Answers
Option B:
f(3) = 5
Solution:
Given function:
[tex]f(x)=\left\{\begin{aligned}-x^{2}, \ \ & x<-2 \\3, \ \ &-2 \leq x<0 \\x+2, \ \ & x \geq 0\end{aligned}\right.[/tex]
If x value is less than –2, that is –3, –4, –5, –6, ... then f(x) = –x².If x value is greater than or equal to –2 and less than 0, that is –2 and –1 then f(x) = 3.If x value is greater than or equal to 0, that is 0, 1, 2, 3,... then f(x) = x +2.To find the value of f(3):
Here x value is 3 which is greater than 0 (3 > 0).
Therefore, f(x) = x + 2.
Substitute x = 3 in the above function.
f(3) = 3 + 2
f(3) = 5
Hence option B is the correct answer.
Related Questions
Clare and Hoah play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty. Clare makes 6 goals and 3 penalties, ending the game with 6 points. Noah earns 8 goals and 9 penalties and ends the game with -22 points. Write a system of equations that describe Clare and Hoahs outcomes. Use x to represent the number of points for a goal and y to represent the number of points for a penalty
Answers
Answer:
The system
6*x - 3*y = 6
8*x - 9*y = - 22
Solution:
x = 4
y = 6
Step-by-step explanation:
We have:
"x" number of points for a goal
"y" number of points for a penalty
Then according to problem statement, we get the two equation system
Clare 6*x - 3*y = 6 And
Hoah 8*x - 9*y = - 22
If we are going to solve it, we can:
6*x - 3*y = 6 ⇒ 2*x - y = 2
8*x - 9*y = - 22
y = 2*x - 2
8*x - 9 *( 2*x -2) = - 22 ⇒ 8*x - 18*x + 18 = - 22
-10*x = - 40 x = 4
And then y = 2*x - 2 ⇒ y = 8 - 2 ⇒ y = 6
Plz Help i dont understand this the diameter of a bicycle wheel is 29in how many revolutions does the wheel make when the bicycle moves 200ft round your answer to the nearest whole number use 3.14 for pi
Answers
Answer:
26
Step-by-step explanation:
The diameter of the wheel is 29 in.
The circumference of the wheel is 3.14 × 29 in = 91.06 in.
For each revolution, the bike moves forward one circumference. So the number of revolutions is (200 ft × 12 in/ft) / 91.06 in ≈ 26.
A teacher writes the name of each of her 25 students on a slip of paper and places the papers in a box. To call on a student, she draws a slip of paper form the box. Each paper is equally likely to be drawn, and the papers are replaced in the box after each draw.
If the class contains 11 boys and 14 girls, what is the probability of calling on a girl?
a.
0.0016
c.
0.56
b.
0.36
d.
Answers
Answer:
0.56
Step-by-step explanation:
There are 14 girls, and a total of 25 students. So the probability of selecting a girl is P = 14/25 = 0.56.
The probability of calling on a girl will be 0.56. The correct option is C.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.
The probability of calling on a girl can be calculated by dividing the number of girls by the total number of students in the class:
Probability of calling on a girl = Number of girls / Total number of students
Number of girls = 14
Total number of students = 11 + 14 = 25
Therefore, the probability of calling on a girl is:
Probability of calling on a girl = 14 / 25 = 0.56
So, the correct answer is (c) 0.56.
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If you are given the graph of h(x)=log6x, how could you graph m(x)=log6(x+3)?
Translate each point of the graph of h(x) 3 units up.
Translate each point of the graph of h(x) 3 units down.
Translate each point of the graph of h(x) 3 units right.
Translate each point of the graph of h(x) 3 units left.
Answers
Answer: last option.
