Which graph represents the function? f(x)=(x+2)^2 if x<−1
|x|+1 if −1≤x≤1
−√x if x>1
Answers
Answer:
option B
Step-by-step explanation:
To get the graph of piecewise function
We make a table for each function
Plug in end points and make a table
First function f(x) = (x+2)^2 if x<-1
x <-1 so we pick number for x less than -1. Also we use -1 but we use open circle at x=-1
x y = (x+2)^2
-3 (-3+2)^2= 1
-2 (-2+2)^2 = 0
-1 (-1+2)^2 = 1
Now plot the table on graph
second function f(x) = |x| + 1 if -1<=x<=1
Make a table, we use -1, 0 and 1 because we have -1<=x<=1 (-1 and 1 are included)
x y=|x| +1
-1 |1| + 1 = 2
0 |0|+1 = 1
1 |1|+1= 2
Third function [tex]y=-\sqrt{x}[/tex] if x>1
We find out y when x=1 and make a open circle at x=1 because we have x>1
x [tex]y=-\sqrt{x}[/tex]
1 [tex]-\sqrt{1}=-1[/tex]
4 [tex]-\sqrt{4}=-2[/tex]
Plot all the point on the graph
Correct graph is attached below
Related Questions
Statewide, there are 20 full-time employees to every 3 part-time employees. If there are 250,000 full-time employees, how many part-time employees are there statewide?
Answers
Divide total full time employees by 20 to find how many groups of 20 there are, then multiply that number by 3 to find total part time employees:
250,000 / 20 = 12,500
12,500 x 3 = 37,500 part time employees.
Eric made two investments: Investment Q Q has a value of $ 5 0 0 $500 at the end of the first year and increases by $ 4 5 $45 per year. Investment R R has a value of $ 4 0 0 $400 at the end of the first year and increases by 1 0 % 10% per year. Eric checks the value of his investments once a year, at the end of the year. What is the first year in which Eric sees that investment R R's value exceeded investment Q Q's value?
Answers
Answer: After 8 year from the first year Eric will see that investment R's value exceeded investment Q's value.
Step-by-step explanation:
Let after x year from the first year Eric sees that investment R's value exceeded investment Q's value.
Investment Q has a value of $ 500 at the end of the first year and increases by $ 45 per year.
Thus, after x year from the first year the total amount of Investment Q,
500 + 45 x
Similarly, after x year from the first year the total amount of Investment R,
⇒ [tex]400(1+\frac{10}{100} )^x = 400(1.1)^x[/tex]
Thus, [tex]500 + 45 x = 400(1.1)^x[/tex]
By plotting the equations in the graph,
We get, x = -6.178 or 8.069
But year can not be negative,
Therefore, x = 8.069
Thus, Approx after 8 year from the first year Eric will see that investment R's value exceeded investment Q's value.
Answer: it’s 10 I’m 100% sure
Brandy is trying to factor the quadratic $3x^2 - x - 10.$ She starts by assuming that the quadratic factors as \[3x^2 - x - 10 = (x + B)(3x + D),\]for some integers $B$ and $D.$ After some work, Brandy successfully factors the quadratic. Find the ordered pair $(B,D).$
Answers
Answer:
(B , D) = (-2,5)
Step-by-step explanation:
The given quadratic expression is
[tex]3x^{2} -x-10[/tex]
compare the given expression with [tex]ax^{2} +bx+c[/tex]
so we have [tex]a = 3 , b = -1 ,c = -10[/tex]
now [tex]ac=3 (-10)=- 30[/tex] and [tex]b= -1[/tex]
we need to find two numbers such that their product is -30 and sum is -1
-6 and 5 are such numbers
so we have
[tex]3x^{2} -6x+5x-10[/tex]
grouping first two terms and last two terms
[tex](3x^{2} -6x)+(5x-10)[/tex]
factor out 3x from first two terms and 5 from last two terms
[tex]3x(x-2) +5(x-2)[/tex]
[tex](x-2)(3x+5)[/tex] ( factor out (x-2))
[tex](x+(-2))(3x+5)[/tex]
hence B =-2 and D= 5
(B,D)= (-2,5)
The price of a pair of jeans was $45 after a 50% markup. What was the price of the jeans before the markup?
Answers
Answer:
$30
Step-by-step explanation:
Mark up is the profit on cost. if the pair of jeans was $45 after a 50% markup
Let the price of the jeans before the markup be p then;
p + 50%p = 45
1.5p =45
p = 45/1.5
p = 30
The price before mark up was $30, while the mark up or profit is $15. This shows 50% of the price before mark up.
