The functions that have a range of all real numbers include the following:
Option 1; f(x) = -x + 2
Option 3; \(h(x) = 2^x +1\)
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range for f(x) and h(x):
Range = {-∞, ∞}, y|y ∈ R, or all real numbers.
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A circular tablecloth has a diameter of 70 inches. Max wants to add a decorative fabric around the edge of the tablecloth. Approximately how many inches of the decorative fabric does Max need? Use 3.14 for π. Enter your answer as a decimal in the box.
Answer:
219.8
Step-by-step explanation:
Two fire-lookout stations are 13 miles apart, with station B directly east of station A.
Both stations spot a fire. The bearing of the fire from station A is N35°E and the
bearing of the fire from station B is N49°W. How far is the fire from station B?
Choose the correct formula given below.
The distance between the fire and station B is 10.7miles
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The angle at A = 90- 35
= 55°
The angle at B = 90-49
= 41°
Angle at the fire = 180-(41+55)
= 180-96 = 84°
Using sine rule
sin84/13 = sin55/x
xsin84 = 13sin55
0.995x = 10.65
x = 10.65/0.995
x = 10.7 miles
Therefore the distance between the fire and station B is 10.7 miles.
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JKLM is a rhombus.
m/JMN = (-x+69)*
mZLMJ = (-6x +166)
K
N
M
Find the mZLKN.
label optional
The angle LKN in the rhombus is 62 degrees.
How to find angles in a rhombus?A rhombus is a quadrilateral that has 4 sides equal to each other. The sum of angles in a rhombus is 360 degrees.
Opposite angles are equal in a rhombus. The diagonals bisect each other at 90 degrees. Adjacent angles add up to 180 degrees.
Therefore, let's find ∠LKN as follows:
m∠JMN = (-x + 69)
m∠LMJ = (-6x + 166)
Therefore,
1 / 2 (-6x + 166) = -x + 69
-3x + 83 = -x + 69
-3x + x = 69 - 83
-2x = -14
x = -14 / -2
x = 7
Therefore,
∠LKN = 1 / 2 (-6x + 166)
∠LKN = 1 / 2 (-6(7) + 166)
∠LKN = 1 / 2 (-42 + 166)
∠LKN = 62 degrees
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please help!! need it fast, will give brainliest!! and pls show work !!
Find the measure of angle AEB
Answer:
An acute angle
Step-by-step explanation:
An acute angle is smaller than an obtuse ad right angle.
hope this helps and hope it was right 'cause I really don't know what you meant. :)
I need help on this question 4 4/5 - 1 9/10 also show the work.
Answer:
29/10 or 2 9/10
4 4/5 - 1 9/10
make them into improper fractions
4 4/5 = 24/5
1 9/10 = 19/10
24/5 - 19/10 we need to get common denominators
24/5 × 2 = 48/10
48/10-19/10 = 29/10 = 2 9/10
Algebra 2
Can you help me pls
Answer:
In50=3.912023005
Step-by-step explanation:
press it on your calculator
Please solve this. I need help on it
Answer:
look at the photo............
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Answer:
∠PTQ = 40°
∠PTR = 140°
Step-by-step explanation:
The two marked angles are "vertical" angles, so are congruent.
∠PTQ = ∠STR
(x +28)° = (2x +16)°
12 = x . . . . . . . . . . . . . . . divide by °, subtract x+16
Then the measure of angle PTQ is ...
∠PTQ = (x +28)° = (12 +28)° = 40°
That and angle PTR form a linear pair, so are supplementary.
∠PTR = 180° -∠PTQ = 180° -40° = 140°
Needing to find the answer to this question attached. Thank you
\(\sin \theta -1 =0\\\\\ \implies \sin \theta = 1\\\\ \implies \theta = \dfrac{\pi}2 + 2\pi n\\\\\text{For n =0,}\\\\\theta = \dfrac{\pi}2\)
PLEASE HELP ME, I DON'T UNDERSTAND THIS! :(
Answer:
1/204
Step-by-step explanation:
6/18 * 5/17 * 4/16 * 3/15
= 1/3 * 5/17 * 1/4 * 1/5
= 1/204
One number is 5 more than twice another and their sum is 23. Find the numbers.
The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
One number is 5 more than twice another and their sum is 23.
Let the two numbers be 'x' and 'y'. Then the equations are given as,
y = 2x + 5 ...1
x + y = 23 ...2
From equations 1 and 2, then we have
x + 2x + 5 = 23
3x + 5 = 23
3x = 23 - 5
3x = 18
x = 6
Then the value of the variable 'y' will be given as,
6 + y = 23
y = 23 - 6
y = 17
The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
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After 2 weeks of training Amanda learned a total of 5 appetizer recipes after 6 weeks of training how much appetizers will she learn
Answer:
15
Step-by-step explanation:
After 6 weeks of training, Amanda will learn 15 recipes.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Recipes learned by Amanda after 2 weeks of training = 5.