Step-by-step explanation:
There are several transformations for a function f(x). Some of them are shown below:
1. If [tex]f(x)+k[/tex], then the function is translated "k" units up.
2. If [tex]f(x)-k[/tex], then the function is translated "k" units down.
3. If [tex]f(x+k)[/tex], then the function is translated "k" units left.
4. If [tex]f(x-k)[/tex], then the function is translated "k" units right.
In this case you have the following function:
[tex]h(x)=log_6x[/tex]
And the function m(x) is obtained by transformating the function h(x). This function is:
[tex]m(x)=log_6(x+3)[/tex]
Then, based on the transformatios shown before, you can identify that:
[tex]m(x)=h(x+3)[/tex]
Therefore, you can determine that you could graph the function [tex]m(x)=log_6(x+3)[/tex] by translating each point of the graph of the function h(x) 3 units left.
Tracy works at a hot dog stand.
• She sells 3 hot dogs and 2 pretzels for $15.00.
• She sells 5 hot dogs and 1 pretzel for $21.50.
This situation can be modeled by the system of the equations shown below.
3h+2p=15
5h+p=21.5
Then Tracy sells 2 hot dogs and 4 pretzels. What is the total cost of this order?
Answers
Answer: the total cost of this order is $14
Step-by-step explanation:
She sells 3 hot dogs and 2 pretzels for $15.00.
She sells 5 hot dogs and 1 pretzel for $21.50. The system of linear equations used to model the situation is
3h+2p=15 - - - - - - - - - - - -1
5h+p=21.5 - - - - - - - - - - -2
Multiplying equation 1 by 5 and equation 2 by 3, it becomes
15h + 10p = 75
15h + 3p = 64.5
Subtracting, it becomes
7p = 10.5
p = 10.5/7
p = 1.5
Substituting p = 1.5 into equation 1, it becomes
3h + 2 × 1.5 = 15
3h + 3 = 15
3h = 15 - 3 = 12
h = 12/3 = 4
If Tracy sells 2 hot dogs and 4 pretzels, the total cost of this order would be
(4 × 2) + (4 × 1.5)
= 8 + 6 = $14
William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles the last jar holds 17 marbles write an expression using parentheses to show how many marbles each boy will get.
Answers
Answer:
Each boy will get 25 marbles.
Step-by-step explanation:
Given:
William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles the last jar holds 17 marbles.
Now, to write an expression using parentheses to find number of marbles each boy get.
Let the number of marbles each boy get be [tex]x.[/tex]
Total number of boys = 2.
Number of marbles first jar holds = 12.
Second jar holds = 21.
And third jar holds = 17.
As given, William shares marbles equally with his brother.
Now, we write the expression to find the number of marbles each boy get:
[tex]x=\frac{(12+21+17)}{2}[/tex]
[tex]x=\frac{12}{2} +\frac{21}{2} +\frac{17}{2}[/tex]
[tex]x=6+10.5+8.5[/tex]
[tex]x=25.[/tex]
Therefore, each boy will get 25 marbles.
Everett and marie are going to make fruit bars for their family reunion they want to make 4 times the amount the recipe makes if the recipe calls for 2/3 cup of oil, how much oil will they need?
Answers
40. What is the system of inequalities associated with the following graph?
Answers
Answer:
The bottom answer
Step-by-step explanation:
Jim and Stephanie just got married and are thinking about changing their health care insurance plans to be more affordable. Currently, both Jim and Stephanie are insured through their own employers. Jim’s employer pays 42% of his $378 monthly premium. His insurance plan will also pay for 23% of the $345 premium for additional beneficiaries. Stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30% of the $349 premium for each additional beneficiary. Insurance Jim's Employer Beneficiary Monthly Premium Employer Contribution Jim $378 42% Additional (each) $345 23% Stephanie's Employer Beneficiary Monthly Premium Employer Contribution Stephanie $298 35% (+10% for each additional beneficiary) Additional (each) $349 30% Which would be the most economical way for the couple to purchase health insurance? a. They should both add each other to their plans. b. Stephanie should add Jim to her health care plan. c. Jim should add Stephanie to his health care plan. d. They should each purchase a plan from their own employer. Please select the best answer from the choices provided A B C D
Answers
Answer:
Option B is correct.
Stephanie should add Jim to her health care plan.
Step-by-step explanation:
Let's take the options one by one.
Option 1
If Jim's employers insure him and his wife.
