ready first
its
Soup ready first
Sandwich ready first
Salad ready first
Answer:
Soup ready first
Sandwich ready first
Salad ready first
Step-by-step explanation:
Joey has football practice every 3rd day and baseball practice every 7th day
Answer:
The 21st day
Step-by-step explanation:
If we mark the days, they will clash on the 21st day.
[tex]3*7=21[/tex]
Hope this helped. Have a nice day! Please mark brainliest!
Answer:
if i think u are talking about when these will over lap then they will over lap on the 21st day
Step-by-step explanation:
(0,-1) and (-2,0)
What is the slope of the graph?
What is the y-intercept of the graph?
Answer:
slope -1/2
y intercept -1
Step-by-step explanation:
To find the slope given two points
m = (y2-y1)/(x2-x1)
=(0--1)/(-2-0)
= (0+1) /(-2-0)
=1/-2
= -1/2
The y intercept is when x = 0
(0,-1) is when x =0 so the y intercept is -1
Answer:
-½; -1
Step-by-step explanation:
(0 - -1)/(-2 - 0)
1/-2
= -½
y intercept is where x = 0,
So it is -1
Solve the following:
5,138 ÷ 302
Answer:
17.0132
Step-by-step explanation:
Note: if one letter is incorrect in a term, that part of the puzzle will be graded as a missed answer.
- Across
2) A two-word phrase in a word problem that is a key word for subtraction.
4) A word used to show multiplication in a word problem.
7) A word that means something has been added.
8) A phrase in a word problem that tells you to subtract.
9) This is characterized by the symbol <, and is always read from left to right.
10) A word or phrase used to show division in a word problem.
- Down
1) A verbal phrase in a word problem that is a key word for subtraction.
3) A two-word phrase in a word problem that means to add.
5) A mathematical term that does not include an equal or inequality sign is called an _ _ _ _ _ _ _ _ _ _.
6) A verbal phrase in a word problem that means to add.
Submit
Find the value of c that will make 9x2 + 30x + ca perfect square trinomial.
Answer:
Step-by-step explanation:
(a+b)²=a²+2ab+b²
9x²+30x+ca
=(3x)²+2×3x×5+c
=(3x)²+2×3x×5+5²-5²+c
=(3x+5)²-25+c
it is a perfect square if -25+c=0
or c=25
The value for c to make 9x²+30x+ca perfect square trinomial is 25.
What is Quadratic Equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
We have Equation,
9x²+30x+ca
Using algebraic identity
(a+b)²=a²+2ab+b²
So, 9x²+30x+ca
=(3x)²+2×3x×5+c
=(3x)²+2×3x×5+5²-5²+c
=(3x+5)²-25+c
The given equation is a perfect square if -25+c=0
c = 25
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How can you find the area of a two-dimensional composite figure, or the surface area of a three-dimensional composite figure?
A.
Multiply the number of sides by the area of one side of the composite figure.
B.
Add the areas of all shapes or all faces that make up the composite figure.
C.
Multiply the length times the width times the height of the shapes that make up the composite figure.
D.
Add the measures of all angles of the composite figure.
NEED HELPP
Answer: D
Step-by-step explanation: To find the surface area of a composite 3D figure, add the areas of each geometric figure making up the composite 3D figure. To find the volume of a composite 3D figure, draw any necessary planes to view the figure as basic three dimensional figures, then: add basic figure volumes belonging to the composite shape.
Dividing the number of sides by the area of one of the composite figure's sides. and adding the areas of all the forms or faces that comprise the composite figure helps to find the area of a two-dimensional composite figure. Options A and B are correct.
What is surface area?The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.
The area of a two-dimensional composite figure or the surface area of a three-dimensional composite figure may be calculated by;
Dividing the number of sides by the area of one of the composite figure's sides. and add the areas of all the forms or faces that comprise the composite figure.
Hence, options A and B are correct.
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Which pair of angles must be supplementary?
Which pair of angles must be supplementary?
2 lines intersect to form right angles. Another line goes through the lines diagonally to form 6 angles. From top left, clockwise, the angles are 2 (90 degrees), 1, 6, 5 (90 degrees), 4, 3.
