The equation of the graph after translation is y = |2x + 9|
What is the equation for the translation of the function one unit to the left?To translate the graph of y = |2x + 7| one unit to the left, we need to replace x with (x + 1) in the equation. This will shift the entire graph one unit to the left. The equation for the translated graph is:
y = |2(x + 1) + 7|
Simplifying this equation, we have:
y = |2x + 2 + 7|
y = |2x + 9|
Therefore, the equation for the translation of the graph of y = |2x + 7| one unit to the left is y = |2x + 9|.
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Type the correct answer in each box.
Find the elements of matrix A.
help PLS!!
Answer:
a = 2
b = 11
c = 11
d = -2
Step-by-step explanation:
[tex]\sf \left[\begin{array}{cc}a&b\\c&d \end{array}\right] *\left[\begin{array}{ccc} 22&11&7\\ 6&-9&-15 \end{array}\right] =\left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \end{array}\right][/tex]
[tex]\sf \left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \\ \end{array}\right] =\left[\begin{array}{ccc} 110&-77&-151\\230&139&107 \\ \end{array}\right][/tex]
On comparing to right side, we get,
22a + 6b = 110
Divide the entire equation by 2
11a + 3b = 55 ------------(I)
11a - 9b = -77 -------------(II)
Subtract equation (II) from (I)
11a + 3b = 55
11a - 9b = -77
- + + {Now subtract}
12b = 132
b = 132/12
[tex]\sf \boxed{\bf \ b = 11}[/tex]
Substitute the value of b in eqaution (I)
11a + 3*11 = 55
11a + 33 = 55
11a = 55 - 33
11a = 22
a = 22/11
[tex]\sf \boxed{\bf \ a = 2}[/tex]
22c + 6d = 230
Divide by 2
11c + 3d = 115 -----------------(III)
11c - 9d = -139 ------------------(IV)
Subtract (IV) from (III)
11c + 3d = 115
11c - 9d = 139
- + -
12d = -24
d = -24/12
[tex]\sf \boxed{\bf \ d = -2}[/tex]
Plugin d = - 2 in equation (III)
11c + 3*(-2) = 115
11c - 6 = 115
11c = 115 + 6
11c = 121
c = 121/11
[tex]\sf \boxed{\bf \ c = 11}[/tex]
Theresa needs twice as many feet of wood as samuel how many pieces of wood does teresa need?
Using addition or multiplication, Teresa has twice a number of wood as Samuel.
According to the question,
Teresa needs twice as many feet of wood as Samuel in order to find the number of pieces of wood Teresa need only if we add the number Teresa has by itself or multiply it by 2.
Hence, we need to do only multiply it by 2
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A lab received and produce a sample of plutonium which has a half life of 138 days suppose you have an initial sample of 52 g which equation can be used to calculate the remaining amount of the sample “t” days after being processed by the lab
The remaining amount of the sample after 't' days would be 51. 74g
How to determine the amountWe have the formula for amount to be;
A = Ao × (1/2)^ t/t^1/2
Where
t1/2 = half -life = 138 days
t = 1
Ao = 52g
A = Amount after decay
Substitute into formula
A = 52 × (1/2) ^ 1/138
A = 52 ×
[tex] { \frac{1}{2} }^{0.00724} [/tex]
A = 52 × 0. 9950
A= 51. 74 g
Thus, the remaining amount of the sample after 't' days would be 51. 74g
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If a and b are rational numbers and a+b√3=1/2-√3,find a:b=?
The value of the ratio a:b is 2:1
What is a surd?Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.
Example of some surds are the square root of prime numbers.
