Answers
The equation of the graph in the figure is f(x) = |x - 3| + 5
How to find the equation of the graph line?Given that the graph is an absolute value graph
We start by calculating the vertex of the graph
In this case, the graph has it minimum point located at the coordinate (3, 5)
This coordinate can then be interpreted as
(h, k) = (3, 5)
As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = |x - 3| + 5
Hence, the equation of the graph is f(x) = |x - 3| + 5
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Related Questions
Two sailboats are sailing up a river. The relationship between the distance (d ), in miles, from the starting point to the time (t ), in hours, it takes to sail a distance d for each boat is given.
Answers
The correct statement regarding the proportional relationships is given as follows:
Boat A travels at a faster rate than Boat B.
What is a proportional relationship?A proportional relationship is a special case of a linear function with intercept zero in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:
y = kx
The function for boat A is:
d = 10.5t.
Hence the rate is:
10.5 miles per hour.
From the graph, the rate for boat B is obtained as follows:
k = 90/10 = 9 miles per hour.
A higher constant means a faster rate, 10.5 is greater than 9, hence boat A travels faster.
Missing InformationThe problem is given by the image shown at the end of the answer.
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you would like to create a rectangular vegetable patch with an area of 32 sq. ft. to grow oranges. the fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. what are the dimensions of the vegetable patch with the least expensive fence? let the variable x denote the length of the east and west sides of the garden and let the variable y denote the length of the north and south sides of the garden. you and your friends individually set up a solution for the optimization problem using these variables. who set up the problem properly?
Answers
The maximum and minimum measurements are 5 and -3 respectively.
f ( x ) = -x^3 +3x^2+ 45 x + 10
f' l x ) = 0
0 = - 3x^2 +6x +45
x = 5,- 3.
f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174
f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58
f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1
+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185
Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}
= 185 at x=5
Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}
= - 71 at x= -3
In light of this, the maximum and minimum values are 5 and -3, respectively.
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find the volume, curved surface area and the total surface area of a cone having base radius 35 cm and height 12 cm.
Answers
The volume of the cone is 15393.80 cm³
The curved surface area of a cone is 4068.36 cm²
The total surface area of the cone is 7916.81 cm²
Given parameters;
The base radius( r ) of the cone is 35cm
The height( h ) of the cone is 12cm
Case (I): To find the volume of the cone;
The volume of the cone = [tex]\pi r^{2}\frac{h}{3}[/tex]
= π *(35)² * 12/3
= 15393.80 cm³
Case (II): To find the curved surface area of the cone;
The curved surface area of the cone = πrl
We know that;
Slant height l = [tex]\sqrt{(r^2 + h^2)}[/tex]
By substituting the values;
l = [tex]\sqrt{35^2 + 12^2}[/tex]
l = 37
We know that;
The curved surface area of a cone = πrl
= π * 35 *37
= 4068.36 cm²
Case (III): The total surface area of the cone;
The total surface area of the cone = πr(l + r)
= π * 35 * (37 + 35)
= 7916.81 cm²
Therefore,
The volume of the cone is 15393.80 cm³
The curved surface area of a cone is 4068.36 cm²
The total surface area of the cone is 7916.81 cm²
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1. Of the three lines in the graph, one has slope 1, one has slope 2, and one has slope
Label each line with its slope. HELP IM REALLY STUCK ON THIS
Answers
The presense of a midpoint will result in what type of segments?
Answers
The presense of a midpoint will result in congruent segments.
What are congruent segments?Congruent segments are just equal-length line segments. Congruent means similar. Congruent line segments are typically represented by drawing the same number of little tic lines perpendicular to the segments in the middle of the segments.
A congruent line segment is any line segment with equal measure. Congruent line segments, for example, are the sides of an equilateral triangle since they all have the same length.
When we insert a midpoint to a line segment, it divides the line into two equal portions. Because equal segments are congruent, we can say that congruent segments are generated.
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Which of the following would be a good estimate for -7.94 - 2.31?
-10
-5
-9
-6
will mark brainiest
Answers
Answer:-10.25
Step-by-step explanation:
Just because ;) -10.25= -10.00
Answer:
-10
Step-by-step explanation:
Estimate between the two numbers?
Add them together first
Which equals -10.25
The closest would be -10
Help!! Can someone state all the statements and reasons to prove that triangle WXY is congruent to triangle WZY!! It’s geometry proofs.
Whoever gives me the answer I’ll give them 20!
Answers
It is true that WXY ≅ WZY.
What is a congruent?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
Properties of Congruence
Reflexive Property: An angle is congruent to itself.
Symmetric Property: The order of congruence does not matter.
Transitive Property: If two angles are both congruent to a third angle, then the first two angles are also congruent.
Here, It is given that
Angle ZWY is congruent to angle XWY
Segment WZ is congruent to Segment WX
Segment WY is congruent to Segment WY - Reflexive Property of Congruence (which states that one thing is congruent to itself.
Hence, Triangle WXY is congruent to Triangle WZY because of Side Angle Side (SAS) postulate.
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A line passes through points
(8, - 2) and
(-5, 7). Which ratio can be used to determine the slope of the line?
7+2/
8+5
7-2/
-5-8
8+5/
-2+7
7+2/
-5-8
Answers
Answer:
7+2/8+5
Step-by-step explanation:
how many units apart are -6 and 4 on the number line
Answers
-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4
So that’s 10 units apart
If the public debt of a country in 2009 was $11,982,000,000,000and the
budget for 2010 was in deficit by $101,347,000,000 , what was the public debt
in 2010? Do not include commas in your answer.
Answers
If a country's public debt in 2009 was $11,982,000,000,000 and its budget for 2010 was $101,347,000,000 in deficit, the public debt in 2010 is $12083347000000.
What is public debt?Government obligations, particularly those evidenced by securities, to pay certain sums to holders at some future time. Private debt, which includes the obligations of individuals, businesses, and nongovernmental organizations, is distinct from public debt. A debt-to-GDP ratio compares a country's total debt to its economic productivity. Divide a country's debt by its GDP to calculate the debt-to-GDP ratio. Governments can use public debt to raise funds to expand their economies or pay for services. Politicians would rather increase the national debt than raise taxes. The national debt includes public debt, and when the national debt reaches 77% or more of GDP, the debt begins to slow growth.As given
if the public debt of a country in 2009 was $11,982,000,000,000 and the budget for 2010 was in deficit by $101,347,000,000 .
Total public debt in 2010 = Public debt in 2009 + Amount by which 2010 budget deficit .
= $ 11982000000000 + 101347000000
= $ 12083347000000
Therefore the public debt in 2010 is $12083347000000.
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A positive integer M divided by six gives a remainder of three. Another positive integer N divided by six gives a remainder of five. What is the remainder when the sum M+N is divided by six?
Answers
When the sum M+N is divided by 6 , the remainder is 8
What is Remainder?The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). We always have remainder when the denominator is a factor of numerator.
For example 5/2, diving 5 with 2, 2 is not a factor of 5,
There are 2 2s in 5 with remainder 1.
M/6= x y/6
where is the factor and y is the remainder
therefore m/6= (6x+y)/6
y= 3,. m/6= (6x+3)/6
N/6= (6x+5)/6
therefore dividing both sides by 6
m= 6x+3
n= 6x+5
adding m and n
m+n= 12x+8
dividing m+n by 6
(m+n)/6 = (12x+8)/6
relating (12x+8)/6 with (6x+y)/6
y = 8
Therefore the remainder is 8
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A band expects to put 16 songs on their next CD. The band writes and records 62.5% more songs than they expect to put on the CD. During the editing process, 50% of the songs are removed. How many songs will there be on the final CD?
Answers
Answer:
songs in the final CD 13
Step-by-step explanation:
the 100% = 16
-------------------
16/x=100/62.5
(16/x)*x=(100/62.5)*x
16=1.6*x
16/1.6=x
10=x
x=10
This is the 62.5% of 16
---------------------
now the new 100% is 10 + 16 = 26
but during the editing process 50% are removed
and the 50% of 26 (half of it) is = 13
Hooke's Law states that the displacement, d, that a spring is stretched by a hanging object varies directly as the mass, m, of the object. If the distance is 12cm when the mass is 4kg, what is the distance when the mass is 5kg.
Answers
The distance when the mass is 5kg is 15cm.
What is the distance?When two values vary directly, it means that both values move in the same direction. If one of the value increases, the other value increases and if one of the values decreases, the other value decreases.
The equation that is used to represent direct variation is:
d = km
Where:
d = distance k = constant of variation m = massThe first step is to determine the value of k:
12 = 4k
k = 12 / 4
k = 3
d = 3 x 5 = 15cm
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What is the correct standard form for 400+3+0.07+0.001
Answers
What is the correct standard form for 400+3+0.07+0.001
403.071
Answer:
=4.03071×10²
Step-by-step explanation:
400+3=403
=403+0.07=403.07
=403.07+0.001=403.071
so 403.071 to standard form is 403.071 divide by 100 is 4.03071 and 10 and and also change to 2 zeros and Chang it to powers so =4.03071×10²
Use prime factorization to find the exponent. Show all of your work in good form.
625 as a power of 5
343 as a power of 7
216 as a power of 6
169 as a power of 13
256 as a power of 4; as a power of 2
729 as a power of 9; as a power of 3
Answers
The use of prime factorization to find the exponents of the given numbers gives 625 = 5⁴, 343 = 7³, 216 = 6³, 169 = 13², 256 = 4⁴; 256 = 2⁸ and 729 = 9³; 729 = 3⁶
How to express numbers as a product of prime factors?
When a number is written as a product of its prime factors, we have the prime factorization of the number e.g 8 = 2×2×2
An exponent is defined as a way of expressing large numbers in terms of powers e.g 81 = 3×3×3×3 = 3⁴
Thus, you can use prime factorization to find the exponent of the given numbers as follows:
625 as a power of 5
625 = 5×5×5×5 = 5⁴
343 as a power of 7
343 = 7×7×7 = 7³
216 as a power of 6
216 = 6×6×6 = 6³
169 as a power of 13
169 = 13×13 = 13²
256 as a power of 4; as a power of 2
256 = 4×4×4×4 = 4⁴
256 = 2×2×2×2× 2×2×2×2 = 2⁸
729 as a power of 9; as a power of 3
729 = 9×9×9 = 9³
729 = 3×3×3×3×3×3 = 3⁶
Therefore, 625 as a power of 5, 343 as a power of 7, 216 as a power of 6, 169 as a power of 13, 256 as a power of 4; as a power of 2 and 729 as a power of 9; as a power of 3 are 5⁴, 7³, 6³, 13², 4⁴; 2⁸ and 9³; 3⁶ respectively
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Help!! Direct and Inverse Variations
Answers
The value of y is 24 when x is -2.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
There are direct variations
y= 24 when x=2
We need to find value of y when x =-2
This can be found by forming an equation.
Let the value of unknown y be a
2/24=-4/a
Apply cross multiplication
2a=24(-2)
2a=-48
We need to divide by 2 on both sides
a=-24
Hence the value of y is 24 when x is -2.
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9. If mBED=(15x-47) and mBD = (9x-1), find m/CBD.
Answers
125° is the angle of CBD
An angle pair that forms a straight line is referred to as a straight angle pair. This pair's sum of any two or more angles is always equal to 180°.
What is the straight-angle angle?A straight angle has a 180° angle.
The two angles are from a straight line, and they sum to 180 degrees.
A + B + C = 180
8x -41+ 9x+17 = 180
Conjoin similar terms
17x -24 = 180
24 more on each side
17x -24+24 = 180 +24
17x = 204
multiply by 17
17x/17 = 204/17
x =12
We desire CBD angled.
CBD = 9x+17
= 9*12+17=108+17
= 125
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Can someone help me with this please! I really need it done PLS
increase the amount of the ingredients by 5 and by 20
Answers
Answer:
it's 50 g
Step-by-step explanation:
it's like a multiplying assberry kehe
we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can i. change the z value to a smaller number. ii. take a larger sample. iii. take a smaller sample.
Answers
Using the concepts of errors and measurement, we got that by taking a larger sample 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence.
In science, experimental errors may be caused due to the human inaccuracies like a wrong experimental setup in the science experiment or choosing the wrong set of people for the social experiment. Systematic error refers to that error which is actually inherent in the system of experimentation.
Hence, if we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can take a larger sample.
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for each of the following determine the n -unit percent change. the 19-unit percent change is 45 %. what is the 17-unit percent change? % the 16-unit percent change is 43 %. what is the 12-unit percent change? % the 20-unit percent change is -25 %. what is the 18-unit percent change? % the 5-unit percent change is -50 %. what is the 8-unit percent change?
Answers
Hence, 17-unit percent change is (45/19)×17% = 40.26%
12-unit percent change is (43/16)×12% = 32.25%
18-unit percent change is (-25/20)×18% = -22.5%
8-unit percent change is (-50/5)×8% = -80%
Given, that
The 19-unit percent change is 45 %
Now, 1-unit percent change is 45/19
17-unit percent change is (45/19)×17%
= 40.26%
The 16-unit percent change is 43 %
Now, 1-unit percent change is 43/16
12-unit percent change is (43/16)×12%
= 32.25%
The 20-unit percent change is -25%
Now, 1-unit percent change is -25/20
18-unit percent change is (-25/20)×18%
= -22.5%
The 5-unit percent change is -50 %
Now, 1-unit percent change is -50/5
8-unit percent change is (-50/5)×8%
= -80%
Hence, 17-unit percent change is (45/19)×17% = 40.26%
12-unit percent change is (43/16)×12% = 32.25%
18-unit percent change is (-25/20)×18% = -22.5%
8-unit percent change is (-50/5)×8% = -80%
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PLEASE HELP!! I NEED SOMEONE TO HELP ME!
Use distributive property to remove parenthesis.
-9( -3w + 3u - 4)
Answers
The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)
Given,
In the question:
Use distributive property to remove parenthesis.
-9(-3w + 3u - 4)
Now, According to the question:
First, we know:
What does parentheses mean distributive property?
The distributive property allows us to multiply all terms in a parentheses by a number outside of it. a(b +c) = ab + ac.
We have:
-9(-3w + 3u - 4)
Solve by Distributive Property :
-9(-3w + 3u - 4)
Open the bracket:
27w - 27u +36
Hence, The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)
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Which rational number is equivalent to 0 . ¯¯¯¯¯¯ 36 ?
Answers
The rational number is equivalent to 0.36 is 9/25
How to determine the equivalent rational number?From the question, we have the following decimal number that can be used in our computation:
Decimal number = 0.36
To start with, we need to express the decimal number as a fraction
This is represented as follows:
So, we have the following representation
Decimal number = 36/100
Change the label of the above representation to rational number
Rational number = 36/100
Simplify the rational number (divide the numerator and the denominator by 2)
Rational number = 18/50
Simplify the rational number (divide the numerator and the denominator by 2)
Rational number = 9/25
Hence, the equivalent rational number is 9/25
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In any triangle the sum of the measures of the angles is 180°. And ABC is three times as large as B and also 16° larger than C. Find the measure of each angle
Answers
The measures of the each angle of the triangle is 84, 28 and 68 degrees.
How to find the measure of angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The triangle has the sum of the measures of the angles as 180°.
Angle A is three times as large as angle B and also 16° larger than C.
Therefore,
let
angle A = x
Angle B = x / 3
Angle C = x - 16
Therefore,
x + x - 16 + x /3 = 180
7 / 3 x - 16 = 180
7 / 3 x = 180 + 16
7 / 3 x = 196
cross multiply
7x = 196 × 3
7x = 588
divide both sides by 7
x = 588 / 7
x = 84
Therefore,
A = 84 degrees
B = 84 / 3 = 28 degrees
C = 84 - 16 = 68 degrees
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Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
Answers
The formula of nth term is = 10 - 3n
What is AP?
A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. Take the numbers 5, 7, 9, 11, 13, and 15 as an example. . . is a sequence of numbers having a common difference of two.The n-th term of the sequence is given by:, if the beginning term of an arithmetic progression is and the common difference between succeeding members is, thenIf the AP contains m phrases, then denotes the final term, which is given by:The term "finite arithmetic progression" or "arithmetic progression" refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.Acc to our question-
For the nth term in an algebraic seriesU(n) = a + (n - 1)dthe number of terms is n.The first term is a.d is the typical differenceFrom the preceding sequencea = 7d = 4 - 7 = - 3The nth term's formula isU(n) = 7 + (n - 1)-3= 7 - 3n + 3The ultimate solution is= 10 - 3nHence,The formula of nth term is = 10 - 3n
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The demand function for a certain make of replacement cartridges for a water purifier is given by the equation p=−0. 01x2−0. 1x+21 where p is the unit price in dollars and xis the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $9/cartridge. (Round your answer to two decimal places. )
Answers
The demand function for a certain is given by the equation p=−0. 01x2−0. 1x+21 then the determined values will be −50.905557, −0.427737,41.333295.
From the given values,
R=px
9 = (−0. 01x2−0. 1x+21) x
0.01x3+0.1x2−21x−9=0
By reducing the equation,
X = −50.905557, −0.427737,41.333295.
Therefore, the determined values will be −50.905557, −0.427737,41.333295.
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Mrs. Wong is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Lakeside Florist charges $19 for each smaller arrangement, plus $50 for the large centerpiece. Spencer's Flowers, in contrast, charges $42 for the large centerpiece and $23 per arrangement for the rest. If Mrs. Wong orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be?
Answers
Step-by-step explanation:
so, we have 2 cost functions. each consisting of 1 large centerpiece, and x smaller arrangements.
cost1(x) = 19x + 50
cost2(x) = 23x + 42
to get the value for x we know that the cost is the same either way.
that means
cost1(x) = cost2(x) = 19x + 50 = 23x + 42
19x + 50 = 23x + 42
50 = 4x + 42
8 = 4x
x = 2
so, she orders 2 small arrangements.
the total cost is
19×2 + 50 = 38 + 50 = $88
cross check with the other function :
23×2 + 42 = 46 + 42 = $88
correct
One of the support wires for a radio tower is
100 feet long. One end of the wire is 40 feet from
the base of the tower, as shown in the diagram
below.
Support wire
Note: The figure is not drawn to scale.
What angle (x), in degrees, does the support wire
make with the ground?
Answers
Using the trigonometry ratio, the value of angle x is 66.42°.
In the given question,
One of the support wires for a radio tower is 100 feet long.
One end of the wire is 40 feet from the base of the tower.
We have to find the angle (x), in degrees, that the support wire make with the ground.
To find the angle of x we use trigonometry ratio.
According to the ratio cosine is the ratio between base and hypotenuse.
So the formula is Cos x= B/H
where H = Hypotenuse
B = Base
From the given figure we know that, H=100 feet, B=40 feet
Now putting the value
Cos x= 40/100
Simplifying
Cos x = 2/5
Cos x = 0.4
So x = arccos(0.4)
x = 66.42
Hence, the value of angle x is 66.42°.
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There are 40 coins in a roll of nickels .there are 50 coins in a roll of dimes and 20 coins in a roll of half -dollars.alondra has 3 rolls of coins. she has a total of 90 coins. make an organized list to show all the combinations of coin rolls. what coins does alondra have?
Answers
Answer:
she has 2 half dollors and 1 dimes
Step-by-step explanation:
2 half dollors means 2x20=40 coins
1 dimes means 1x50=50 coins
when you total it you get 50+40=90
so it is 3 rolls and it totally has 90
How to solve for x step by step 3x-1=20
Answers
21/3=7
(X=7) is the answer
Answer:
x = 7
Step-by-step explanation:
Given equation,
→ 3x - 1 = 20
Now the value of x will be,
→ 3x - 1 = 20
→ 3x = 20 + 1
→ x = 21/3
→ [ x = 7 ]
Hence, the value of x is 7.
help i have no clue what this even means
Answers
Case 1: largest surface area: 2120 sq. in.
Case 2: smallest surface area: 1380 sq. in. of the wooden block.
What is defined as the cuboid?A three-dimensional shape called a cuboid is described as having six rectangular face, eight vertices, and twelve edges.Twelve edges plus eight vertices and corners to up a cuboid.For the given question, the dimensions of the wooden block are given.
Length l = 50 inchesWidth w = 5 unitsHeight h = 2 unitsSurface area of a cuboid is = 2lw + 2lh + 2 hw
Case 1: largest surface area.
To get the largest surface area, join the wooden cube along length 50 cm.
Total length = 50 + 50 + 50 = 150 inches.
Put in formula.
Surface area = 2×150×5 + 2×5×2 + 2×2×150
Surface area = 2120 sq. in.
Case 2: smallest surface area.
To get the smallest surface area, join the wooden cube along height 2 cm.
Total length = 2 + 2 + 2 =8 inches.
Put in formula.
Surface area = 2×8×50 + 2×50×5 + 2×5×8
Surface area = 1380 sq. in.
Thus, the smallest surface area of the wooden cube is found as 1380 sq. in.
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The correct question is-
There are 3 identical wooden blocks that are 50 inches long, 5 inches wide and 2 inches thick. If you glue them together , what is the largest and smallest outer surface area can get?