Angle 1 and Angle 6
Angle 2 and Angle 5
Angle 5 and Angle 4
Angle 6 and Angle 2
Answer:
I think 2 and 5
Step-by-step explanation:
The pair of angles must be supplementary are ∠2 and ∠5.
The correct option is (B)
What is supplementary angle?Two angles are called supplementary when their measures add up to 180 degrees.
Given that:
∠2=90 and ∠5=90
So,
∠2+∠5
=90+90
=180
Hence, angle 2 and 5 makes supplementary angles.
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There are 4 jacks and 13 clubs in a standard, 52-card deck of playing cards. What is the probability that a card picked at random from a standard deck of playing cards is a club or a jack?
Answer:
16/52, or 4/13.
Step-by-step explanation:
First, since we know that the question is asking for the probability of a club or a jack, we know that we have to add the two probabilities. The first probability is that of picking a club, which is 13/52. The probability of picking a jack (be sure not to overlap; don't double count the jack of clubs) is 3/52. Adding these two gives us 13/52+3/52=16/52, which simplifies to 4/13.
A swimming pool sets a maximum number of swimmers that can be in the pool based on the number of lifeguards on duty.
The points on the following coordinate plane show the maximum number of swimmers that can be in the pool when 2, 4, and 5 lifeguards are on duty.
What is the maximum number of swimmers that can be in the pool with 3 lifeguards on duty?
Answer:120
Step-by-step explanation:
Final answer:
The maximum number of swimmers with 3 lifeguards on duty is 31/3.
Explanation:
To find the maximum number of swimmers with 3 lifeguards on duty, we need to look at the pattern shown by the points on the coordinate plane. From the given information, we know that with 2 lifeguards, the maximum number of swimmers is 8. And with 4 lifeguards, the maximum number of swimmers is 12. With 5 lifeguards, the maximum number of swimmers is 15. So, we can assume that the pattern follows a linear relationship. To find the maximum number of swimmers with 3 lifeguards, we can create a linear equation using the two known coordinates: (2, 8) and (5, 15). Using the slope-intercept form of a linear equation, y = mx + b, we can solve for b. The slope, m, is (15-8)/(5-2) = 7/3. Plugging in one of the coordinates, such as (2, 8), we can solve for b: 8 = (7/3)(2) + b. Solving for b, we get b = 8 - 14/3 = 10/3. So, the equation for the line is y = (7/3)x + 10/3. Plugging in x = 3, we can find the maximum number of swimmers: y = (7/3)(3) + 10/3 = 21/3 + 10/3 = 31/3. Therefore, the maximum number of swimmers with 3 lifeguards on duty is 31/3.
A teacher needs to find out how many seventh-grade students will be going on a field trip. Which best describes the population that the teacher should survey?
A) the parents of all the students in the school
B) the parents of the seventh-grade students
C) each teacher in the school
D) each student in the school
Answer:
B
Step-by-step explanation:
The parents of the seventh-grade students, best describe the population that the teacher should survey. Option B is correct.
What is a survey?A survey in human subjects research is a set of questions designed to elicit specific information from a specific group of people.
As mentioned in the question, the teacher needs to find out how many seventh-grade students will be going on a field trip. For this teacher must ask to the students of seventh grade as well as survey the parents of the seventh-grade students.
Thus, the parents of the seventh-grade students, best describe the population that the teacher should survey. Option B is correct.
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3 packets of French fries, 2 cheeseburgers, and one drink cost $10.95. 1 packet of French fries, 2 cheeseburgers, and 3 drinks cost $11.25. Find the price of 1 packet of French fries, 1 cheeseburger, and one drink?
Answer:
The price of 1 packet of French fries, 1 cheeseburger, and one drink cost $5.55
Step-by-step explanation:
Let
x ----> the price of 1 packet of French fries
y ---> the price of 1 cheeseburger
z ---> the price of one drink
we know that
[tex]3x+2y+z=10.95[/tex] ----> equation A
[tex]x+2y+3z=11.25[/tex] ---> equation B
Adds equation A and equation B
[tex]3x+2y+z=10.95\\x+2y+3z=11.25\\------------\\3x+x+2y+2y+z+3z=10.95+11.25\\4x+4y+4z=22.2[/tex]
Divide both sides of the equation by 4
[tex]x+y+z=5.55[/tex] ----> equation C
The equation C means ----> The price of 1 packet of French fries, 1 cheeseburger, and one drink cost $5.55
Area of rectangle with a length of 3 2/3m and a height of 1 1/4m.