5a + 5b + 5c + 5d
Which expression is another way to write the expression shown here?
A) 5abcd
B) 5a + bcd
C) 5(a + b + c + d)
D) (5a)(5b)(5c)(5d) what the answer
Answers
The correct way to rewrite the expression 5a + 5b + 5c + 5d using the distributive property is option C) 5(a + b + c + d).
The expression given is 5a + 5b + 5c + 5d. This is a sum where each term is multiplied by 5. According to the distributive property, also known as the distributive law of multiplication, a common factor can be factored out of a sum. The distributive property is represented as (A + B)C = AC + BC. In this case, the common factor is 5, and the sum of the variables a, b, c, and d is grouped, giving us 5(a + b + c + d).
So, the correct representation of the expression is 5(a + b + c + d), which corresponds to option C).
Janie receives an allowance of \$3$3 per week. In addition, she can earn \$2$2 for each chore she does. This week, she wants to earn enough money to buy a CD for \$13$13. Janie can do fractions of chores. Write an inequality to determine the number of chores, cc, Janie must do this week to earn enough money to buy a CD.
Answers
Answer:
Number of chores done by Janie are 5.
Step-by-step explanation:
Janie's allowance per week is $3.
For each chore she earns $2.
Now we assume that number of chores in a week she does = c
Then total earning from chore = $2 × c
So for the purchase of CD total earning this week inequality will be
⇒ 3 + 2c [tex]\geq[/tex]13
⇒ 2c [tex]\geq[/tex] 13-3
⇒ c [tex]\geq[/tex] 10÷2
⇒ c [tex]\geq[/tex] 5
What are the zeroes of the polynomial function f(x)=x^3+2x^2-x-2
Answers
[tex]f(x)=x^3+2x^2-x-2\\\\f(x)=0\iff x^3+2x^2-x-2=0\\\\x^2(x+2)-1(x+2)=0\\\\(x+2)(x^2-1)=0\iff x+2=0\ \vee\ x^2-1=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\\\boxed{x=-2}\\\\x^2-1=0\qquad\text{add 1 to both sides}\\\\x^2=1\to x=\pm\sqrt1\\\\\boxed{x=-1\ \vee\ x=1}\\\\Answer:\ -2,\ -1,\ 1[/tex]
Answer: -2, -1, 1
Step-by-step explanation:
f(x) = x³ + 2x² - x - 2
0 = x³ + 2x² - x - 2
= x²(x + 2) -1(x + 2)
= (x² - 1) (x + 2)
= (x - 1) (x + 1) (x + 2)
0 = x - 1 0 = x + 1 0 = x + 2
1 = x -1 = x -2 = x
In first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft. Finally, in third, or high gear, the engine runs at the same speed as the drive shaft. Engine speed = 4,100 r.p.m. Transmission in first gear Drive-shaft speed (to nearest r.p.m.) =
a) 1367
b) 12,300
c) 6560
Answers
Answer:
A 1367
Step-by-step explanation:
A triangle has two side of length 10 and 14 what value could the length of the third side be check all that apply
A) 26
B) 16
C) 10
D) 8
E) 5
F) 2
Answers
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
A) 10, 14, 26
10 + 14 = 24 < 26 INCORRECT :(
B) 10, 14, 16
10 + 14 = 24 > 16 CORRECT :)
C) 10, 10, 14
10 + 10 = 20 > 14 CORRECT :)
D) 8, 10, 14
8 + 10 = 18 > 14 CORRECT :)
E) 5, 10, 14
5 + 10 = 15 > 14 CORRECT :)
F) 2, 10, 14
2 + 10 = 12 < 14 INCORRECT :(
Answer: B) 16, C) 10, D) 8, E) 5Options B, C, D and E are correct answers.
Given that, a triangle has two sides of lengths 10 and 14.
We need to find what value could the length of the third side be and check all that apply.
What is the triangle inequality theorem?Triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
Now, from the given options:
A) 10, 14, 26
10 + 14 = 24 < 26 the triangle can not be formed
B) 10, 14, 16
10 + 14 = 24 > 16 the triangle can be formed
C) 10, 10, 14
10 + 10 = 20 > 14 the triangle can be formed
D) 8, 10, 14
8 + 10 = 18 > 14 the triangle can be formed
E) 5, 10, 14
5 + 10 = 15 > 14 the triangle can be formed
F) 2, 10, 14
2 + 10 = 12 < 14 the triangle can not be formed
Therefore, options B, C, D and E are correct answers.