Jim’s employer pays 42% of his $378 monthly premium. His insurance plan will also pay for 23% of the $345 premium for additional beneficiaries.
It means Jim will pay (0.58 of $378) for himself plus (0.73 of $345) for his wife.
Amount Jim pays = (0.58 × 378) + (0.73 × 345) = $471.09
Option 2
If Stephanie's employers insure both of them.
Stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30% of the $349 premium for each additional beneficiary.
It means Stephanie would pay (0.65 of $298) she'll pay for herself plus (0.70 of $349) she'll pay for her husband minus (10% of $298) that her company wants to pay out of the insurance fee of any of her additional beneficiary.
Amount Stephanie will pay = (0.65 × 298) + (0.70 × 349) - (0.10 × 298) = $408.2
Option 3
If each of them does an insurance plan with their respective employers
Jim’s employer pays 42% of his $378 monthly premium.
Stephanie’s employer pays 35% of her $298 monthly premium
Jim would pay (0.58 × $378) for himself = $219.24
Stephanie would pay (0.65 × $298) for herself = $193.7
Total they would pay in this option = $219.24 + $193.7 = $412.94
Of all the three options, the option that minimizes their expenses is when Stephanie insures herself and Jim with her employers for a total cost of $408.2 compared to a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they respectively insure each other with their respective employers.
Hope this Helps!!!
Insurance is termed as the process of safeguarding against financial loss. It's a type of risk management that's used mostly to protect against the danger of a speculative or unpredictable loss.
An insurer, an insurance company, an insurance carrier, an underwriter is a business that sells insurance.
The correct answer is option B. Stephanie should add Jim to her health care plan.
The evaluation of each and every option is as follows:
Option 1
If Jim and his wife are covered by Jim's employer's insurance.
Jim's $378 monthly premium is covered by his company to the tune of 42 percent. Additional beneficiaries will be covered by 23 percent of his insurance plan's $345 cost.
Jim will have to pay 0.58 of $378 for himself and 0.73 of $345 for his wife.
Jim's payment = = $471.09
Option 2
If both of them are protected by Stephanie's company's insurance.
Stephanie's company pays 35% of her $298 monthly premium, but she has the choice of paying a further 10% of her discount for each beneficiary she adds to her plan. For each new beneficiary, her employer would pay 30% of the $349 payment.
Stephanie would pay (0.65 of $298) for herself plus (0.70 of $349) for her husband, minus (10 percent of $298) that her firm wants to pay out of any of her extra recipients' insurance payments.
Stephanie will pay $408.2 by multiplying (0.65 298) by (0.70 349) by (0.10 298).
Option 3
If they both join an insurance plan via their companies, Jim's employer will cover 42 percent of his $378 monthly payment.
Stephanie's $298 monthly charge is compensated by the business to the tune of 35%.
For himself, Jim would pay [tex](0.58 \times \$378)[/tex]= $219.24
Stephanie would pay (0.65 $298) for herself = $193.7 The total cost of this option would be $219.24 + $193.7 = $412.94.
Stephanie ensures herself and Jim with her employers for a total cost of $408.2, against a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they insure each other with their respective jobs.
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Taylerbarne can you help me learn to find percentages. Please ASAP!
Answers
Sure, what do you need help finding?
Answer:
to find a percentage of a number u multiply/divide 100
A survey showed that 9 every 25 students like dogs while 13th of every 20 students like cats. How many more of the students like cats than dogs? So how do you answer that question
Answers
Answer:
29/100 (Every 100 students, 29 more students like cats than dogs)
Step-by-step explanation:
First we need to put these numbers in fractions
The fraction that represents students that like dogs is 9/25
The fraction that represents students that like cats is 13/20
Now, we just need to subtract the fraction of cats by the fraction of dogs:
13/20 - 9/25
To do that, we need to make the denominators equal. We do that making multiplying the first fraction by 5 and the second by 4, so we have:
13/20 = 65/100
9/25 = 36/100
Then, subtracting then, we have:
65/100 - 36/100 = 29/100
So every 100 students, 29 more students like cats than dogs.
