Predict which statements are true about the intervals of the continuous function. Check all that apply.
Answers
Answer:
the answer is:
b
d
e
Functions are used to show relationships between variables. The true statements are:
f(x) ≤ 0 over the interval [0, 2].f(x) > 0 over the interval (–2, 0).f(x) ≥ 0 over the interval [2, [tex]\infty[/tex])I've added as an attachment, the table of values of f(x)
Next, we test the given options
(a) f(x) > 0 over the interval ([tex]-\infty[/tex], 3).
Using the table of f(x), the values in ([tex]-\infty[/tex], 3) are values less than 3; i.e. -3 to 2.
If f(2) = 0, then f(x) > 0 is not true
(b) f(x) ≤ 0 over the interval [0, 2].
The values in [0, 2] are values from 0 to 2; i.e. 0, 1 and 2.
If f(0) = 0, f(1) = -3 and f(2) = 0
Then, f(x) ≤ 0
(c) f(x) < 0 over the interval (−1, 1).
Using the table of f(x), the values in (-1, 1) are values between -1 and 1; i.e. 0
If f(0) = 0, then f(x) < 0 is not true
(d) f(x) > 0 over the interval (–2, 0).
Using the table of f(x), the values in (-2, 0) are values between -2 and 0; i.e. -1
If f(-1) = 3, then f(x) > 0 is true
(e) f(x) ≥ 0 over the interval [2, [tex]\infty[/tex])
Using the table of f(x), the values in [2, [tex]\infty[/tex]) are values from 2; i.e. 2 and 3
If f(2) = 0 and f(3) = 15, then f(x) ≥ 0 is true
Hence, the true statements are:
f(x) ≤ 0 over the interval [0, 2].f(x) > 0 over the interval (–2, 0).f(x) ≥ 0 over the interval [2, [tex]\infty[/tex])Read more about functions over interval at:
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Related Questions
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.
Answers
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]
On a map, 1 inch equals 7.2 miles. Two houses are 1.5 inches apart on the map. What is the actual distance between the houses
Answers
Answer:
10.8
Step-by-step explanation:
7.2 X 1.5 = 10.8
Assuming two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.
Actual distanceLet x represent the actual distance
Given:
1 inch = 7.2 miles
1.5 inch =? miles
Hence:
1/ 7.2 = 1.5/ x
x= 7.2×1.5
x=10.8 miles
Inconclusion assuming two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.
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I need help with question 15 parts a b and c
Answers
Answer:
(a)
let m represents renting movie and c represents the total cost of buying a rental card.
As per the given statement: A video store charges $10 for a rental card plus $2 per movie.
⇒ c(m) = 2m + 10 ......[1]
which implies that this equation represents the slope intercept form(i.e y = ax+b) where 2 is the slope and a y-intercepts of 10.
(b)
Graph of the given equation:
c(m) = 2m + 10
you can see in the figure given below.
(c)
now, to find the cost of buying a rental card and renting 6 movies.
⇒ m = 6 [ as m represents renting movie]
Substitute this m =6 in equation [1];
c(6) = 2(6) + 10
c(6) = 12 + 10
c(6) = 22.
Therefore, the total cost of buying a rental card and renting 6 movies is, $22.
A rectangular coffee table has an area measure of 10x² + 13x - 3 square units. which of the following could represent the perimeter of the rectangle in terms of x?
Answers
To find the perimeter of a rectangle in terms of x, add up the length and width and multiply by 2.
Explanation:The perimeter of a rectangle can be found by adding up all four sides. In this case, the length and width of the rectangle are represented by the factors of the area measure:
10x² + 13x - 3 = (2x - 1)(5x + 3)
So the length is (2x - 1) and the width is (5x + 3). The perimeter can be calculated using the formula:
Perimeter = 2(length + width)
Substituting the values, the perimeter in terms of x is:
Perimeter = 2((2x - 1) + (5x + 3))
Simplifying further:
Perimeter = 2(7x + 2)
Perimeter = 14x + 4
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Ham costs $3.40 a pound. How much is 1.2 pounds
Answers
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 coach has 3 positions to fill on his basketball team. There are 9 students who are interested in being on the team. How many combinations of the three positions can he choose for the team?
A: 94
B:84
C:27
D:12
Answers
Answer: Option 'c' is correct.
Step-by-step explanation:
Since we have given that
Number of students who are interested in being on the team = 9
Number of positions to fill on his basket ball team = 3
So, the combinations of the three positions he can choose for the team is given by
[tex]3\times 9=27[/tex]
Hence, Option 'c' is correct.
The coach can choose 84 different combinations of the three positions from 9 interested students for the basketball team.