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(-2/3, sqrt5/3) is a point on a unit circle. Find the cosine, cosecant, and sine of the angle.
Answers
Look at the picture.
[tex]\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}[/tex]
We have the right triangle x, y and r. From the Pythagorean theorem we have:
[tex]r^2=x^2+y^2\to r=\sqrt{x^2+y^2}[/tex]
We have the point
[tex]\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)[/tex]
Substitute:
[tex]r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1[/tex]
[tex]\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}[/tex]
The cosine of the angle is -2/3, the sine is √5/3, and the cosecant, being the reciprocal of the sine, is √5/5 after rationalization.
The point (-2/3,√5/3) on a unit circle represents the cosine and sine of a specific angle. Here, the x-coordinate is the cosine of the angle, and the y-coordinate is the sine of the angle.
Therefore, the cosine of the angle is -2/3, and the sine is √5/3.
To find the cosecant of the angle, we take the reciprocal of the sine, which gives us 3/√5 or √5/5 after rationalizing the denominator.
Mr robbins earns a commission on each airfare he books. At the end of the day,he had booked $208.60 worth if airfare and earned $31.29. Approximately what is Mr. Robins commision rate.
Answers
Answer:
Mr. Robins commision rate is 15%.
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
Mr robbins earns a commission on each airfare he books.
At the end of the day,he had booked $208.60 worth if airfare and earned $31.29.
Here
Part value = $31.29
Total value = $208.60
Put in the formula
[tex]Percentage = \frac{31.29\times 100}{208.60}[/tex]
[tex]Percentage = \frac{312900}{20860}[/tex]
Percentage = 15%
Therefore the Mr. Robins commision rate is 15%.
An airplane with a speed of 160 knots is headed east while a 24-knot wind is blowing from 240°. Explain how you would use the result of finding the ground speed to find the course of the airplane.
Answers
Question: Explain how you would use the result of finding the ground speed to find the course of the airplane.
Answer: 181.2
Explanation: vertical speed of 20.78 knots
new course is (-148 , 20.78) = inverse tan ( 20.78 / -148) = 172° or 8° N of East at 149.45 knots
New speed (- 148)² + ( 20.28)² = 149.45 knots round and you get 181.2
question answered by
(jacemorris04)
The ground speed of the airplane is 181.18 knots (approx).
What is the formula to find ground speed of airplane ?
The formula of ground speed of a airplane is given below,
[tex]v_{g} =\sqrt{}[/tex][tex](v_{a} ^{2}+v_{w} ^{2}-2v_{a} v_{w}cos\alpha)[/tex]
where, [tex]v_{g}[/tex] = Ground speed of airplane
[tex]v_{a}[/tex] = Speed of the airplane relative to the air
[tex]v_{w}[/tex] = Wind speed
[tex]\alpha[/tex] = Internal angle
How to find the ground speed of given airplane ?Given, [tex]v_{a}[/tex] = 160 knots, [tex]v_{w}[/tex] = 24 knots
Here, the angles increase clockwise and east is 90° heading.
The airplane is flying a heading of 90° at 160 knots speed & wind is blowing from 240° at 24 knots speed.
So, the internal angle[tex](\alpha)[/tex] = 240°-90° = 150°
∴ Ground speed, [tex]v_{g} =\sqrt{}[/tex][tex](v_{a} ^{2}+v_{w} ^{2}-2v_{a} v_{w}cos\alpha)[/tex]
⇒ [tex]v_{g}[/tex] [tex]=\sqrt{}[/tex][tex](160^{2}+24^{2}-2*160*24*cos(150))[/tex]
⇒ [tex]v_{g}[/tex] = 181.18 knots (approx)
Hence the ground speed of airplane is 181,18 knots (approx).
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Please help me out!!!!!!!
Answers
Answer: 1%
Explanation:
Add up the frequencies in the bottom row: 350+200+245+125+66+10+4 = 1000
There are 1000 families total. Of this total, 10+4 = 14 families have more than six people. I added up the frequency counts for "7 people" and "8 people" to get 14.
Divide 14 over 1000 and we get 14/1000 = 0.014 = 1.4% which rounds to 1%
(a+b+c)(d+e+f)(a+b+c)(d+e+f). The expression consists of 3 factors, and each factor contains 2 terms.
Answers
Answer:
Not true
Step-by-step explanation:
It is in fact an expression with 4 factors, each with 3 terms.