After 6 weeks of training, the number of recipes are required.
To find the number of recipes,
Use ratio property,
After 2 weeks of training = 5 recipes
After 1 week of training = 5/2 recipes.
Therefore, after 6 weeks of training = (5/2) x 6 = 15 recipes.
Amanda will learn 15 recipes after 6 weeks of training.
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Sam invest $4000 in an account that compounds interest continuously and earns 5.5% how long will it take for his money to reach $80,000 round to the nearest 10th of a year
Answer:
54.5 years.
Step-by-step explanation:
From the above question, we are asked to find the time
The formula for Time(t) =
t = log(A/P) / n[log(1 + r/n)]
A = Amount accumulated after a particular interest and period of time = $80,000
P = Principal (Money invested) = $4,000
r = rate = 5.5% = 0.055
n = compounding frequency = compounding continuously
n = number of days in a year × number of hours in a day
= 365 days × 24 hours = 8760
t = log(A/P) / n[log(1 + r/n)]
t = log(80,000/4,000) /8760[log(1 + 0.055/8760)]
t = log(80000 ÷ 4000) ÷ (8760 × [log(1 + 0.0000062785)]
t = 54.468367222 years
Approximately to the nearest tenth of a year, therefore, the length of time it will it take for his money to reach $80,000 is 54.5 years
Answer:
54.5
Step-by-step explanation:
cindy throws one red and one blue dice. find the probability that the sum of the two dice is less than 4.
The probability that the sum of the two dice is less than 4 is 3/36, which simplifies to 1/12.
What is dice probability?Dice probability refers to the likelihood of a certain outcome when rolling one or more dice. The probability of rolling a particular number on a fair six-sided die, for example, is 1 in 6 or approximately 16.67%. The probability of rolling any number from 1 to 6 on a single die is always the same since each face has an equal chance of landing face up.
Given by the question.
To finds the probability that the sum of the two dice is less than 4, we need to list all the possible outcomes when Cindy throws one red and one blue dice, and then count the number of outcomes that satisfy the condition.
Possible outcomes when throwing two dice:
Red Blue
1 1
1 2
1 3
1 4
1 5
1 6
2 1
2 2
2 3
2 4
2 5
2 6
3 1
3 2
3 3
3 4
3 5
3 6
4 1
4 2
4 3
4 4
4 5
4 6
5 1
5 2
5 3
5 4
5 5
5 6
6 1
6 2
6 3
6 4
6 5
6 6
There are 36 possible outcomes when throwing two dice.
Outcomes where the sum of the two dice is less than 4:
Red Blue
1 1
1 2
2 1
There are 3 outcomes where the sum of the two dice is less than 4.
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Find all points on the x-axis that are 16 units from the point (4,-8)
Step-by-step explanation:
all points on the x axis have a y value of 0.
so, we need to find all points (x, 0) with a distance of 16 to (4, -8).
the distance to a point is the Hypotenuse of the right-angled triangle with the coordinate differences as legs.
and so Pythagoras applies :
c² = a² + b²
with c being the Hypotenuse (side opposite of the 90° angle).
so, in our case we have
16² = (4-x)² + (-8 - 0)²
256 = 16 - 8x + x² + 64 = x² - 8x + 80
x² - 8x - 176 = 0
if we have no other idea of factorization the general solution of such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -8
c = -176
x = (8 ± sqrt((-8)² - 4×1×-176))/(2×1) =
= (8 ± sqrt(64 + 704))/2 = (8 ± sqrt(768))/2 =
= (8 ± sqrt(256×3))/2 = (8 ± 16×sqrt(3))/2 =
= 4 ± 8×sqrt(3)
x1 = 4 + 8×sqrt(3) = 17.85640646...
x2 = 4 - 8×sqrt(3) = -9.856406461...
so, the points on the x axis that are 16 units apart from (4, -8) are
(x1, 0) and (x2, 0)
I am not sure in what format you need the answer.
please fill in for x1 and x2 from above what you need.
Luke's pencil case measure 1.5 inches by 4 inches by 6 inches. How many pencils can he fit in his pencil case if each pencil has a volume of 3 square inches?
Answer:
b
Step-by-step explanation:
Ernie Rolph borrowed $6700 at 4% annual simple interest. If exactly 1 year later he was able to repay the loan without penalty, how much interest would he owe? Ernie will owe $___ in interest.
Ernie will owe an interest of $268
What’s the answer to this, help plzzzzz
Double checking but is this A
Answer:
si
Step-by-step explanation:
si
What is the scale factor of figure B to figure A?
Scale factor =_________
(40 points)
The scale factor of figure B to figure A is 1/2.
How to find the scale factor?To find the scale factor of figure B to figure A, we need to determine how much the corresponding sides of the two figures have been multiplied or divided by.
Looking at the figures, we can see that the corresponding sides of figure B are half the length of the corresponding sides of figure A. For example, the length of side AB in figure A is twice the length of side AB' in figure B, and the length of side BC in figure A is twice the length of side B'C' in figure B.
Since the corresponding sides of figure B are half the length of the corresponding sides of figure A, the scale factor of figure B to figure A is 1:2 or 1/2.
Therefore, the scale factor of figure B to figure A is 1/2.
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Mookie, Gandalf, and O’Malley are selling tickets to a play. Gandalf sold five less than three times the number of tickets Mookie sold. O’Malley sold one more than seven times the number of tickets Mookie sold. The number of tickets O’Malley sold is four more than twice the number of tickets that Mookie and Gandalf sold together. How many tickets did they sell in total?
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Answer:
73
Step-by-step explanation:
Let m, g, o represent the numbers sold by Mookie, Gandalf, and O'Malley, respectively. Then the relations between these values are ...
g = 3m -5
o = 7m +1
o = 4 +2(m +g)
Equating expressions for o, we have ...
7m +1 = 4 +2(m +g)
Substituting for g, we have ...
7m +1 = 4 +2(m +(3m -5))
7m +1 = 8m -6
7 = m . . . . . . . . add 6-7m
g = 3·7 -5 = 16
o = 7·7 +1 = 50
The number sold in total is ...
m + g + o = 7 +16 +50 = 73
They sold 73 tickets in total.
Complete the table below to find solutions to the linear equation −10x−y=−20.
Answer:
−10x − y = −20
y = -10x + 20
hope this helps, good luck :)
Write an equation of the line that passes through the given point as is (a) parallel and (B) perpendicular to the given line
A. y=
B. y=
Calculate how much money Carlos has after 4 years if he originally invested $3675 at 8.3% compounded continuously. Use Pe rt, where A is the final amount, P is the original amount deposited, r is the interest rate, and t is the number of years.
Answer:
$5122.04
Step-by-step explanation:
Continous interest formula:
\(P*e^{rt}\)=A
we have
\(3675*e^{4*.083}\\3675*1.39375284861\\5122.04171828\)
Which rounds to
5122.04
please help!! i also have to show work!
write the equation in vertex form y = x^2 - 12x + 15
Question 1
Is V8 a rational or irrational number?
A
irrational, because its decimal expansion does not repeat
B
rational because all radicals are rational
D
rational because its decimal expansion eventually repeats
D
irrational, because all radicals are ichtional
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9514 1404 393
Answer:
A irrational, because its decimal expansion does not repeat
Step-by-step explanation:
8 is not a perfect square integer. The closest ones are 2² = 4 ad 3² = 9. The square root of an integer that is not a perfect square is irrational. That is, the decimal expansion does not end and does not repeat.
√8 is irrational
Overview
10
Question Progress
Homework Progress
43 / 50 Marks
Which two numbers have a mean of 10 and a range of 4?
Answer:
I belive the correct answers are 8 and 12
Step-by-step explanation:
Determine the equation of the circle with center (0, -2) containing the point
(√12,-5).
Answer:
i think its
x^2 + (y + 2)^2 = 21.
Step-by-step explanation:
The main show tank has a radius of 70 feet and forms a quarter-sphere. What is the volume
of the quarter-sphere shaped tank? Round your answer to the nearest whole number You
must explain your answer using words, and you must show all work and calculations to
receive credit. (2 points)
The following question has two parts. First, answer part A. Then, answer part B.
Answer:
Step-by-step explanation:
Step-by-step explanation:
area of rectangle= l*b
2and 2/3 * 7 and 3/4
8/3 * 31/4
62/3 sq . feet
20 and 2/3 feet
Please help 10points!
Find x.
Answer:
The value of x is 19.
Step-by-step explanation:
Given:
m∠1 = (4x + 9)°
m∠2 = (x - 14)°
Since m∠1 and m∠2 are complementary angles, we have:
m∠1 + m∠2 = 90°
Substituting the given expressions for m∠1 and m∠2:
(4x + 9)° + (x - 14)° = 90°
Combining like terms:
4x + 9 + x - 14 = 90
Combining the x terms and the constant terms:
5x - 5 = 90
Adding 5 to both sides:
5x = 90 + 5
Simplifying:
5x = 95
Dividing both sides by 5:
x = 95 / 5
Simplifying further:
x = 19