Answer:
4.5834m^2
Step-by-step explanation:
You do (length)*(width) which is (3 3/2m)*(1 1/4m) = 4.5834m^2 This is rounded because it was 4.5833333333 repeating.
Answer: the answer is 4 7/12m
Step-by-step explanation: Multiply both 3 2/3 and 1 1/4 to get 4 7/12. i know it isn't an explanation.
An international cake competition attracted 50 bakers from around the world. The graph below shows the relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
What is the best description of this relationship?
Choose 1 answer:
A
Positive linear association
B
Negative linear association
C
Nonlinear association
D
No association
Positive linear association shows the relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
An international cake competition attracted 50 bakers from around the world.
We have to tell relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
Scores were highest for cakes that had between 15 and 25 grams of sugar per 100 grams of cake.
Positive linear association shows the relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
Hence Positive linear association shows the relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
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The solutions to the equation x4 + 2x3 + 24 = 13x2 + 14x occur at x = –4, x = –2, x = 1, and x = 3. At what points does the graph of the function f(x) = x4 + 2x3 – 13x2 – 14x + 24 intersect the x-axis?
A) (0, –4), (0, –2), (0, 1) and (0, 3)
B) (0, 4), (0, 2), (0, –1) and (0, –3)
C) (–4, 0), (–2, 0), (1, 0), and (3, 0)
D) (4. 0), (2, 0), (–1, 0), and (–3, 0)
Answer:
C. (–4, 0), (–2, 0), (1, 0), and (3, 0).
Step-by-step explanation:
The points where the graph intersects the x axis have y coordinates of zero and the given x coordinates.
(–4, 0), (–2, 0), (1, 0), and (3, 0) is the answer.
Theo bought 8 packs of pencils for $4 each and 3 packs of
erasers that were on sale for $2 off their regular price of $5
each. Which keys could be entered into the calculator to
determine the total amount he spent?
O C8*4+385
C8*4+3*3
C8*4+3-2*
C8*4+3* 2-
Answer:
8*4+3*3
Step-by-step explanation:
It can't be the last answer because he buys three packs of erasers for three dollars each. It can't be the third answer because you have to multiply to get the price. It can't be the first answer because it's three of the numbers given put together. So it has to be 8*4+3*3
Final answer:
The total amount Theo spent can be calculated on a calculator with the input: 8 × 4 + 3 × 3, which represents the cost of pencils plus the discounted cost of erasers.
Explanation:
To determine the total amount Theo spent, you need to calculate both the cost of the pencils and the cost of the erasers, taking into account the sale on erasers.
For pencils, Theo bought 8 packs at $4 each. For erasers, he bought 3 packs at a $2 discount from their regular price of $5 each, meaning each pack of erasers cost $5 - $2 = $3 per pack on sale.
The correct calculation on the calculator for the total amount spent would be the cost of pencils plus the cost of erasers: 8 packs × $4 per pack for pencils, plus 3 packs × $3 per pack for erasers on sale.
This can be entered into the calculator as 8 × 4 + 3 × 3.
help me;( i dont understand
Given:
Line l and line m are parallel.
Co-interior angles are (12x - 8)° and 104°.
To find:
The value of x.
Solution:
Sum of co-interior angles = 180°
12x° - 8° + 104° = 180°
12x° + 96° = 180°
Subtract 96° from both sides.
12x° + 96° - 96° = 180° - 96°
12x° = 184°
Divide by 12° on both sides.
x° = 7°
x = 7
The value of x is 7.