Factors are things you multiply, terms are things you add.
which type of correlation is suggested by the scatter plot
Answers
Answer:
Negative Correlation
Step-by-step explanation:
As you can see in the image I added, a negative correlation happens when the variables move in opposite directions, in other words, one variable increases as the other decreases. We can see this correlation represented by a value of -1 slope.
I hope you find this information useful and interesting! Good luck!
Answer: That's negative.
Step-by-step explanation: hope this helps.
Taylor has $97.23 and her checking account she uses debit card to spend 29 .74 and then deposits 118.08 into her accounts what is Taylor's new balance
Answers
Answer:
Taylor's new balance is $ 185.57 .
Step-by-step explanation:
As given
Taylor has $97.23 and her checking account.
she uses debit card to spend $29 .74 .
Than
Balance in the account after uses debit card = $97.23 - $29.74
= $ 67.49
As given
Then deposits $118.08 into her accounts.
Total balance of the account = $118.08 + $67.49
= $ 185.57
Therefore Taylor's new balance is $ 185.57 .
Answer:
$185.57
Step-by-step explanation:
A police officer investigating an accident finds a skid mark 115 feet long approximately how fast was the car traveling when the driver applied the brakes
Answers
The speed that describes how fast the car was traveling when the driver applied the brakes is 49 mph.
What was the speed?
The formula that is often used by police officers to determine the speed from a skid mark is this s = √21d.
So, in this case, the length or distance of the skid mark is 115 feet. We can substitute this value in the formula to get;
Speed of car = √21(115)
Speed of car = √2,415
Speed of car = 49.1426 approximately 49 mph.
So, the speed that describes how fast the car was traveling when the driver applied the brakes is 49 mph.
Complete Question:
A police officer investigating an accident finds a skid mark 115 feet long. Approximately how fast was the car traveling when the driver applied the brakes?
Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.
Answers
Answer:
Option (a)
Step-by-step explanation:
The given equation is
y = 4 (2ˣ)
To find y-intercept, substitute x=0 in the equation.
y = 4 (2⁰) = 4 (1) =4
Hence y-intercept is 4.
Since y-intercept is 4, the equation should pass through the point (0,4).
The only graph passing through the point (0,4) is the graph in option (a).
Hence the answer is option (a).
Answer:
a
Step-by-step explanation:
Carlotta drove 72.6 miles on Monday. She drove 84.18 miles on Tuesday. Which gives the best estimate for how many more miles Carlotta drove on Tuesday?
A)84 – 73 = 11 miles
B)73 – 84 = 11 miles
C)85 – 72 = 13 miles
D)84 – 71 = 13 miles
Answers
Answer:
A)84 – 73 = 11 miles
Step-by-step explanation:
On Tuesday she drove 84 miles (rounding to the nearest mile)
On Monday she drove 73 miles (rounding to the nearest mile)
Tuesday's mileage - Mondays miles = difference in miles
84-73 = 11 miles
Answer: A. 84 – 73 = 11 mi
Find the first six terms of the sequence.
a1 = -2, an = 3 • an-1
-6, -18, -54, -162, -486, -1458
-2, -6, -18, -54, -162, -486
-2, -6, -3, 0, 3, 6
0, 3, -6, -3, 0, 3
Answers
[tex]a_1=-2\\\\a_n=3\cdot a_{n-1}\\-----------------------------------\\a_1=-2\\\\a_2=3\cdot a_{2-1}=3\cdot a_1\to a_2=3(-2)=-6\\\\a_3=3\cdot a_{3-1}=3\cdot a_2\to a_3=3(-6)=-18\\\\a_4=3\cdot a_{4-1}=3\cdot a_3\to a_4=3(-18)=-54\\\\a_5=3\cdot a_{5-1}=3\cdot a_4\to a_5=3(-54)=-162\\\\a_6=3\cdot a_{6-1}=3\cdot a_5\to a_6=3(-162)=-486\\\\Answer:\ \boxed{-2,\ -6,\ -18,\ -54,\ -162,\ -486}[/tex]
Jayda is cutting a roll of biscuit dough into slices that are 3/4 inches thick if the roll is 10 1/2 inches long how many slices can he cut?
Answers
Answer:
Jayda can cut 14 slices of dough that are 3/4 inches thick.