33. The following statement calls a function named half, which returns a value that is half that of the argument passed to it. Assume that result and number have both been defined to be double variables. Write the half function. result = half(number);
Answers
Answer:
Step-by-step explanation:
#using java
Double result;
public Double half(Double number){
return number/2;
}
result=half(number);
Final answer:
The function named 'half' is demonstrated using C++ code, where it takes a double as an argument and returns its half. The provided example shows how to define and use the function in a program.
Explanation:
The student's question involves writing a function in a programming language that effectively halves the value of the passed argument. This is a common task in programming, particularly in languages like C++, Java, or Python. Let's consider a simple function in C++ for illustrative purposes.
Example of a half function in C++:
double half(double number) {
return number / 2.0;
}
This function, half, takes a double (a data type that stores floating-point numbers) as an argument and returns a value that is half of the argument's value. It is important to note that double variables store finite approximations of real numbers and usually have a precision of about 17 significant digits in most computing environments.
To use this function, you would write the following code in your main program:
double number = 10.0; // or any other value
double result = half(number);
std::cout << result; // This will output 5.0
Understanding the code:
When invoked, the function will return half of the input value, effectively operating as number / 2.0.
Which ordered pair is the solution to the system of linear equations y = negative 7 x + 2 and y = 9 x minus 14? (negative 5, 1) (1, negative 5) (5, negative 1) (Negative 1, 5)
Answers
Answer:
B. [tex](1,-5)[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to choose the ordered par that is the solution to the given system.
[tex]y=-7x+2...(1)[/tex]
[tex]y=9x-14...(2)[/tex]
To solve our given system, we will equate both equations as:
[tex]9x-14=-7x+2[/tex]
Combine like terms:
[tex]9x+7x-14+14=-7x+7x+2+14[/tex]
[tex]16x=16[/tex]
[tex]x=\frac{16}{16}=1[/tex]
Upon substituting [tex]x=1[/tex] in equation (1), we will get:
[tex]y=-7(1)+2\\\\y=-7+2\\\\y=-5[/tex]
Therefore, the ordered pair [tex](1,-5)[/tex] is the solution of the given system and option B is the correct choice.
Answer:
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm its b
Step-by-step explanation:
Replace ∗ with a monomial so that the result is an identity:
1. (2a + ∗)(2a - ∗) = 4a^2–b^2
2. (∗− 3x )(∗ +3x) = 16y^2–9x^2
3. 100m^4–4n^6 = (10m^2−∗)(∗ +10m^2)
4. m^4–225c^10 = (m^2−∗)(∗ +m^2).
Answers
Answer:
Each of these is based on the principle of difference of two squares where:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Step-by-step explanation:
1.[tex](2a + *)(2a - *) = 4a^2-b^2[/tex]
[tex]4a^2-b^2=(2a)^2-b^2=(2a+b)(2a-b)[/tex]
2. [tex](*- 3x )(*+3x) = 16y^2-9x^2[/tex]
[tex]16y^2-9x^2=(4y)^2-(3x)^2=(4-3x)(4+3x)[/tex]
3. [tex]100m^4-4n^6 = (10m^2-*)(*+10m^2)[/tex]
[tex]100m^4-4n^6 = (10m^2-(2n^3)^2)= (10m^2-2n^3)(2n^3+10m^2)[/tex]
4. [tex]m^4-225c^{10} = (m^2-*)(* +m^2)[/tex]
[tex]m^4-225c^{10} =(m^2)^2-(15c^5)^2= (m^2-15c^5)(15c^5 +m^2)[/tex]
An aircraft departs an airport in the mountain standard time zone at 1515 MST for a 2-hour 30-minute flight to an airport located in the Pacific standard time zone. What is the estimated time of arrival at the destination airport
Answers
The flight departing at 3:15 PM MST, after 2 hours and 30 minutes, arrives at an estimated time of 4:45 PM PST considering that PST is one hour behind MST.
Explanation:The subject of this question revolves around time conversion between different standard global time zones. The departure time is 15:15 or 3:15 PM Mountain Standard Time (MST). A flight taking 2 hours and 30 minutes is added onto this original departure time. Therefore, in MST, the arrival time would be 17:45 or 5:45 PM MST. However, we must consider the time difference to Pacific Standard Time (PST) which is one hour behind MST. This means, to reflect PST, we subtract one hour from the MST arrival time, giving us an estimated arrival time of 16:45 or 4:45 PM PST.
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PLEASE HELP!!! NEED HELP ASAP !!! WILL MARK BRAINLIEST !!!
What is the area of a circle whose radius is 6ft? (Use Π)
Question 4 options:
6 Π ft2
9 Π ft2
36 Π ft2
72 Π ft2
Answers
Answer:
36 π square feet
Step-by-step explanation:
so the formula for area of a circle is πr^2
so the radius is 6, which we can just plug in
π(6)^2
36π
so option 3
24p
8
–
36p
6
+
36p
2
Answers
Answer:
24p8 - 36p6 + 36p2 = 48p
Step-by-step explanation:
I hope this helps!
The formula A=6 2/3 relates the surface area A, in square units, of a cube to the volume V, in cubic units. What is the volume, in cubic inches, of a cube with surface area 486 in2
Answers
Answer:
This is the volume of cube V = 729 [tex]in^{3}[/tex]
Step-by-step explanation:
Surface area of cube = 486 [tex]in^{2}[/tex]
Surface area of the cube is given by A = 6 × [tex]a^{2}[/tex]
⇒ 6 × [tex]a^{2}[/tex] = 486
⇒ [tex]a^{2}[/tex] = 81
⇒ a = 9 in
This is the value of side of the cube. so volume of the cube is given by
⇒ V = [tex]a^{3}[/tex]
Put the value of a in above formula w get,
⇒ V = [tex]9^{3}[/tex]
⇒ V = 729 [tex]in^{3}[/tex]
This is the volume of cube
To find the volume of a cube with a surface area of 486 in², calculate the side length using the formula A=6s², leading to a side length of 9 inches, and then calculate the volume as V=s³, resulting in 729 cubic inches.
The volume of a cube with a given surface area using the formula A=6s², where A is the surface area and s is the side length of the cube. First, find the side length by dividing the given surface area by 6, then take the square root. After finding the side length, calculate the volume using the formula V=s³.
Given the surface area A=486 in², the side length s can be found as follows:
Calculate the side length: s = √(A/6) = √(486/6) = √81 = 9 inches.Calculate the volume: V = s³ = 9³ = 729 cubic inches.Branson and his sister Beatrice combined their allowance of $7 each, so they could buy a movie for $12. They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. How many containers of fruit salad did they each get?
Answers
Answer:
Step-by-step explanation:
Branson and his sister Beatrice combined their allowance of $7 each. This means that the total amount they had is 7 + 7 = $14
They bought a movie for $12. The amount that they have left is
14 - 12 = $2
They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. This means that the number of containers that they bought is
2/1 = 2
If they split the containers evenly between themselves, then each person would get
2/2 = 1 container of fruit salad
please look at this multiple choice. thanks!!!!
Answers
Step-by-step explanation:
[tex]y = - 2x + 3[/tex]
The slope of the above line = -2
slope of the line perpendicular to the above line = 1/2
If it passes through point (4,-3) , it's equation
[tex] \frac{y - ( - 3)}{x - 4} = \frac{1}{2} [/tex]
[tex] \frac{y + 3}{x - 4} = \frac{1}{2} [/tex]
[tex]2(y + 3) = x - 4[/tex]
[tex]2y + 6 = x - 4[/tex]
[tex]x - 4 - 2y - 6 = 0[/tex]
[tex]x - 2y - 10 = 0[/tex]
A = 1, B = -2 and C = -10
A+B+C= 1+(-2)+(-10)
= 1-2-10
= 1-12
= -11
Answer:
A = 1, B = -2 and C = -10
Step-by-step explanation:
Use the given information to find the exact value of each of the following. a. sine 2 theta b. cosine 2 theta c. tangent 2 theta sine theta equals five sixths comma theta lies in quadrant II
Answers
Answer:
(a) [tex]sin 2\theta = -\frac{5\sqrt{11} }{18}[/tex]
(b)[tex]cos 2\theta= -\frac{7}{18}[/tex]
(c)[tex]tan 2\theta=[/tex][tex]\frac{5\sqrt{7} }{11}[/tex]
Step-by-step explanation:
If [tex]sin \theta =\frac{5}{6} , 90\leq \theta\leq 180[/tex]
Using Pythagoras,
Opposite=5, Hypotenuse =6, Adjacent=?
[tex]6^2=5^2+Adj^2\\Adj^2=36-25=11\\Adjacent=\sqrt{11}[/tex]
In the Second Quadrant,
[tex]sin \theta =\frac{5}{6} , cos \theta =-\frac{\sqrt{11} }{6}, Tan \theta =-\frac{5 }{\sqrt{11}}[/tex]
(a) [tex]sin 2\theta=2sin\theta cos\theta=2 X \frac{5}{6} X -\frac{\sqrt{11} }{6} = -\frac{5\sqrt{11} }{18}[/tex]
(b)[tex]cos 2\theta= cos^2\theta-sin^2\theta=(-\frac{\sqrt{11} }{6})^2-(\frac{5}{6})^2= -\frac{7}{18}[/tex]
(c)[tex]tan 2\theta=\frac{2tan\theta}{1-tan^2\theta}[/tex]
[tex]tan 2\theta=\frac{2(-\frac{5 }{\sqrt{11}})}{1-(-\frac{5 }{\sqrt{11}})^2} =\dfrac{-\frac{10 }{\sqrt{11}}}{1-\frac{25}{11}} =\dfrac{-\frac{10 }{\sqrt{11}}}{-\frac{14}{11} }=\frac{5\sqrt{7} }{11}[/tex]
HELP ASAP!! The time taken for a journey on a motorway varies inversely as the average speed for the journey. The journey takes 1.5 h when the average speed is 54 miles per hour. Identify the time taken in hours for this journey when the average speed is 45 miles per hour.
Answers
Answer: it will take 1.8 hours
Step-by-step explanation:
The time taken for a journey on a motorway varies inversely as the average speed for the journey. Let t represent taken for the journey. Let s represent the average speed. If we introduce a constant of varistion, k, the expression becomes
t = k/s
The journey takes 1.5 h when the average speed is 54 miles per hour. This means that
1.5 = k/54
k = 54 × 1.5 = 81
The equation becomes
t = 81/s
Therefore, when the average speed is 45 miles per hour, the time taken would be
t = 81/45
t = 1.8
The Cole family owns an above-ground circular swimming pool that has walls made of aluminum. Find the length of aluminum surrounding the pool if the radius is 14 feet.
Answers
Answer:
Therefore the length of aluminum surrounding the pool is 88 feet.
Step-by-step explanation:
Circle:
The line is drawn from the center to the arc is the radius of the circle.The value of diameter of a circle is 2 times of the value of radius.The formula of area of a circle = [tex]\pi r^2[/tex] The formula of circumference of a circle [tex]= 2\pi r[/tex].Given that the circular swimming pool has walls made of aluminum.
To find out the length of the of aluminum, we need to find out the circumference of the pool.
The radius of the circular pool is = 14 feet.
Therefore the circumference of the pool is =[tex]2\pi r^2[/tex]
[tex]=2\times \frac{22}{7} \times 14[/tex] feet
=88 feet
Therefore the length of aluminum surrounding the pool is 88 feet.
help asap pls ty so much !
Answers
Answer: 275 cm squared
Step-by-step explanation: We need to divide the shapes first into smaller areas, and since all the areas we need are given to us, we just need to break it apart into smaller parts that we can find the area for.
Length x Width = Area
Subtract -7a^2+3a-9−7a
2
+3a−9minus, 7, a, squared, plus, 3, a, minus, 9 from 5a^2-6a-45a
2
−6a−45, a, squared, minus, 6, a, minus, 4.
Answers
When subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45, subtract each corresponding term: a^2 terms, a terms and constant terms. The result is 12a^2 - 9a - 36.
Explanation:To subtract one polynomial from another, we simply subtract the corresponding terms. In the given problem, we are subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45. Let's subtract term by term:
Subtract the a^2 terms: 5a^2 - (-7a^2) = 12a^2.Next, subtract the a terms: -6a - 3a = -9a.Lastly, subtract the constants: -45 - (-9) = -36.So, the result of the subtraction is 12a^2 - 9a - 36.
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The solution set for -18 < 5x - 3 is _____.
-3 < x
3 < x
-3 > x
3 > x
Answers
Answer:
[tex]x > - 3[/tex]
Step-by-step explanation:
[tex] - 18 < 5x - 3 \\ \Leftrightarrow 5x > - 15 \\ \Leftrightarrow x > - 3[/tex]
In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree.
Answers
The formula for arc length is s=r*angle theta where s is the arc length, r is the radius, and angle theta is central angle formed by the arc in radians.
In this case, the angle would be s/r or 4.2/4 which is 1.05 radians. We have to convert this into degrees and so you would multiply 1.05 by (180/pi) which results in approximately 60 degrees. Remember, if you want to convert radians into degrees, the conversion factor is 180/pi and for degrees into radians, it is pi/180.
Answer:
Step-by-step explanation:
Length of a circular arc is given by:
S = rФ
where Ф is the angle in radians subtended at the center by the arc.
Ф = S/r = 4.2 / 4 = 1.05 radians = (1.05*180)/π = 60.16° ≅ 60°
Measure of minor arc AB is 60°
19. Which of the following is not a solution to the system of inequalities
A. (1-, -1)
B. (0, 1)
C. ( -3, 3)
D. (-3, 2)
Answers
Answer: The answer should be C!
Step-by-step explanation:
I took the quiz
The pair of coordinates which is not a solution to the system of inequalities is; Choice C: (-3, 3).
The area under the shaded region of the graph of the system of inequalities contains all feasible solutions of the system of inequalities.
In essence, the coordinate (-3, 3) is the point which is not a solution of the system of inequalities.
This is so because it doesn't fall under the shaded area.
This is due to the broken horizontal line; y < 3.
Read more:
https://brainly.com/question/14681811
A ladder leans against a side of a building, making a 63-degree angle with the ground, and reaching over a fence that is 6 feet from the building. The ladder barely touches the top of the fence, which is 8 feet tall. Find the length of the ladder.
Answers
Answer:
22.19 feet
Step-by-step explanation:
You want the length of a ladder that makes a 63° angle with the ground and reaches over an 8 ft fence to a building 6 ft beyond.
Trig functionsThe relevant trig relations are ...
Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse = Adjacent/Cos
ApplicationUsing these relations, we can find the lengths of the segments of the ladder between the ground and the fence, and between the fence and the building.
Referring to the attached diagram, we have ...
CE = 8/sin(63°) ≈ 8.9786
FC = 6/cos(63°) ≈ 13.2161
Then the total length of the ladder is ...
FE = CE +FC
FE = 8.9786 +13.2161 = 22.1947
The length of the ladder is about 22.19 feet.
The vertex of this parabola is at (-5, -2). When the x-value is -4, the
y-value is 2. What is the coefficient of the squared expression in the parabola's equation?
A 1
B 4
C -1
D 5
Answers
Answer:
The answer to your question is letter A
Step-by-step explanation:
Data
Vertex = (-5, -2)
Point = (-4, 2)
This is a vertical parabola the opens upwards.
The equation is
(x - h)² = 4p(y - k)
Substitution
(-4 + 5)² = 4p (2 + 2)
Simplification
1² = 4p(4)
1 = 16p
p = 1/16
Equation of the parabola
(x + 5)² = 4/16(y + 2)
x² + 10x + 25 = 1/4y + 1/2
Conclusion
The coefficient of the squared expression is 1