The coach needs to choose 3 out of 9 students to fill the positions on his basketball team. This is a combination problem, and the number of ways to choose [tex]\( r \)[/tex] items from [tex]\( n \)[/tex] items is given by the combination formula:
[tex]\[ C(n, r) = \frac{n!}{r!(n-r)!} \][/tex]
Here, [tex]\( n = 9 \) (number of students) and \( r = 3 \)[/tex] (number of positions to fill).
[tex]\[ C(9, 3) = \frac{9!}{3!(9-3)!} \][/tex]
[tex]\[ C(9, 3) = \frac{9!}{3!6!} \][/tex]
[tex]\[ C(9, 3) = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \][/tex]
[tex]\[ C(9, 3) = \frac{504}{6} \][/tex]
[tex]\[ C(9, 3) = 84 \][/tex]
So, the coach can choose from 84 different combinations for the team positions.
The correct answer is:
B: 84
Part A: What is Leslie’s number and why. Part B: what is the least number that can be made using each digit exactly once and explain why the value of the 4 is greater than the value of 6
Answers
Answer:
976 421; 124 679
Step-by-step explanation:
Part A. Largest number
Leslie's number was 976 421.
This is because the largest numbers are in the positions of largest value.
For example, 9 in the hundred thousands place, the next largest number in the ten thousands place, and so on.
===============
Part B. Smallest number
The smallest possible number is 124 679.
The value of the 4 is greater than the value of the 6 because the 4 is in the thousands place and the 6 is only in the hundreds place.
4000 > 600.
Estimate then record their products 3 × 46
Answers
Answer:
Estimate is 150 and actual product is 138.
Step-by-step explanation:
To estimate products, we round the numbers to nearest unit place, 10th, 100th, 1000th, and so on.
Given are the numbers 3 and 46.
We can round 46 ≈ 50.
So Estimation would be 3 x 46 ≈ 3 x 50
3 times 5 is 15 and we can add zeros after it.
So estimation is 3 x 46 ≈ 150.
Now actual product would be...
3 times 6 is 18, so we note down 8 and 1 goes to carry over 4.
3 times 4 is 12 and carry 1 will be added in it, so 12 + 1 = 13.
It means the actual product is 3 x 48 = 138.
at a concession stand 9 slices of pizza and 5 soft pretzels cost $33.25. If 4 slices of pizza and 6 soft pretzels cost $19.50. What is the cost of a soft pretzel?
Answers
Answer:
The cost of soft pretzel is $1.25
Step-by-step explanation:
Let $x be the price of one slice of pizza and $y be the price of one soft pretzel.
1. 9 slices of pizza cost $9x and 5 soft pretzels cost $5y. Together they cost $33.25, then
9x+5y=33.25.
2. 4 slices of pizza cost $4x and 6 soft pretzels cost $6y. Together they cost $19.50, then
4x+6y=19.50.
3. Solve the system of two equations:
[tex]\left\{\begin{array}{l}9x+5y=33.25\\4x+6y=19.50\end{array}\right..[/tex]
Multiplythe first equation by 4, the second equation by 9 and subtract them:
[tex]4(9x+5y)-9(4x+6y)=4\cdot 33.25-9\cdot 19.50,\\ \\36x+20y-35x-54y=133-175.5,\\ \\-34y=-42.5,\\ \\y=\$1.25.[/tex]
Then
[tex]4x+6\cdot 1.25=19.50,\\ \\4x=19.50-7.50,\\ \\4x=12,\\ \\x=\$3.[/tex]
Answer: Each soft pretzel cost $1.25
Step-by-step explanation:
Hi, we have to write an equation for each case:
9 x + 5 y = 33.25
4x +6 y = 19.50
Where x is the price of 1 slice of pizza, and y is the price of each soft pretzel.
Multiplying the first equation by 4, and the second equation by 9
36x +20y =133
36x +54y =175.5
And subtracting the first equation to the second equation
36x +54y =175.5
-
36x +20y =133
____________
34 y = 42.5
Solving for y
y =42.5/34
y = $1.25
Each soft pretzel cost $1.25
Simplify the expression using the laws of exponents. (x^2/3y^1/3)^3
Answers
Answer:
X^2 y
Step-by-step explanation:
So now you can make this x^2 y because the ^3 cancels it out
Answer:
x^6/27y
Step-by-step explanation:
(x^2/3y^1/3)^3
x^2 ^3/ (3^3 y^1/3 ^3)
Using the power of power rule, when a power is raised to a power, we multiply the powers.
x^ (2*3)/ (3^3 y^(1/3*3))
x^6/(27 y^1)
x^6/27y
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?
Answers
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
The rectangle below has an area of 15x^3y^415x 3 y 4 square meters and a length of 3x^2y3x 2 y meters.What is the width of the rectangle?
Answers
Answer:
The width of the rectangle is [tex]5xy^3[/tex].
Step-by-step explanation:
The area of a rectangle is the product of length and width of the rectangle.
[tex]A=length\times width[/tex]
It is given that the area of the rectangle is [tex]15x^3y^4[/tex] square meters and the length of the rectangle is [tex]3x^2y[/tex].
[tex]15x^3y^4=3x^2y\times width[/tex]
[tex]width=\frac{15x^3y^4}{3x^2y}[/tex]
[tex]width=\frac{3\times 5\times x^2\times xy^3\times y}{3x^2y}[/tex]
Cancel out common factors 3x²y.
[tex]width=5xy^3[/tex]
Therefore the width of the rectangle is [tex]5xy^3[/tex].
Joan picks a random counter out of a bag 10 times, and she got a yellow counter 7 times. What is the experimental probability of picking a yellow?
Answers
Answer:
she has a 70 percent chance of getting a yellow one
Step-by-step explanation:
Answer:
7/10 is your answer.
You are planning a trip to the United States. The exchange rate is $1 = 78p Approximately how many dollars will you get if you change 160 pounds for dollars?
Answers
Answer: If the rate of change is $1 = 78p, then if you have 160p, how much dollars you will get?
(if p are penys)
100p = 1 pound
if $1 = 78p = 0.78 pound
→ 1 pound = $1/0.78 = $1.28
→ 160*1 pound = $160/0.78 = $205.13
So if you change 160 pounds, you will get 205 dollars and 13 cents.
The number of dollars when 160 pounds is exchanged will be 205.13.
You may multiply the pounds by the exchange rate to get how many dollars you will receive for 160 pounds if the exchange rate is $1 = 78p.
160 pounds multiplied by the 78p to the dollar conversion rate results in:
160 pounds multiplied by 100 pence equals 16,000 pence.
Since there are 100 pence in a pound, we divide the amount in pence by 100 to get dollars:
16,000 p divided by 78p is $205.13
Consequently, if you convert 160 pounds to dollars at the current exchange rate of $1 = 78p, you will get around 124.80 dollars in return.
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which values of a and b make the expression true (2xy)^4/4xy = 4x^a y^b
A. a=0,b = 0
B. a=3,b =3
C. a=4,b =4
D. a=5,b =5
Answers
Answer: (B) a=3, b=3
Step-by-step explanation:
[tex]\dfrac{(2xy)^4}{4xy}[/tex]
[tex]=\dfrac{2^4x^4y^4}{4xy}[/tex]
[tex]=\dfrac{16x^4y^4}{4xy}[/tex]
[tex]=4x^{4-1}y^{4-1}[/tex]
[tex]=4x^3y^3[/tex]
Answer:
b
Step-by-step explanation:
Which expression represents “y less than 6”?
Answers
Answer:
6-y
Step-by-step explanation:
Six less than y means you take away y from six.
Hope this helps
Given: 1/3 x + y = 15. Which if the following are ordered pairs of this equation?
{(-3, 14), (0, 15), (3, 16)}
{(-3, 16), (0, 15), (3, 14)}
{(16, -3), (15, 0), (14, 3)}
Answers
Answer:
Option B - {(-3, 16), (0, 15), (3, 14)}
Step-by-step explanation:
Given : Equation [tex]\frac{1}{3}x+y=15[/tex].
To find : Which if the following are ordered pairs of this equation?
Solution :
Re-write the equation in linear equation format,
[tex]y=-\frac{1}{3}x+15[/tex]
Taking point, (-3,16)
We substitute x=-3,
[tex]y=-\frac{1}{3}(-3)+15[/tex]
[tex]y=1+15[/tex]
[tex]y=16[/tex]
It is true.
Taking point, (0,15)
We substitute x=0,
[tex]y=-\frac{1}{3}(0)+15[/tex]
[tex]y=0+15[/tex]
[tex]y=15[/tex]
It is true.
Taking point, (3,14)
We substitute x=3,
[tex]y=-\frac{1}{3}(3)+15[/tex]
[tex]y=-1+15[/tex]
[tex]y=14[/tex]
It is true.
Therefore, the ordered pairs are {(-3, 16), (0, 15), (3, 14)}.
So, option B is correct.
The circumference of a circle can be found using the formula C = 2pi r. Which is an equivalent equation solved for r?
Answers
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 student government snack shop sold 32 items this week
Answers
The completed table would look like this:
Snack Type Number Sold Percentage
Fruit Cup 6 18.75%
Veggie Sticks 6 18.75%
Chips 14 43.75%
Water 4 12.5%
Veggie Sticks:
Look at the "number of items sold" column for veggie sticks. It shows 6.
Divide the number of veggie sticks sold by the total number of snacks sold (32) and multiply by 100% to find the percentage.
(Number of veggie sticks) / (Total number of snacks) * 100%
= 6 / 32 * 100%
= 0.1875 * 100%
= 18.75% (round to two decimal places)
Chips:
Look at the "number of items sold" column for chips. It shows 14.
Follow the same steps as for veggie sticks:
(Number of chips) / (Total number of snacks) * 100%
= 14 / 32 * 100%
= 0.4375 * 100%
= 43.75% (round to two decimal places)
Water:
Look at the "number of items sold" column for water. It shows 4.
Follow the same steps as for veggie sticks and chips:
(Number of water bottles) / (Total number of snacks) * 100%
= 4 / 32 * 100%
= 0.125 * 100%
= 12.5% (round to two decimal places)
Therefore, the completed table would look like this:
Snack Type Number Sold Percentage
Fruit Cup 6 18.75%
Veggie Sticks 6 18.75%
Chips 14 43.75%
Water 4 12.5%
For complete question refer to image:
Multiply. Express your answer in simplest form. 3 3/4 × 2 2/9
Answers
Answer:
The answer is 8 1/3.
The answer will be 8 1/3
[tex]e = \frac{o + 4m + p}{6} [/tex]
find in terms of p
Answers
[tex]\dfrac{o+4m+p}{6}=e\qquad\text{multiply both sides by 6}\\\\o+4m+p=6e\qquad\text{subtract o and 4m from both sides}\\\\\boxed{p=6e-o-4m}[/tex]
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
Answers
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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Rates/ratio $1.00 for 5 apples
Answers
20 cents per apple
1/5=.20
Is 5x+y=7 linear or nonlinear
Answers
Answer:
Linear
Step-by-step explanation:
This can be written in slope intercept form (y=-5x+7) and there are no exponents.
Find the distance between points (3, 5) and (4, 6) to the nearest tenth.
A) 3.2
B) 2
C) 2.8
D) 1.4
Answers
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (3, 5) and (4, 6). Substitute:
[tex]d=\sqrt{(4-3)^2+(6-5)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt2\approx1.4[/tex]
Answer: D) 1.4The distance between the two points is 1.4.
Option D is the correct answer.
What is the distance between two points of a line?The distance between two points of a line is given as:
Distance = √(c - a)² + (d - b)²
We have,
To find the distance between the two points (3, 5) and (4, 6)
We can use the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Substituting the given values, we get:
d = √((4 - 3)² + (6 - 5)²)
d = √(1² + 1²)
d = √2
To the nearest tenth, the distance is approximately 1.4.
Therefore,
The distance between the two points is 1.4.
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Ice is placed around a bowl of water to lower the temperature. The equation D=-7/5+ 22, shows the time, t , measured in minutes and temperature, D, measured in degrees Celsius. Which statement is correct?
Answers
Answer:
Before cooling begins, the temperature of the water is 22°C.
Step-by-step explanation:
I think this is right
Answer:
Before cooling begins, the temperature of the water is 22°
22
°
C
.
Step-by-step explanation:
What is the total number of students in Ms. perron class
Answers
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
which of the following is a valid exclusion for the algebraic fraction 8ab^2x/4a^2b-8ab^2
Answers
Answer:
a ≠ 2b
Step-by-step explanation:
The given expression is
[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}}[/tex]
[tex]=\frac{8ab^{2}x}{4ab(a-2b)}[/tex]
Simplifying it, we have
[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}} = \frac{bx}{a-2b}[/tex]
For the above fraction to exist, the denominator must not be equal to zero.
i.e, a-2b ≠ 0
=> a≠2b
∴ The algebraic fraction exists when a≠2b.
Answer:
A valid exclusion for the algebraic fraction is when a=2b
Step-by-step explanation:
You have:
[tex]8ab^2x/4a^2b-8ab^2[/tex]
First you must to simplify:
Taking out common factor 4ab
[tex]4ab(2bx)/4ab(a-2b)[/tex]
[tex]2bx/a-2b[/tex]
The fraction can be written only if the denominator is different to zero, then
a-2b[tex]\neq[/tex]0
the excluded values are where
a-2b=0
this expression is equal to 0 when a=2b
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)
Answers
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)
I need help on number 12,13,24
Answers
Answer:
12.=0.06
13. =-5.12
14. =0.5
Step-by-step explanation:
12. .1 + .2 -.3 x.4/.5
.1+.2 -.12/.5
.1+.2-.24
.3-.24=.06
13. 3.2^2
10.24-15.36=-5.12
14. 4.2 x5/6 /10 +3/20
3.5 / 10 + 3/20
0.35+3/20
7/20+3/20=10/20
0.5