Analysis:
a + b[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2 - \sqrt{3} }[/tex]
Rationalizing the right hand side by the conjugate surd which is 2 + [tex]\sqrt{3}[/tex]
[tex]\frac{1}{2 - \sqrt{3} }[/tex] x [tex]\frac{2 + \sqrt{3} }{2 +\sqrt{3} }[/tex] = [tex]\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}[/tex] = [tex]\frac{2 + \sqrt{3} }{1}[/tex] = 2 + [tex]\sqrt{3}[/tex]
Equating,
a + b[tex]\sqrt{3}[/tex] = 2 + [tex]\sqrt{3}[/tex]
Comparing the variables,
a = 2, b[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex], b = 1
The ratio, a: b = 2:1
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The graph at left in the ap-plane shows p, the atmospheric pressure of Earth in pounds per square inch (psi),
The best interpretation of 0.8^a in this exponential equation is that: C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.
What is an exponential function?An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = aeˣ
How to interpret this equation modeling the atmospheric pressure?Based on the information provided, we can logically deduce that the atmospheric pressure (p) exerted on an airplane flying at an altitude of a miles above sea level is defined by the following exponential function:
p = 14.63 × 0.8^a
Next, we would evaluate as follows;
At a = 0, we have:
p = 14.63 × 0.8^(0)
p = 14.63 psi.
At a = 1, we have:
p = 14.63 × 0.8^(1)
p = 11.704 psi, and this is 20% less than a mile before.
At a = 2, we have:
p = 14.63 × 0.8^(2)
p = 9.3632 psi, and this is 20% less than a mile before.
At a = 2, we have:
p = 14.63 × 0.8^(3)
p = 7.4906 psi, and this is 20% less than a mile before.
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Complete Question:
Atmospheric pressure, measured in pounds per square inch (psi) is the force exerted by Earth's atmosphere over a given area. The atmospheric pressure, p, exerted on an airplane flying at an altitude of a miles above sea level can be approximated by the model shown below. What is the best interpretation of 0.8^a in this equation?
p = 14.63 × 0.8^a
A. If the airplane reaches the outer extent of the Earth's atmosphere, the atmospheric pressure will be 0.8 psi.
B. If the airplane is at sea level, the atmospheric pressure will be 0.8 psi.
C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.
D. For each mile that the altitude increases, the atmospheric pressure increases 20%.
Which of the following is correct based on this picture?
Applying the trigonometry ratios, the correct option is: B. none of these are correct.
What are the Trigonometry Ratios?The trigonometry ratios are SOH CAH TOA, which are used for solving a right triangle.
Use the trigonometry ratio to find out which option is correct.
Cos Z = adj/hyp = 61/CZ, so option A is incorrect.
Sin Z = opp/hyp = 73/CZ, so option C is incorrect.
Tan Z = opp/adj = 73/61, so option D is incorrect.
Thus, the answer is: B. none of these are correct.
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Need some help with trigonometry
Answer:
e) B. 45°
f) A. 30°
Step-by-step explanation:
e) sec theta = 1/ cos theta
the value of cos theta is 1/√2 at 45°
so , sec 45° = √2 and theta = 45°
f) cot theta = 1/ tan theta
the value of tan theta is 1/ √3 at 30°
so, cot 30° = √3 , theta = 30°
The answers are :
e) B
f) A
For part (e), convert into terms of cosθ.
secθ = 1/cosθcosθ = 1/√2θ = cos⁻¹ (1/√2)θ = 45°For part (f), convert into terms of tanθ.
cotθ = 1/tanθcotθ = 1/√3θ = cot⁻¹ (1/√3)θ = 30°Charlie owns a computer repair service. For each computer, they charge $50 plus $45 per hour of work. A linear equation that expresses the total amount of money Charlie earns per computer is y
The linear equation is 45x+50
Linear equation is the equation having the degree 1
Given that the charge per computer repair service is $50
The charge per hour of work is $ 45
We need to show the linear equation that expresses the total amount of money Charlie earns per computer is y
So , Let the number of hours be x
Therefore, the Charlie working hours charge will be 45x
The total amount of money Charlie earns per computer is y
Therefore the linear equation will be
y = 50+45x
Where y = Total amount of money
x = number of hours
Hence the linear equation is y = 45x+50
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A square has side lengths of 9, which of the following is a correct formula for finding the area of a square
Answer:
9 x 9 = 81
Step-by-step explanation:
area = width x height
Since it's a square, width = height
Q1. suppose that lim(,)â(3,1)(,)=6. what can you say about the value of (3,1) ? what if is continuous?
Answer:39084620
Step-by-step explanation:
New questions in Mathematics
19 ft 4 ft l Find l. l = √ [?] ft
flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet stream, the same jet travels 5360 miles in 4 hours. What is the rate…e of the jet in still air and what is the rate of the jet stream?
Please help! Express the area of the region bounded by the x-axis, y = 1/2x - 2, and y equals the cubed root of x, using definite integrals.
Solve the equation 7/4x-2=-5x+1
How to Convert 11010112 to base 10?
Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation…. (b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.
Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)
Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)
The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k2 x,k2 y,k2 z)
Evaluate each expression if a=2,b=-3,C=-1, and d=4 5+d(3b-2d)
Which sequence of transformations produces A’B’C’ from ABC?
On a coordinate plane, triangle A B C has points (3, negative 1), (4, negative 4), (1, negative 2). Triangle A prime B prime C prime has points (negative 2, 3), (1, 4), (negative 1, 1).
a translation up 3 and then a 90º counterclockwise rotation about the origin
a 90º counterclockwise rotation about the origin and then a translation up 3
a reflection over the x-axis and then a translation left 2 and down 1
a translation left 5 and down 2 and then a reflection over the x-axis
Answer:
The first chose is correct
Step-by-step explanation:
You can see in the first picture that graphed both of the triangles and then I followed the directions. It is very, very helpful if you have tracing paper. You can trace the original and then translate it three up. For the 90 rotation, put a small + on the origin of your tracing paper, then move the tracing paper one one turn on the plus sign. That would be 90 degrees.
I WILL GIVE BRAINLY A dairy farmer wants to mix a 60% protein supplement and a standard 20% protein ration to make 1400 pounds of a high-grade 40% protein ration. How many pounds of each should he use?
The number of pounds of 60% protein and 20% protein supplement used is 700 and 700 pounds respectively.
Simultaneous equationlet
Pounds of 60% protein used = xPounds of 20% protein used = yx + y = 1400
0.60x + 0.20y = 1400×0.40
0.60x + 0.20y = 560
From (1)
x + y = 1400
x = 1400 - y
Substitute into (2)
0.60x + 0.20y = 560
0.60(1400 - y) + 0.20y = 560
840 - 0.60y + 0.20y = 560
- 0.60y + 0.20y = 560 - 840
-0.40y = -280
y = -280/-0.40
y = 700 pounds
Recall,
x + y = 1400
x + 700 = 1400
x = 1400 - 700
x = 700 pounds
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The table shows your height on a water slide at various time intervals
1. Find the average rate of change in a riders height between 1 and 3 seconds
2. Find the average rate of change in a riders height between 0 and 5 seconds
3. What is another word for rate of change in this situation?
Time(s) Height (ft)
0 120
1 90
2 60
3 30
4 0
5 0
1. The average rate of change in a riders height between 1 and 3 seconds -30 ft/s
2. The average rate of change in a riders height between 0 and 5 seconds -24 ft/s
3. Another word for rate of change in this situation is speed
What is speed?Speed is defined as the rate of change of the distance travelled with time. Mathematically, it can be expressed as:
Speed = distance / time
With the above idea, we can obtain the answers to the question given above.
1. How to determine the rate of change between 1 and 3 secondsChange in height = 30 - 90 = -60 ftChange in time = 3 - 1 = 2 sRate of change =?Rate = Change in height / change in time
Rate = -60 / 2
Rate = -30 ft/s
2. How to determine the rate of change between 0 and 5 secondsChange in height = 0 - 120 = -120 ftChange in time = 5 - 0 = 5 sRate of change =?Rate = Change in height / change in time
Rate = -120 / 5
Rate = -24 ft/s
3. what is another word for rate of change?From the definition of speed given above, we can say that: another word for rate of change is speed
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Can someone help please?
