Answers
Answer:
f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}
Step-by-step explanation:
To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.
__
Left PieceThe domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.
The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.
The first piece can be written ...
f(x) = x-3 for x ≤ -1
__
Right PieceThe domain is shown as 5 to ∞, with 5 not included.
The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...
y -(-1) = -3(x -5)
y = -3x +15 -1 = -3x +14
The second piece can be written ...
f(x) = -3x +14 for x > 5
__
Whole functionPutting these pieces together, we have ...
[tex]\boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}[/tex]
_____
Additional comment
Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, x > 5.
Related Questions
options are
a) -2 and 12/5
b) 1 and 2
c)8/3 and 2
d) 3 and 4
Answers
That is the correct answer
Find the x-intercept and y-intercept of the line
4x-6y=36
Answers
Step-by-step explanation:
4x - 6y = 36
x intercept: 9, 0
y intercept: 0, 6
Please help with this i will give a big reward on god.
Answers
Answer: 2.9
Step-by-step explanation:
area of roof = (.5)(base of house)(left side - right side)
area of roof = (.5)(2)(2.8 - 1.8)
area of roof = (.5)(2)(1) = 1
area of bottom = left height x base of house
area of bottom = 1.8 x 2 = 3.6
area of house = area roof + area bottom
area of house = 1 + 3.6 = 4.6
area without door = area house - area door
area door = door height x door width
area door = 1.7 x 1
area door = 1.7
area without door = 4.6 - 1.7 = 2.9
x is proportional to root y where y>0
Answers
Answer:
x is proportional to √y where y > 0
Step-by-step explanation:
name the two operations used for converting weight measurement
Answers
Answer:
grams and kilograms it got delted for some reason
Step-by-step explanation:
9. Instructions: Find the missing side of the triangle.
Answers
Good luck ♡
7^2+24^2=x^2
49+576=x^2
625=x^2
x=25
Hi I could use some help with this, thank u!
Answers
Alright let's solve this step by step:
Question 1: Find the perimeter of the baseDefinition of Perimeter: is all the side length of the shapes added up⇒ Perimeter = 6 + 6 + 6 + 6 + 6 + 6 + 11 + 11 = 58 km
Question 2: Height of PrismDefinition of height: is the distance from the base of the figure to the top base of the figure
⇒ Height = 4.3km
Question 3: Lateral AreaDefinition of Lateral Area: area of nonbase face only
⇒ area of the two rectangles on the narrower side of the figure
⇒ plus the area of the pentagon on the wider side of the figure
Area of Pentagon= [tex]\frac{1}{2}(base1+base2)*height = \frac{1}{2} *(6 + 11) *4.3=36.55km^2[/tex]
Area of Rectangle = 6 * 5 = 30 km^2Total Area = 36.55 + 36.55 + 30 +30 = 133.1 km^2
Question 4: Find the area of the base
Area of the two bases = 6 * 6 + 6 * 11 = 36 + 66 = 102 km^2
Question 5: Find the surface area of the figureDefinition of the Surface Area: it is a measure of the total area that the surface of the object occupies
⇒ Surface Area = Lateral Area + Base area = 133.1 + 102 = 205.1 km^2
Hope that helps!
John is 62 inches tall. He is stacking algebra books on his desk. His teacher tells him not to make the stack taller than his own height. The top
of his desk is 32 inches from the floor, and each book is 1.5 inches thick. John wants to write an inequality to show how many books he could
stack.
Which inequality sign should John use?
Answers
Answer:
The answer would be [tex]\leq[/tex] :)
Step-by-step explanation:
The equation would look like this :)
1.5x + 32 [tex]\leq[/tex] 62
Have an amazing day!!
Please rate and mark brainliest!!
Find the length of the segment indicated. Round your answer to the nearest tenth. Please and thank you so very much!!!
Answers
Answer:
14.7
Step-by-step explanation:
The given horizontal line is in the center of the circle (indicated by the black dot in the middle), so you can divide 17.5 by 2 in order to find the length of the leftmost segment of the triangle (8.75).
To solve for x, we use the pythagorean theorem as this is a right triangle:
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]11.8^{2} + 8.75^{2} = x^{2}\\139.24 + 76.5625 = x^{2}\\215.8025 = x^{2}\\x = 14.6902178...[/tex]
This is 14.7 when rounded to the nearest tenth
If p and q vary inversely and p is 8 when q is 6, determine q when p is equal to 12.
Answers
Answer:
q = 4
Step-by-step explanation:
given p and q vary inversely then the equation relating them is
p = [tex]\frac{k}{q}[/tex] ← k is the constant of variation
to find k use the condition p = 8 when q = 6 , that is
8 = [tex]\frac{k}{6}[/tex] ( multiply both sides by 6 )
48 = k
p = [tex]\frac{48}{q}[/tex] ← equation of variation
when p = 12 , then
12 = [tex]\frac{48}{q}[/tex] ( multiply both sides by q )
12q = 48 ( divide both sides by 12 )
q = 4
Answer:
4
Step-by-step explanation:
-
Which equation has a vertex at (3, –2) and directrix of y = 0?
y + 2 = StartFraction 1 Over 8 EndFraction (x minus 3) squared
y + 2 = 8 (x minus 3) squared
y + 2 = negative StartFraction 1 Over 8 EndFraction (x minus 3) squared
y + 2 = negative 8 (x minus 3) squared
Answer: C
Answers
Answer:
The square below represents one whole.
What percent is represented by the shaded area?
The square below represents one whole.
What percent is represented by the shaded area?The square below represents one whole.
What percent is represented by the shaded area?The square below represents one whole.
What percent is represented by the shaded area?The square below represents one whole.
What percent is represented by the shaded area?vvvvStep-by-step explanation:
A tree is 7 feet tall. If it grows 9 inches each year, how tall will the tree be in 10 years
Answers
Answer:
174 in.
14.5 ft.
Step-by-step explanation:
1. 7ft = 84in
2. 9in x 10 = 90
3. 84in + 90in = 174 in
The price of an item has been reduced by 45 percent The original price was 99
awnser pls
Answers
The scores of an eighth-grade math test have a normal distribution with a mean mu = 83 and a standard deviation sigma = 5. if din’s test score was 92, which expression would she write to find the z-score of her test score? z = startfraction 92 minus 83 over 83 endfraction z = startfraction 83 minus 92 over 5 endfraction z = startfraction 92 minus 83 over 5 endfraction z = startfraction 5 minus 83 over 92 endfraction
Answers
The z-score is the ratio of the difference of sample and means to the standard deviation. Then the correct option is A.
What is a z-score?The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The scores of an eighth-grade math test have a normal distribution with a mean of 83 and a standard deviation of 5. If the x is 92. Then the test score will be
The z-score will be given as
[tex]z = \dfrac{x - \mu}{\sigma }\\\\z = \dfrac{92 - 83 }{5}[/tex]
More about the z-score link is given below.
https://brainly.com/question/15016913
Answer:
A
Step-by-step explanation:
edge 2022
Simplify: [(13 + 8) ÷ 3] − 4 =
Answers
Answer:
3
Step-by-step explanation:
First you do 13 + 8
13 + 8 = 21
Then you divide by 3
21 divided by 3 is 7
Finally you subtract 4
7 - 4 = 3
Hope this helps!!
Answer:
3
________________________________________________________
SolveWhen doing problems, remember PEMDAS, the order of operations:
parenthesesexponentsmultiplicationdivisionadditionsubtractionGo by the list from top to bottom, and prioritize the higher-up orders first.
Start with 13 + 8
[tex]13 + 8 = 21[/tex]
Next, divide by 3
[tex]21 / 3 = 7[/tex]
Lastly, subtract by 4
[tex]7 - 4 = 3[/tex]
________________________________________________________
Questions?Ask me in the comments box, please.
A) tan
B) tan^2
C) 1
D) -1
Answers
Answer:
A) [tex]\tan \theta[/tex]
Step-by-step explanation:
[tex] \frac{\sin \theta}{ \sqrt{1 - { \sin}^{2} \theta } } \\ \\ = \frac{\sin \theta}{ \sqrt{ { \cos}^{2} \theta } } \\ \\= \frac{\sin \theta}{{ { \cos} \theta } } \\ \\ = \tan \theta[/tex]
what us the circumference of circular ground of diameter d m ? find it.
answer:
[tex]\pi d \: m[/tex]
can you explain me how?
Answers
Here the diameter = dm
Formula of circumference for circle: 2πr or πd
where "d" is diameter and "r" is radius
diameter = 2(radius)For this question:
circumference:
π(d)π(dm)πdmThe measure of an angle is eighty-nine times it's supplementary angle. what is the measure of each angle.
I need two answers,
Answers
Answer:
178 and 2
Step-by-step explanation:
sum of supplementary angles are 180
so, x+ 89x = 180
=> x+89x = 180
=> 90x = 180 [the transposing method]
=> x = 180/90
=> x = 2
now we have the value of one angle
as the other angle is 89 times x,
=> 89x
=> 89*2
=> 178
now, we have the measure of both the angles which equals 180 degree
178 degree and 2 degree
What property of a rhombus is used in this proof of showing that a triangle is an equilateral triangle?
Answers
Answer:
Step-by-step explanation:
The property of rhombus that can be used to proof that a triangle is an equilateral triangle is that when it is split into two equal parts, an equilateral triangle is formed.
What is a rhombus?A rhombus is defined as a quadrilateral that has four equal straight sides with opposite sides parallel and equal opposite angles.
A rhombus with two 60 degree angles and two 120 degree angles can be split by one of its diagonals (the one that bisects the 120 degree angles) into two congruent, equilateral triangles.
Therefore, the property of rhombus that can be used to proof that a triangle is an equilateral triangle is that when it is split into two equal parts, an equilateral triangle is formed.
Learn more about quadrilaterals here:
https://brainly.com/question/26690979
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Question Factor −1/4 out of −1/2x−5/4y.
Answers
-1/2 x - 5/4 y
=(-1/4 * 2x) + (-1/4 * 5y)
= -1/4 (2x + 5y)
I know it's not A. I need help please
Answers
Answer:
139 degrees
Step-by-step explanation:
The sum of the interior angles of a polygon :
sum = ( n-2) * 180 where n = number of sides
For this one there are 5 sides
so ( 5-2) * 180 = 540 degrees
angle U = 90 degrees
90 + 82 + Y + 121 + 108 = 540 Y=139 degrees
Answer:
It is C. 139
Step-by-step explanation:
Angles of TVXXYZ is 720 degrees. We know that angles Z, W and X are 82 degrees, 108 degrees and 121 degrees (311 degrees after adding them). T= 180-28=152 degrees
V=90+28=118 degrees
152+118=270 degrees
270+311=581
720-581=139 degrees
The answer is C. 139 degrees
A 50:1 scale drawing of your garden shows dimensions of 12 cm by 10.5 cm. how many
square cm are covered by your real garden?
Answers
50:1 scale drawing -> Both sides of the garden is shrinked by 50 times.
We can calculate the area of the shrinked scale drawing : 12 x 10.5 = 126 (cm2)
Since both sides are shrinked by 50 times -> The real area get shrinked by 2500 times.
So, we can find the real area : 126 x 2500 = 315000 (cm2)
A proportional relationship is shown in the table below:
X - 0 0.3 0.6 0.9 1.2
Y- 0 1 2 3 4
What is the slope of the line that represents this relationship?
Graph the line that represents this relationship.
Answers
Answer:
slope intercept for is y=MX+b and to find the slope it's y1-y2/x1-x2
The slope would be 10/3.
And the line should intersect at the origin (0,0) and the second dot should be at the point (3,10)
What’s the scale factor? Quick
This is on ixl and I have to get at least a 90
Answers
Answer:
4
Step-by-step explanation:
We start with the smaller shape. We look at each coordinate and we multiply by 4. That will give us the coordinates for the bigger shape.
CAN SOMEONE HELP ME 50 POINTS
What are m∠1 and m∠2?
A. ∠1 = 30°, m∠2 = 35°
B. ∠1 = 35°, m∠2 = 30°
C. ∠1 = 65°, m∠2 = 60°
D. ∠1 = 85°, m∠2 = 80°
Answers
Describe and correct the error in the given statement: The relation (1,-5), (2,-5), (3,6), (4,11) is not a function because the inputs 1 and 2 are both paired with the output -5.
Answers
Answer:
15-5+38+8+595+2+8+6+9+7-5+29-8+8-5-5+2+8+3+9
Apply properties of operations to show why 3.5n + 4 (5 1/4n - 1.5) is equivalent to -21 (2/7 - 7/6n)
Answers
Applying the properties of operations; it follows that; 3.5n + 4 (5 1/4n - 1.5) is equivalent to -21 (2/7 - 7/6n).
Properties of OperationsThere are four (4) basic properties of real numbers which apply to addition and multiplication: namely; commutative, associative, distributive and identity.
Hence, by the cumutative property of multiplication and associative property of addition, it follows that;
4× -1.5 = -21(2/7)3.5n + 4(5 1/4n) = -21(7/6n)Hence, it follows that the expressions are equivalent.
Read more on properties of operations;
https://brainly.com/question/16136176
Round 15.209 to the nearest hundreth
A. 15.21
B. 15.20
C. 15.2
D. 16
Answers
Answer:
A.15.21
Step-by-step explanation:
In rounding of numbers when the next number is greater than 5 u round it on next number by adding one
Eighth grade
CC. 14 Box plots Y Z
Mrs. James, a sixth grade teacher, recorded how many minutes each student reported
reading over winter break.
Time spent reading (min. )
+
0
100
200
300
400
500
What was the upper quartile of the time spent reading?
minutes
Submit
Answers
The upper quartile of the time spent reading, as shown in the box plot is: 300.
What is the Upper Quartile of a Data in a Box Plot?In a box plot, the upper quartile is represented by the data point located at the end of the edge of the rectangular box in the box plot.
In the box plot, 300 is the value located at the end of the edge of the rectangular box.
Therefore, the upper quartile of the time spent reading, as shown in the box plot is: 300.
Learn more about upper quartile on:
https://brainly.com/question/10353201
Solve for h. h - 45 = -35A.h = -10B.h = 10C.h = -80D.h = 80
PLS HELP HURRY
Answers
Explanation: 10 - 45 = -35