Factor completely 5x2 − 40
Answer:
-30
Step-by-step explanation:
I am assuming that x here is a multiplication sign. If so than the simplification is easy:
First, 5 x 2 is 10Next, 10 - 40 = -30Select the possible dimensions of a rectangular prism with volume of 72 cubic meters . HInt: V = B x h (Area of base times the height) points A. 2 m x 6 m x 7 m B.3 m x 4 m x 6 m C.3 m x 8 m x 4 m D.9 m x 8 m x 1 m E.12 m x 2 m x 3 m (more than one posible answer)
Final answer:
The possible dimensions for a rectangular prism with a volume of 72 cubic meters are options B (3 m x 4 m x 6 m), D (9 m x 8 m x 1 m), and E (12 m x 2 m x 3 m), as their product of dimensions equals 72 cubic meters.
Explanation:
The question presents a schoolwork problem related to finding the possible dimensions of a rectangular prism with a given volume. According to the formula for volume, V = B x h, where V stands for volume, B is the area of the base, and h is the height. For a prism to have a volume of 72 cubic meters, the product of its dimensions (length x width x height) must equal 72.
For option A (2 m x 6 m x 7 m), the volume is 2 x 6 x 7 = 84 cubic meters, which is not equal to 72.
For option B (3 m x 4 m x 6 m), the volume is 3 x 4 x 6 = 72 cubic meters, which is correct.
For option C (3 m x 8 m x 4 m), the volume is 3 x 8 x 4 = 96 cubic meters, which is not equal to 72.
For option D (9 m x 8 m x 1 m), the volume is 9 x 8 x 1 = 72 cubic meters, which is also correct.
For option E (12 m x 2 m x 3 m), the volume is 12 x 2 x 3 = 72 cubic meters, which is another correct possibility.
Therefore, the possible dimensions for the rectangular prism with a volume of 72 cubic meters are represented by options B, D, and E.
Suppose a fair 6-sided die is tossed five times. What is the probability that we see at least one three in the five tosses?
a. 0.5981
b.0.8300
C. 0.1667
d. 0.4019
Answer:
C. 0.1667
Step-by-step explanation:
1/6 +0/6 + -1/6
The closest answer is C. 0.1667
Based on 2nd throw of dice shows zero then 0.1667 of the answer is shown on the 3rd throw in decimal form of -1/6
*respond AsAp*
How can you use technology and the structure of a polynomial expression to make connections between a polynomial and its graph?
Grayson baked 24 sugar cookies. His family ate 1/3 of the cookies. How many cookies did they eat? How many cookies are left
Answer:
His family ate 8 cookies, 16 cookies left
Step-by-step explanation:
Multiply 24 by 1/3 to find what the family ate
24*1/3=8
So, his family ate 8 cookies
To find how many are left, subtract what the family ate from the total
24-8=16
So, 16 cookies are left
Hope this helps! :)
how to compare box plots.
Box plots, or box-and-whisker plots, show data distribution through five main points: minimum, Q1, median, Q3, and maximum. A wider box indicates greater variability within the middle 50% of the data. To compare box plots, assess the spreads, medians, and potential outliers.
Explanation:A box plot, also known as a box-and-whisker plot, is a graphical representation of a data set that shows the distribution through five main data points: minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value.
To construct a box plot, you typically start with a number line that has been properly scaled. Using a ruler for this purpose ensures accuracy.
The box in a box plot represents the middle 50 percent of the data, spanning from Q1 to Q3.
The 'whiskers' of the plot stretch from the box to the minimum and maximum values, indicating the entire range of the dataset.
Comparing the spread of the middle 50 percent of the data involves looking at the width of the box: a wider box suggests a greater spread, meaning the data is more varied within the interquartile range (IQR).
If you are using a graphing calculator, you can enter the data into a list and then select the box plot function to graphically display the data.
When comparing two or more box plots, look for differences in their central values (medians), spreads (IQRs), and potential outliers (which lie beyond 1.5 times the IQR from the quartiles).
there are 32 students in your freshman spanish class. Your teacher randomly chooses one student at a time to take a verbal exam. what is the probability that you are not one of the first 4 students chosen
Answer:
25% chance
Step-by-step explanation:
32/4=8
8 out of 32 is a 25% chance
PLEASE HELPPPPPPP!!!!!!
You buy a new video game for $60.
The sales tax is 8%.
What is the total cost for the game including sales tax?
Choices:
$4.80
$64.80
$68
$125.80
Answer:
$64.80
Step-by-step explanation:
First, calculate the sales tax
Convert 8% into a decimal
8/100=0.08
Multiply the decimal by the cost of the game
60*0.08=4.8
$4.80 is just the tax, we have to find the total cost
Add the tax and the cost of the game
60+4.80=64.80
So, the total cost is $64.80
Hope this helps! :)
The ratio of petunias to geraniums in the greenhouse was 15 to 2. The combined numbernof petunias and geraniums was 1020.
ILL GIVE YOU BRAINLIEST!! How many geraniums were in the greenhouse?
A. 30
B. 510
C. 68
D. 2040
E. 120
Answer:
E. 120
Step-by-step explanation:
Let's say the number of total flowers is (15+2)x
That means the number of geraniums is 2x.
That also means that 1020 = 17x, which makes x = 60
Because 2x = geraniums and x = 60, the number of geraniums is 120
What is the answer??
What is 5(x+20) = 7x+30?
Answer: 35
Step-by-step explanation:
Simplifying
5(x + 20) = 7x + 30
Reorder the terms:
5(20 + x) = 7x + 30
(20 * 5 + x * 5) = 7x + 30
(100 + 5x) = 7x + 30
Reorder the terms:
100 + 5x = 30 + 7x
Solving
100 + 5x = 30 + 7x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-7x' to each side of the equation.
100 + 5x + -7x = 30 + 7x + -7x
Combine like terms: 5x + -7x = -2x
100 + -2x = 30 + 7x + -7x
Combine like terms: 7x + -7x = 0
100 + -2x = 30 + 0
100 + -2x = 30
Add '-100' to each side of the equation.
100 + -100 + -2x = 30 + -100
Combine like terms: 100 + -100 = 0
0 + -2x = 30 + -100
-2x = 30 + -100
Combine like terms: 30 + -100 = -70
-2x = -70
Divide each side by '-2'.
x = 35
Simplifying
x = 35
Answer:
[tex]x=35[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]5(x + 20) = 7x + 30[/tex]
[tex](5 * x) + (5 * 20) = 7x + 30[/tex]
[tex]5x + 100 = 7x + 30[/tex]
Step 2: Subtract 5x from both sides
[tex]5x + 100 - 5x = 7x + 30 - 5x[/tex]
[tex]100 = 2x + 30[/tex]
Step 3: Subtract 30 from both sides
[tex]100 - 30 = 2x + 30 - 30[/tex]
[tex]70 = 2x[/tex]
Step 4: Divide both sides by 2
[tex]70 / 2 = 2x / 2[/tex]
[tex]35 = x[/tex]
Answer: [tex]x = 35[/tex]
A packing box has the dimensions 3 by 2 by 51
2 feet. What is the volume of the box?
( A rectangular prism with a length of 3 feet, width of 2 feet, and height of 5 and one-half feet. )
Use the formula V = Bh to calculate the volume of the packing box.
The area of the base of the box, B, is __ ft.2.
The volume of the box is __ ft.3.
Answer:the area of the base of the box, B, is 6 ft2
The volume of the box is 33ft3
Step-by-step explanation:
Formula to find area of the base is bh (bass x height)
Formula for volume is (base x length)
The required volume of the packing box is 33 ft^3 and area of the base B is 6 ft^2
Area of the Rectangular Prism:
The area of the rectangular prism having a length and b width with h height is
Volume = a b h
If we are interested t find area of the base then
B = a b
How to calculate volume of rectangular prism?here we have given that
a = 3 feet
b = 2 feet
h = [tex]5\frac{1}{2}[/tex] = 11/2 feet
Therefore the area of the base B = a b = 3 x 2 = 6 ft^2
Now the volume of the object is
V = B h
V = 6 x 11/2 = 33 ft^3
This is the required volume of the rectangular prism
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Casey surveyed the members of his soccer team to ask them what their favorite sport is
Answer:
yes, that is very correct
Step-by-step explanation:
yes