The situation in which a function behaves differently over different parts of its domain is modeled by considering it to be a piecewise function.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable
Such a situation can be explained through an example:
f(x) = { x, for x > 0
{ 1, for x = 0
{ -x, for x < 0
now, when we take x value less than 0, say x= -1
thus, f(x)= f(-1)= -(-1) = 1 , here we used f(x) given x<0
now, when we take x value more than 0, say x= 1
thus, f(x)= f(1)= (1) = 1, here we used f(x) given x>0
now, when we take x = 0,
thus, f(x)= f(0)= 1, here we used f(x) given x=0
this is how we model piecewise function, we use f(x) as per the value of x. Following image shows plotted answer for this example.
Since inequalities given are exclusive of 0, we leave the dot at the origin unfilled. Now, for x = 0. Since the value is constant at f(x) =1, we pointed a point at (0,1)
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I need the word problem translated to an inequality.
Half of 7 added to product of h and 4 is at least 1
Based on theword problem, the inequality of the word problem is 7/2 + 4h >= 1
What are inequalities?Inequalities are used to represent expressions that do not have equal values i.e. unequal expression
How to translate the word problem to an inequality?The word problem is given as
Half of 7 added to product of h and 4 is at least 1
At least 1 means greater than or equal to 1
So, the word problem becomes
Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to product of h and 4 >= 1
The product of h and 4 means 4h
So, the word problem becomes
Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to 4h >= 1
Half of 7 means 7/2
So, the word problem becomes
Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 added to 4h >= 1
added to means +
So, the word problem becomes
Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 + 4h >= 1
Hence, the inequality of the word problem is 7/2 + 4h >= 1
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Jocelyn has a points card for a movie theater. She receives 25 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs 170 points for a free movie ticket. How many visits must Aria make to earn a free movie ticket?
she needs to make 12 visits to the movie theatre to earn the rest of the 145 points and get a free movie ticket.
We are given that:
Jocelyn received 25 reward points just for signing up.
She earns 12.5 points for each visit that she makes to the movie theatre.
The free movie ticket is available when she has 170 points with her.
Points to be collected more for a free movie ticket will be:
Points = 170 points - 25 points = 145 points.
So, the number of visits she has to make to the movie theatre will be calculated with the help of division.
Number of visits = 145 points / 12.5 points
Number of visits = 11.6 visits that is 12 visits.
Therefore, she needs to make 12 visits to the movie theatre to earn the rest of the 145 points and get a free movie ticket.
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Which equation defines a line that best fits all the points on the graph
The equation that best fits all the points on the graph is y = -2x + 3.
What is the line of best fit?The line of best fit is a line that can be drawn to connect most of the points on the graph. In other words, it best fits the points.
Using a linear regression tool, input the coordinates that are on the graph including:
(-4, 10) (-2, 8) (-1, 5) (1, 3) (2, 0) (2, -3)
The formula you get for line of best fit would be:
y = -2.08564x + 3.01259
Rounding up gives:
y = -2x + 3
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Which of the following statements is true?
A) Two shapes are congruent if their corresponding angles are congruent.
B) Two shapes are not congruent if their corresponding sides and corresponding angles are
congruent.
C) Two shapes are congruent if their corresponding sides and corresponding angles are
congruent.
D) Two shapes are congruent if their corresponding sides are congruent
Answer:
Two shapes are congruent if their corresponding sides and corresponding angles are congruent.
Step-by-step explanation:
This is the definition of congruency.
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Carson is a waiter at a restaurant. Each day he works, Carson will make a guaranteed
wage of $35, however the additional amount that Carson earns from tips depends on
the number of tables he waits on that day. From past experience, Carson noticed that
he will get about $6 in tips for each table he waits on. How much would Carson
expect to earn in a day on which he waits on 18 tables? How much would Carson
expect to make in a day when waiting on t tables?
The total amount earned when he waits 18 tables is $143
The total amount earned when he waits t tables is $35 + $6t
What is the total amount earned?The equation that can be used to determine the total amount Carson earns is a linear equation. A linear equation is an equation that when drawn on a graph yields a straight line.
A linear equation increases by a constant amount. The highest power of a variable in a linear equation is 1.
The form of a linear equation is y = a + bx
Where:
a = y-intercept b = x interceptTotal amount earned = guaranteed wage + (tip per table x total number of tables he waits)
Total amount earned when he waits 18 tables: $35 + ($6 x 18)
$35 + $108 = $143
Total amount earned when he waits t tables: $35 + ($6 x t)
$35 + $6t
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7
Factor the expression below.
O A. 9(x²-2x+9)
O B.
(x-9)(x + 9)
O C.
(x-9)(x-9)
O D. (x + 9) (x + 9)
4
12 181 +81
_what is this this is futo balis subina to amake dis_
Add or subtract if possible. 10√27 - 4√12
The subtraction of the expression 10√27 - 4√12 is 22√3.
Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together.
In mathematics, subtraction involves removing anything from a group or a number of objects. What is left in the group gets smaller when you subtract.
Consider the expression,
y = 10√27 - 4√12
Now, the number in the root can also be written as:
27 = 3 × 3 × 3
12 = 2 × 2 × 3
Therefore,
y = 10√27 - 4√12
y = 10[ √(3 × 3 × 3) ] - 4[ √( 2 × 2 × 3 ) ]
y = 10 × 3√3 - 4 × 2√3
y = √3 ( 10 × 3 - 4 × 2 )
y = √3 ( 30 - 8 )
y = 22√3
The value of the expression 10√27 - 4√12 is 22√3.
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A regulation for riding a certain amusement park ride requires that a child be between 30 inches and 50 inches tall. Provide an inequality that can be used to determine whether or not a child's height "h" satisfies the regulation for this ride.
the inequality to determine if a child's height satisfies the regulation is:
30in < h < 50 in.
How to write the inequality?Here we know that the allowed height of the child can be any value between 30 inches and 50 inches (not included, so we need to use the symbols > and <)
So, if we define h as the height, then h must be larger than 30 inches, so we can wrte:
h > 30 in
And h must be smaller than 50 inches, then:
h < 50 in.
If we write these two inequalities as one, we get:
30in < h < 50 in.
That is the inequality to determine if a child's height satisfies the regulation.
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Pluto is approximately 2.7 miles from the Sun. Venus is approximately 6.7 miles from the Sun.
Approximately how many times greater is the distance of Pluto from the Sun than the distance of Venus from the Sun?
Answer:
C. 40 times greater is the distance of Pluto from the Sun than the distance of Venus from the sun.
Please help I will give brainliest
The congruent figures are given as follows:
LMNOP and YAHFS.EFCD and XUYW.MON and TUE.What are congruent figures?Congruent figures are figures whose outer side lengths have the same measures. They may have different orientations, but the outer side lengths have to be the same.
Hence the congruent figures in this problem are given as follows:
LMNOP and YAHFS.EFCD and XUYW.MON and TUE.They have different orientations(rotated), but same side lengths.
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3x+2y−z=82x+2z=−4x+3y=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
Answer: (1/14, 10/7, -13/14)
Step-by-step explanation:
3x+2y−z=82x+2z=−4x+3y=4 ==> convert this to system of equations
3x+2y−z=4
82x+2z=4
−4x+3y=4
(3x+2y−z=4)*2
6x+4y−2z=8 ==> add this equation
82x+2z=4 ==> add this equation
88x+4y=12 ==> add the top 2 equations
(−4x+3y=4)*4
-16x+12y=16
(88x+4y=12)*3 ==> multiply by 3 to get 12y
264x+12y=36
-16x+12y=16
264x-(-16x)=36-16
264x+16x=20
280x=20
280x/280=20/280
x=1/14
−4x+3y=4
−4(1/14)+3y=4
-4/14 + 3y=4
-2/7 + 3y=4
(-2/7 + 3y=4)*7 ==> multiply equation by 7 to remove fractions
-2+21y=28
21y=30
y=30/21
y=10/7
3x+2y−z=4
3(1/14)+2(10/7)−z=4
3/14 + 20/7 - z=4
(3/14 + 20/7 - z=4)*14 ==> multiply equation by 14 to remove fractions
3 + 20*14/7 - 14z=56
3 + 280/7 - 14z=56
3+40-14z=56
43-14z=56
43-43-14z=56-43
-14z=13
z=-13/14
Answer: (1/14, 10/7, -13/14)
Tyler evaluates the expression -621,044-(-214,318) and gets an answer of -400,080.
is this a reasonable answer?
Answer:
No
Step-by-step explanation:
The correct answer is -406,726
A negative minus a negative is the same as a negative plus a positive
-621,044 + 214,318 = -406,726
Please give a good explanation! Ty
A cruise ship is traveling at a speed of 20 knots. A knot is approximately equal to 1.151 miles per hour. What is the approximate speed the ship is traveling in yards per second? Round to the nearest tenth.
BRAINLY ASAP PLS
i need help
Answer:
option 4 and option 3
Step-by-step explanation:
(3)
using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](x^{\frac{3}{2}) } ^{6}[/tex]
= [tex]x^{\frac{3}{2}(6) }[/tex]
= [tex]x^{9}[/tex]
(4)
using the rule of exponents/ radicals
[tex]x^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{x^m}[/tex] , then
7[tex]x^{\frac{2}{3} }[/tex]
= 7 × [tex]\sqrt[3]{x^2}[/tex]
= 7 [tex]\sqrt[3]{x^2}[/tex]
(5x+8)
∘
and m\angle B=(6x+4)^{\circ}∠B=(6x+4)
∘
, then find the measure of \angle B∠B.
It should be noted that the value of angle B in thee complementary angle is 60°.
How to illustrate the information?It should be noted that the total angles on a complementary angle is illustrated as 90°.
Therefore, based on the information given, it should be noted that we will add the equation and equate them to 90°.
This will be:
5x + 8 + 6x + 4 = 90°
11x + 12 = 90°
11x = 90° + 12°
11x = 102°
Divide
x = 102° / 11
x = 9.27
Therefore the value of angle B will be:
= 6x + 4
= 6(9.27) + 4
= 55.6 + 4
= 59.6°
= 60° approximately
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Solve each equation by factoring. Check your answers.
3 x²+8 x+4=0
The factors for given equation are -2/3 and -2.
Rewriting the equation firstly -
3x² + 8x + 4 = 0
ax² + bx + c = 0
Factorizing the equation as per mentioned two rules -
Sum of the factors should be equal to b (8 in this question)Product of the factors should be equal to product of a and c (12 in this question)6 and 2 are the suitable factors for given expression -
3x² + 6x + 2x + 4 = 0
3x (x + 2) + 2(x + 2) = 0
(3x + 2) (x + 2) = 0
3x + 2 = 0
3x = -2
x = -2/3
x + 2 = 0
x = -2
So, the two factors of equation are -2/3 and -2.
To check the factors, we will keep the value of x in equation -
When x = -2/3
3x² + 8x + 4 = 0
3(-2/3)² + 8(-2/3) + 4 = 0
3(4/9) - 16/3 + 4 = 0
4/3 - 16/3 + 4 = 0
Multiplying the equation with 3/4
1 - 4 + 3 = 0
- 3 + 3 = 0
0 = 0
When x = -2
3x² + 8x + 4 = 0
3(-2)² + 8(-2) + 4 = 0
12 - 16 + 4 = 0
- 4 + 4 = 0
0 = 0
Since for both values of x, Left hand Side and Right Hand Side of equation is same, the two resultant factors are correct.
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3 2/5 minus 2 1/9 please help the test is due today and I’m not finding any help for this one also if you answer this explain the answer
Answer: 1.29
Step-by-step explanation: 2/5 = 0.4.
1/9 = 0.1111...
So, 3-2 = 1.
0.4-0.1111 = .28888889 (its repeating so you are going to have a rounded number)
3-2= 1 --- .4 - .1111 = 2.8888889
= 1.288889 (The 8's are not exact as they keep repeating)
Round up to 1.29 and it will be correct.
Hope this helped:)
1 point If the distance from A(1, 6) to B(x, -2) is 10, then what is a possible value for x? (A) 11 (B) -5 (C) -7 (D) 8 (E) 6
Answer:
B
Step-by-step explanation:
calculate the distance between A and B using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (1, 6 ) and (x₂, y₂ ) = B (x, - 2 )
d = [tex]\sqrt{(x-1)^2+(-2-6)^2}[/tex]
= [tex]\sqrt{(x-1)^2+(-8)^2}[/tex]
= [tex]\sqrt{(x-1)^2+64}[/tex]
given AB = 10, then equating gives
[tex]\sqrt{(x-1)^2+64}[/tex] = 10 ( square both sides to clear the radical )
(x - 1)² + 64 = 10² = 100 ( subtract 64 from both sides )
(x - 1)² = 36 ← take square root of both sides
x - 1 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 1 to both sides )
x = 1 ± 6
then
x = 1 - 6 = - 5
x = 1 + 6 = 7
from the list then x = - 5 is a possible value
Necesito saber entre cuánto multiplicar para tener 3 de resultado15x?
= 3
Step-by-step explanation:
when you use 3 por multiply the answer is 5×
(5×)+3
1. 0.9+0.03+0.007? 2. 20 +0.7 + 0.08 + 0.006 3. 5 + 0.01 _0.009
Answer: 1. 0.937
2. 20.786
3. 35.001
Step-by-step explanation:
1. 0.9+0.03+0.007=
0.900+0.030+0.007=0.937
2. 20 +0.7 + 0.08 + 0.006=
20.000 +0.700 + 0.080 + 0.006=20.786
3. 35 + 0.01 - 0.009=
35.000 + 0.010 - 0.009=
35.010 - 0.009=35.001
help me please
show your solution
Step-by-step explanation:
the first suspicion we get from the first terms is that the creation algorithm is a multiplication by 3.
-1/3 × 3 = -1
-1 × 3 = -3
-3 × 3 = -9
then the next term would be
-9 × 3 = -27
and the next
-27 × 3 = -81
and the 7th term, that we have already defined, would be
-81 × 3 = -243
we are correct !
so, the missing terms are
-27, -81
A cool rock is quickly rolling down one side of a volcano. Compared with the same mass of hot lava that is slowing flowing down the other side, the rock has _____.
1. more thermal energy and more mechanical energy
2. less thermal energy and more mechanical energy
3. less thermal energy and less mechanical energy
4. more thermal energy and less mechanical energy
When the cool rock that is rolling down the side of the volcano is compared to the mass of hot lava that is slowly flowing, the rock has 2. less thermal energy and more mechanical energy.
What is mechanical energy?The mechanical energy that an object has refers to the combination of kinetic and potential energy. The rock will have more mechanical energy than the hot lava as it is moving faster.
Thermal energy on the other hand refers to how much heat/ energy is in an object. The rock is cool as opposed to the hot lava which would have more thermal energy as a result of its heat.
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20 POints!!!
PLSSSSSSS
Answer: ab = 3a + 2b + c subtract 3a from both sides. ab - 3a = 2b + c factor the left side. a (b - 3) = 2b + c divide both sides by ( b - 3).
sorry but only one for then second screenshot :/
Hope this helps! :)
A woman looks out a window of a building. She is 94 feet above the ground. Her line of sight makes an angle of θ with the building. The distance in feet of an object from the woman is modeled by the function d=94 secθ. How far away are objects sighted at angles of 25° and 55°?
The required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.
Function and values in trigonometry identityTrigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given the trigonometry identity;
d=94 secθ.
If the object is sighted at an angle of 25°, then;
d=94 sec25
d = 94 × 1/cos25
d = 94 × 1.1033
d = 103.71feet
If the object is sighted at an angle of 55°, then;
d=94 sec55
d = 94 × 1/cos55
d = 94 × 1.7434
d = 163.88feet
Hence the required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.
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Please Answer Need Badly Will give Brainlyest
What is 9+9
Answer:
that is definitaly 18
Step-by-step explanation:
i will break it down 3+3+3=9 3+3+3=9 again 9+9=18
[tex]answer[/tex]
18
Step by step formula:Break it down: 3+3+3= 9, Another 3+3+3= 9 (3 addition in 6 places will give 18). 9+9 = 18
2x + 9 = x + 12 What’s is the answer to this question
The job paid 25$ for every 2 hours of work.
Write an equation that represents how much the job pays, y, for x hours of work
Answer:
$12.5xy
Step-by-step explanation:
y = how much the jobs pays
x = hours of work
25/2
= 12.5xy
Solve each equation. Check for extraneous solutions. 3√2 x+6=18
The solution of the equation 3√2 x + 6 = 18 is 2√2.
An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Consider the equation,
3√2 x + 6 = 18
Subtracting 6 from each side of the equation.
3√2 x + 6 - 6 = 18 - 6
3√2 x = 12
Dividing each side of the equation by 3.
( 3√2 x / 3 ) = ( 12/3 )
√2 x = 4
Dividing each side of the equation by √2.
( √2x/√2 ) = ( 4/√2 )
x = 2√2
Now checking the extraneous solution:
x = 2√2
[tex]3\sqrt{2}x + 6 = 18\\ 3\sqrt{2} \times 2\sqrt{2} + 6 = 18\\ 6(2) + 6 = 18\\ 18 = 18[/tex]
The solution for the equation is 2√2.
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Solve the following system of equations graphically on the set of axes below.
y= 2x-2
x+y= 4
Answer:
[tex]x = 1 + \frac{y}{2} \\ \\ x = 4 - y \\ y = 4 - x[/tex]
Step-by-step explanation:
[tex]1. \: y + 2 = 2x \\ 2. \: \frac{y + 2}{2} = x \\ 3. \: 1 + \frac{y}{2} = x \\ 4. \: x = 1 + \frac{y}{2} \\ \\ \\ 1. \: x = 4 - y \: or \: y = 4 - x[/tex]
m-a=n-p, solve for a
Answer:
m + n + p = a
Step-by-step explanation:
m - a = n- p
M = a - n - p
M + n = a - p
M + n + p = a