Step-by-step explanation:
In order to solve this problem, we need to take the total amount of dough at 10 1/2 inches and divide it by the thickness of one slide, 3/4 inches, to find the number of slices that can be made from the total amount. You can solve this two different ways. You can either convert your fractions to decimals so that 10 1/2 becomes 10.5 and 3/4 become 0.75 and then divide 10.5/0.75 to get 14. However, you can also keep them as fractions converting 10 1/2 to 21/2 and dividing by 3/4. When we divide with fractions with keep-change-flip, or keep the first fraction-change the sign to multiplication-flip the second fraction. So, we multiply 21/2 x 4/3 and get 84/6, or 14.
H values from the specified set make up the solution set of the inequality? 5w–10>20 ; {5,6,7,8} Select each correct answer. A.5 B.6 C.7 D.8 plz help
Answers
Answer: (C) 7 and (D) 8
Step-by-step explanation:
5w - 10 > 20
+10 +10
5w > 30
÷5 ÷5
w > 6
Anything GREATER than 6 will work.
The vertex of the function graph is given. Find c. Y= c-x^2-2x;(-1,3)
Answers
Answer:
c = 2
Step-by-step explanation:
(x, y) = (-1, 3)
3 = c - (-1)^2 - 2(-1)
3 = c - 1 + 2
3 = c + 1
2 = c
Carmen enters a painting in an art contest. The contest rules say that all paintings must be rectangular, with an area no greater that 3,003.04 cm2. Carmen painting is 16 cm wode. What is the greatest lenth the painting can have and still have an area within the contest rules?
Answers
Answer:
187.69 cm
Step-by-step explanation:
We have that the maximum area allowed for the painting = 3003.04 [tex]cm^{2}[/tex].
Also, the width of Carmen's painting = 16 cm.
It is required to maximum length of Carmen's painting that will be eligible to take part in the competition.
Let the maximum length of the painting = L cm.
Since, Area of a rectangle = length of the rectangle × width of the rectangle.
i.e. 3003.04 = L × 16
i.e. [tex]L=\frac{3003.04}{16}[/tex]
i.e. L = 187.69 cm
Hence, the length of the painting should not exceed 187.69 cm in order to be eligible to participate in the competition.
A baseball team loses twice as many games as it wins.The baseball season is 162 games long.How many games will the team loses?
Answers
Answer:
11
Step-by-step explanation:
I guessed
select the two binomials that are factors of this trinomial x^2+10x+16
A: x+8
B: x+6
C: x+2
D: X-2
Answers
Answer:
The correct options are A: x+8 and C: x+2.
Step-by-step explanation:
We are given the following expression and we are to factorize it:
[tex]x^2+10x+16[/tex]
We are to find such factors that when multiplied they give a result of 16 (1 x 16 = 16) and when added they give a result of 10.
The two such factors of 16 are positive 2 and positive 8.
Factorizing the given expression to get:
[tex]x^2+10+16\\\\x^2+2x+8x+16\\\\x(x+2)+8(x+2)\\\\(x+2)(x+8)[/tex]
Therefore, the two binomial factors of the given expression [tex]x^2+10x+16[/tex] are (x+8) and (x+2).
Answer: x+6 x+2
tell me if I’m wrong because I put x+8 and x+2 and got it wrong it told me it was x+6 and x+2
Jaz was 43 inches tall. 18 months later she was 52 inches tall. Find the constant rate of change for Jaz's height.
Answers
9/18 or 1/2
Half an inch per month
Paws at play made a total of $1,234 grooming 22 dogs. Paws at play charges $43 to groom each small dog and $75 for each large dog. Write a system of equations that can be used to determine the number of small and large dogs that were groomed
Answers
Step-by-step explanation:
We are asked to write a system of equations using our given information.
Let x be number of small dogs and y be number of large dogs.
We have been given that paws at play made a total of $1,234 grooming 22 dogs, which means that number of small dogs and large dogs is 22. We can represent this information as:
[tex]x+y=22...(1)[/tex]
We have been given that paws at play charges $43 to groom each small dog and $75 for each large dog. So the total grooming charges for grooming x small and y large dogs will be 43x+75y, that is equal to total charges for grooming $1234.
We can represent this information as:
[tex]43x+75y=1234...(2)[/tex]
Therefore, our desired system of equations is:
[tex]x+y=22...(1)[/tex]
[tex]43x+75y=1234...(2)[/tex]
HELP PLEASE!! which of the following represents a function?
please explain too i don’t understand this.
Answers
im really bad at explaining but thats the simplest way i learned
Answer:
I think it's c.
Step-by-step explanation:
A graph usually stands as a representation for functions.
BRAINLIEST!!HELPPP!!
Answers
Answer:
the answer if am not wrong would be C.n+5
Step-by-step explanation: