Which function is represented by the graph? f(x) = â’|x â’ 3| 4 f(x) = â’|x 3| 4 f(x) = â’|x â’ 4| 3 f(x) = â’|x 4| 3.
Answers
Functions are used to represent graphs, and vice versa.
The function represented by the graph is [tex]f(x) =- |x + 4| + 3[/tex]
The graph (see attachment) is an absolute value graph.
An absolute value graph is represented as:
[tex]f(x) =a |x - h| + k[/tex]
Where
[tex]Vertex = (h,k)[/tex]
The vertex is the minimum or the maximum point on the graph.
So, we have:
[tex]Vertex = (-4,3)[/tex]
The function becomes
[tex]f(x) =a |x + 4| + 3[/tex]
The function also passes through the point (-1,0).
So, we have:
[tex]0 =a |-1 + 4| + 3[/tex]
[tex]0 =a |3| + 3[/tex]
Remove the absolute bracket
[tex]0 =3a + 3[/tex]
Subtract 3 from both sides
[tex]3a =- 3[/tex]
Divide both sides by 3
[tex]a =- 1[/tex]
Substitute -1 for (a) in [tex]f(x) =a |x + 4| + 3[/tex]
[tex]f(x) =- |x + 4| + 3[/tex]
Hence, the function represented by the graph is [tex]f(x) =- |x + 4| + 3[/tex]
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Related Questions
pls answer quickly
Ryan wants to measure the length of a bed cover which of the following would be the most appropriate unit to use?
A) kilogram
B) kilometer
C) meter
D) mile
Answers
The answer is meter since grams is used to measure weight and kilometer and mile are used to measure something larger.
Answer:
C. Meter
Step-by-step explanation:
1. Kilograms measure weight, not distance/length, so it wouldn't make sense to use them to measure a bed.
2. Kilometers are used to measure very long distances, as are miles, so it wouldn't make sense to use them on something small like a bedframe.
That means the only option left is C. Meter.
Hope this helps.
Solve the system of equations
{y= 15x+9
{y= 1/2x–20
What is the solution to the system?
Answers
[tex]y = 15x +9~~~~.....(i)\\\\y = \dfrac 12 x -20~~~ ....(ii)\\\\\\\text{Substitute equation (i) in equation (ii):}\\\\15x +9 = \dfrac 12 x -20\\\\\ \implies 9 +20 = \dfrac x2 - 15 x\\\\\implies 29 = -\dfrac{29 x}2\\\\\ \implies 1 = -\dfrac x 2\\\\\implies x= -2\\\\\text{Substitute}~ x=-2~ \text{in equation (i):}\\\\y = 15(-2) +9 = -30 +9 = -21\\\\\text{Hence}~ (x,y) = (-2,-21)[/tex]
Bobby and Sue Ellan both ride their bikes to the library. Bobby’s home is 6.5 blocks from the library and Sue Ellan’s home is 1 ½ times farther from the library than Bobby’s home. How much farther must Sue Ellan ride her bike to get to the library than Bobby does?
Answers
Answer:
3.25 blocks
Step-by-step explanation:
6.5 * 1.5 = 9.75 blocks
9.75 - 6.5 = 3.25blocks
Farther 3.25 blocks sue ellan need to ride than Bobby ride
How can you best describe the outside of one of these objects using polygons? The object has sides, so it is. It appears to be because the sides and angles appear to be congruent.
Answers
The classification of a polygon is described on the basis of the number of sides and vertices of these objects using polygons. It appears to be because the sides and angles appear to be congruent.
The object has 6 sides, so it is. It appears hexagon because the sides and angles appear to be congruent.
We have to describe,The outside of one of these objects uses polygons, The object has sides, so it is. It appears to be because the sides and angles appear to be congruent.
According to the question,A polygon shape is any geometric shape that is classified by its number of sides and is enclosed by a number of straight sides. However, a polygon is considered regular when each of its sides measures equal in length.
A minimum of three line segments is needed to draw any closed figure. The corners or points where two line segments meet each other are known as the vertex of a polygon.
The classification of a polygon is described on the basis of its number of sides and vertices.
For example, a polygon of three sides and three angles is known as a triangle whereas a polygon of four sides and four angles is known as a quadrilateral.
A polygon shape is any geometric shape that is classified by its number of sides and is enclosed by a number of straight sides.
However, a polygon is considered regular when each of its sides measures equal in length.
The lengths of each side of a regular hexagon are equal.
The angles of each side of a regular hexagon are equal.
Hence, The object has 6 sides, so it is. It appears hexagon because the sides and angles appear to be congruent.
For more details about Polygon refer to the link given below.
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Answer:
6, hexagon, and regular
Step-by-step explanation:
The object has 6 sides, so it is a hexagon
It appears to be regular because the sides and angles appear to be congruent.
Use the graph of △ABC with midsegments DE, EF and DF. Show that EF is parallel to AC and that EF=1/2 AC
Answers
According to the midsegment theorem, the midsegments are parallel to
and half the length of the opposite side.
The completed statement are as follows;
Because the slopes of [tex]\overline{EF}[/tex] and [tex]\overline{AC}[/tex] are both -4, [tex]\overline{EF}[/tex] ║ [tex]\overline{AC}[/tex]EF = [tex]\underline{\sqrt{17}}[/tex] and AC = [tex]\underline{2 \cdot \sqrt{17} }[/tex]Because [tex]\underline{\sqrt{17} }[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17} }[/tex], [tex]EF = \frac{1}{2} \cdot AC[/tex]Reasons:
From the given graph of ΔABC, we have;
Coordinates of the points A, B, and C are; A(-5, 2), B(1, -2), and C(-3, -6)
The coordinates of the point D and E on [tex]\mathbf{\overline{DE}}[/tex] are; D(-4, -2), and E(-2, 0)
The coordinates of the point F is; F(-1, -4)
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\displaystyle Slope \ of \ line \ \overline{AC} = \mathbf{\frac{(-6) - 2}{-3 - (-5)} = \frac{-8}{2}} = -4[/tex]
[tex]\displaystyle Slope \ of \ line \ \overline{EF} = \frac{0 - (-4)}{-2 - (-1)} = \frac{4}{-1} = -4[/tex]
[tex]Length \ of \ segment,\ l = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]Length of EF = √((-1 - (-2))² + (-4 - 0)²) = √(17)
Length of AC = √((-3 - (-5))² + (-6 - 2)²) = √(4 × 17) = 2·√(17)
Therefore, we have;
Because the slope of [tex]\mathbf{\overline {EF}}[/tex] and [tex]\mathbf{\overline {AC}}[/tex] are both , -4, [tex]\overline {EF}[/tex] ║ [tex]\overline {AC}[/tex]. EF = [tex]\underline{\sqrt{17}}[/tex], and AC
= [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex],. Because [tex]\underline{\sqrt{17}}[/tex] = [tex]\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}[/tex], [tex]EF =\mathbf{ \frac{1}{2} AC}[/tex]
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Someone helppppppp. I swear I will cry for the rest of my life ;-;
Answers
3
Pentagon PQRST is 1/2 the size of ABCDE therefore, x = 3
Answer: there is no x so i can't answer it
Step-by-step explanation:
if each quadrilateral below is a rectangle, find the missing measures.
Answers
Answer:
Recall each angle in a rectangle is 90 degrees. So to find the other portion, subtract the given angle from the 90 degrees.
Step-by-step explanation:
The missing measures of the angles are as follows:
m∠BCD = 90°
m∠ABD = 16°
m∠CBE = 74°
m∠ADE = 74°
m∠AEB = 148°
m∠DEA = 32°
What is a rectangle?A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
here, we have,
to determine the measures of the angles:
The figure that completes the question is added as an attachment
From the figure of the rectangle, we have:
m∠BDC = 16°
A rectangle has four (4) interior angles that are 90 degrees each.
This means that
m∠ADE = 90 - 16
m∠ADE = 74°
Also, we have:
m∠ABD = m∠BDC = 16° by the alternate interior angles
By the complementary angle, we have:
m∠CBE = 90 - 16 = 74°
By the alternate interior angles, we have
m∠ADE = m∠CBE = 74°
Solving further, we have the following equations:
m∠AEB = 180 - 2(16)
m∠AEB = 148°
m∠DEA = 180 - m∠AEB
m∠DEA = 180 - 148
m∠DEA = 32°
Hence, the measure of the angle DEA is 32 degrees
m∠BCD = 90°
m∠ABD = 16°
m∠CBE = 74°
m∠ADE = 74°
m∠AEB = 148°
m∠DEA = 32°
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A quadrilateral regular pyramid, the area of any of its lateral faces equal the area of its base, if the side
length of the base of the pyramid is = 6 cm, then the volume of the pyramid =..........cm3
a) 36
b) 673
c) 36/15
d) 216V15
Answers
Answer:
c) 36√15 cm³
Step-by-step explanation:
We can compute the volume of the pyramid if we know the area of its base, and its height.
__
A regular quadrilateral is a square. If one side of the square is 6 cm, its area will be ...
A = s² = (6 cm)² = 36 cm² . . . . area of the pyramid base
__
Each triangular face will have a slant height that makes its area the same as that of the base.
A = 1/2bh
36 cm² = (1/2)(6 cm)h
(36 cm²)/(3 cm) = h = 12 cm . . . . . divide by the coefficient of h
The slant height of a face is the hypotenuse of a right triangle whose short leg is half the side length, and whose long leg is the height of the pyramid. If that height is represented by h, the Pythagorean theorem tells us ...
(6 cm/2)² +h² = (12 cm)²
h² = (144 -9) cm²
h = 3√15 cm . . . . . height of the pyramid
__
The volume of the pyramid is given by ...
V = 1/3Bh . . . . . . base area B, height h
Using the values we found above, we compute the volume to be ...
V = (1/3)(36 cm²)(3√15 cm) = 36√15 cm³
Given the set of domain D = {-3, -2, -1, 0, 1, 2, 3}
Construct /Do the following:
1. Set of ordered pairs such that the range is one less than the domain.
2. Construct table of values such that the range is 2 more than the domain.
3. Write the equation for numbers 1 and 2.
4. Graph numbers 1 and 2 on separate coordinate plane.
Answers
Given the domain of values D = {-3, -2, -1, 0, 1, 2, 3}
1) If the set of range is one less than the domain, the required range will be:
Range = {-4, -3, -2, -1, 0, 1, 2}
2) If the set of range is 2 more than the domain, the required range will be:
Range = {-1, 0, 1, 2, 3, 4, 5}
The table of values is given as:
x y
-3 | -1
-2 | 0
-1 | 1
0 | 2
1 | 3
2 | 4
3 | 5
2) For equation 1, we will use the coordinate points (0. -1) and (1, 0)
The equation in slope-intercept form is given as y = mx + b
m = 0-(-1)/1-0
m = 1/1 = 1
Since the y-intercept is at (0, -1), hence b = -1
Substitute the given value into the formula:
Recall that y = mx + b
y = 1x + (-1)
y = x - 1
Hence the equation 1 will be y = x - 1
For equation 2, we will use the coordinate points (-1, 1) and (0, 2)
The equation in slope-intercept form is given as y = mx + b
m = 2-1/0-(-1)
m = 1/1 = 1
Since the y-intercept is at (0, 2), hence b = 2
Substitute the given value into the formula:
Recall that y = mx + b
y = 1x + 2
y = x + 2
Hence the equation 2 will be y = x + 2
4) The graph of each equation on a different coordinate plane is attached.
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find the distance between find the distance between following points: a) M(5,4) and N(2, 3)
Answers
Answer:
sqrt(10)
Step-by-step explanation:
[tex] \sqrt[2]{ x_{2} - x_{1}) + ( y_{2} - y_{1})} [/tex]
A roller coaster can acommodate 150 people in 10 minutes How many people could ride the rolloer coaster in 25 minutes?
Answers
Answer:
375
Step-by-step explanation:
150 x 2= 300 -Thats for the 20 minutes
And 150 divided by 2 = 75= Thats for the addtional 5 minutes
37. Briefly explain how the use of credit helped increase the average
American's standard of living in the 20th century.
Answers
Answer: If a person has a better credit, they have better chances of getting the job they had applied for. Getting the job means they get a stable income. Having a stable income helps a person to buy all essential needs.
Step-by-step explanation:
The conditional relative frequency table was calculated by row using data from a survey of one station’s television programming. The survey compared the target audience with the type of show, either live or recorded, over a 24-hour time period. A 4-column table with 3 rows titled television programming. The first column has no label with entries adult, children, total. The second column is labeled live with entries 0. 625, 0. 5, nearly equal to 0. 583. The third column is labeled recorded with entries 0. 375, 0. 5, nearly equal to 0. 417. The fourth column is labeled total with entries 1. 0, 1. 0, 1. 0. Which is the best description of the value 0. 375 in the table? Given that the program was targeted at adults, there is a 37. 5% chance that it was recorded. Given that the program was recorded, there is a 37. 5% chance that it was targeted at adults. 37. 5% of the programs are targeted at adults. 37. 5% of the programs are recorded.
Answers
The conditional relative frequency presents the result of the survey that conveys information about the programming and the audience.
The best description of the value 0.357 in the table is; Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.Reasons:
The table is presented as follows;
[tex]\begin{tabular}{|c|c|c|c|}&Live&Recorded&Total\\Adult&0.625&0.375&1.0\\Children&0.5&0.5&1.0\\Total&\approx 0.583&\approx 0.417&1.0\end{array}\right][/tex]
Based on the given table, we have that the programs are categorized based on the intended audience.
Therefore, the 0.375, indicates that 37.5% of the program targeted at adults are recorded.
Therefore, the correct option is;
Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.
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Answer:
A
Step-by-step explanation:
its a
You can retry this question below
The sum of two numbers is 71. The difference of the two numbers is 41. What are the two numbers.
Let x be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 71."
Write an equation that expresses the information in the sentence "The difference of the two
numbers is 41."
Solve the system you have written above.
The larger number, x is
The smaller number, y is
Calculator
Answers
Answer:
x = 56
y = 15
Step-by-step explanation:
"The sum of two numbers is 71."
x + y = 71
"The difference of the two numbers is 41."
x - y = 41
Solve the system:
From the first eq.
x = 71 - y
Replacing this value in the second eq.
(71-y) - y = 41
71 - 2y = 41
71 - 41 = 2y
30 = 2y
y = 30/2
y = 15
From the second eq.
x - y = 41
x - 15 = 41
x = 41 + 15
x = 56
Check:
from the first eq.
x + y = 71
56 + 15 = 71
If there are 30 boys and 12 girls in a room, fill out all of the possible ratios of boys to girls that could be made
Answers
Answer:
30:12
Step-by-step explanation:
HELP!!!
list the sides of ABC in order from shortest to longest!
Answers
Hamid has gained weight.
he now weighs 88kg, this is 10% more than his normal weight.
what is hamids normal weight?
Answers
Answer:
174.6
Step-by-step explanation:
88 kg = 194.007 - 10%
194 * 10% = 194 - 19.4 = 174.6
Mathematics 13 don’t understand
Answers
Answer:
1/6^3
Step-by-step explanation:
The applicable rules of exponents are ...
a^-b = 1/a^b
(a^b)(a^c) = a^(b+c)
__
Your expression can be simplified as follows:
[tex]\dfrac{6^{-5}}{6^{-2}}=\dfrac{1}{(6^{-2})(6^5)}=\dfrac{1}{6^{-2+5}}=\boxed{\dfrac{1}{6^3}}[/tex]
_____
Additional comment
If you think of an exponent as signifying repeated multiplication, the rules of exponents may be easier to remember. The exponent tells you how many times the base is a factor in the product.
Consider multiplication:
[tex](x\cdot x\cdot x)\cdot(x\cdot x)=x^3\cdot x^2=x^{3+2}=x^5\\\\(x\cdot x\cdot x)\cdot(x\cdot x\cdot x)=(x^3)^2=x^{3\cdot2}=x^6[/tex]
Consider division:
[tex]\dfrac{x\cdot x\cdot x}{x\cdot x}=x\quad\Longleftrightarrow\quad\dfrac{x^3}{x^2}=x^{3-2}=x^1\\\\\dfrac{x\cdot x}{x\cdot x\cdot x}=\dfrac{1}{x}\quad\Longleftrightarrow\quad\dfrac{x^2}{x^3}=x^{2-3}=x^{-1}[/tex]
This may help you see that a positive exponent in the denominator is equivalent to a negative exponent in the numerator (and vice versa).
Answer plz answer !!!
Answers
Answer:
B
Step-by-step explanation:
1/4 yard long, area is 1/3 and we have to find the width so:
1/3(area) divided by 1/49(length) would get you your width
A rock is thrown into a pool 72 inches deep. The rock sinks at a rate of 4 inches per
second (s). The rock's height (h) above the bottom of the pool is given by the
equation: h = 72 – 4s. After how many seconds will the rock be half way to the
bottom?
Answers
Half of 72 is 36. If you divided 36 by 4, you would get 9. So, s = 9 and means that it takes 9 seconds for the rock to be sunk half way.
what is the equation
Answers
Answer:
y = -2x+9
Step-by-step explanation:
To figure out equations of tile patterns simply count the initial value and the rate of change, then convert it into (slope intercept form) which is
y = mx+b
In this case the rate of change is -2x because each figure loses 2 blocks as it goes.
You can also see the the initial figure 1 has 9 blocks so this is our constant
With this information we can create the equation y = -2x+9
m = -2
x = x
b = 9
If more aid is needed a simple search of (Visual Pattern - Writing an Equation and Creating a Table) will help you with a video easily.
Rewrite using the distributive property and the GFC
13+26 ?
Answers
Answer: 13 ( 1 + 2 )
Step-by-step explanation:
13 ( 1 + 2 ) = 13 + 26
mr polaski bought a variety pack of muffins that has 9 apple muffins. the ratio of apple muffins to blueberry muffins in variety pack is 3:5 . how many blueberry muffins are in ms polaski's variety pack?
Answers
Answer:
He has 15 Blueberry Muffins
Step-by-step explanation:
If the ratio is 3 to 5, and he has 9 apples, that means that he has 3 times the normal ratio. So, multiply 5 by 3 and you get 15 blueberries.
Use the translation rule (x, y) --> (x -10, y + 6) to find the image of A(5, - 10).
Answers
Answer:
(-5, -4)
Step-by-step explanation:
Plugin the values:
(x, y) ⇒ (x -10, y + 6)
= x - 10, y + 6
= (5 - 10, -10 +6)
= (-5, -4)
Therefore, A prime is (-5, -4).
Express 0.16 bar as a rational number
Answers
Mark as brainliest
When r= 1 , h=2.4 find r in terms of h
Answers
Answer:
r= 5/12 h
Step-by-step explanation:
r/h = 1/2.4
r =[tex]\frac{10}{24}[/tex]h
r=[tex]\frac{5}{12}[/tex]h
Solve the set of simultaneous equations graphically. Use a scale of 1cm = 1 unit on both axes.
y=4+x
y=1+3x ; 0≤x≤6
Answers
Graphs attached
(x,y)=(1.5,5.5)Maria's test scores for this semester were: 84, 80, 93, 74, 67, 99, 87, 72, 95, & 98. What is the mean of her test scores (rounded to the nearest whole
percent)?
Answers
Answer:
85%
Step-by-step explanation:
Add all the numbers together which gives 849. Divide 849 by 10 because there are ten numbers. This gives 84.9. Round it up to 85%
PLEASE HELP WITH ALGEBRA WILL GIVE BRAINLIEST
Answers
Answer:
[tex]\frac{ad}{bd} + \frac{cb}{bd}[/tex]
Step-by-step explanation:
[tex]\frac{a}{b} + \frac{c}{d}[/tex]
[tex]\frac{ad}{bd} + \frac{cb}{bd}[/tex] Multiply by the LCD (bd)
0.3(y+2)=1.7+(8-y) solve the following equation
Answers
Answer:
y = 7
Step-by-step explanation:
0.3y+0.6 = 9.7 - y
0.3y+y = 9.7 -0.6
1.3y = 9.1
y= 7
sorry it had an error