Answer:
A
Step-by-step explanation:
From left to right of the graph, we can observe that the generally the points are going down. This means that the trend line drawn will have a negative slope.
In the slope-intercept form, which is the form the given equations are in, we have y= mx +c, where m is the slope and c is the y-intercept.
We are only interested in the slope in this case, since no actual values are given. Thus, let's focus on the coefficients of x to determine whether the slope is positive or negative.
Option A: Slope= -⅔ (negative)
Option B: Slope= 3 (positive)
Since we have a negative slope, option A would be the best answer.
The attached image shows 2 graphs. The graph in blue shows the shape of a graph with negative slope, while the graph in red has a positive slope.
Someone help me please
Answer:30 degress
3 angles in a triangle equal 180-120=60 60÷2=30
Step-by-step explanation:
Given the series 2 two-thirds startfraction 4 over 9 endfraction startfraction 8 over 27 endfraction startfraction 16 over 81 endfraction startfraction 32 over 243 endfraction ellipsis, which partial sums are correct? check all that apply. s1 = 2 s2 = 4 s subscript 3 = startfraction 28 over 9 endfraction s subscript 4 = startfraction 10 over 9 endfraction s subscript 6 = startfraction 292 over 81 endfraction
The partial sums are correct are That is: (2) and (28/9).
What is a partial sum?A partial sum (simply put) refers to the sum of the various parts that make up a sequence. One of a series of sums of elements of a given sequence, the first sum being the first element, the second sum being the first element added to the second element, the third sum being equal to the sum of the first three elements, and so on.A partial sum of an infinite series is the sum of a finite number of consecutive terms beginning with the first term. When working with infinite series, it is often helpful to examine the behavior of the partial sums.A partial sum would be:
2 + (2/3).
In this case, thus,
Series 1 = 2 - This is correct.
Series 2 = 2 + (2/3) = 8/3 - incorrect
Series 3 = (8/3) + (4/9) = (28/9) Correct
Series 4 = (28/9) + (8/27) = (92/27)
Series 5 = (92/27) + (16/81) = 292/81
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A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 6, 9, 12. Column 2 is labeled y with entries 3, 9, 18, 27, 36.
Given that y varies directly with x in the table, find the value of y if the value of x is 5.
Given that y varies directly with x in the above table, if the value of x is 5, the value of y is 15.
How to calculate direct variation?According to this question, a 2-column table with 5 rows is given.
Column 1 is labeled x with entries 1, 3, 6, 9, 12 Column 2 is labeled y with entries 3, 9, 18, 27, 36If y varies directly with x, the mathematical representation is as follows:
y = kx
Since y = 3, when x = 1
3 = k × 1
k = 3
The relationship between x and y is as follows: y = 3x
Therefore, if the value of x is 5, the value of y = 3 × 5 = 15.
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Please help thank you
no links
1) in 1992, the average was credit card debt for an
american family was $3275. in 2006, the
average credit card debt for a family was $8900.
find the average rate of change of credit card
debt with respect to time.
a) 390.80
yr
b) 401.79
yr
c) 412.68
yr
d) 423.575
yr
e) 434.46
yr
The average rate of change of credit card is $ 401.79 /year.
What is Average Rate?A single rate that is a weighted average of the different rates that are applicable to property in various locations.An average is a single number calculated as the average of a set of numbers, typically calculated as the sum of the numbers divided by the total number of numbers in the set (the arithmetic mean).Solution
The difference of credit card debt between the year 2006 and 1992 = 8900 - 3275 = $5625
The difference of years between the year 2006 and 1992 = 2006 - 1992 = 14
average rate of change of credit card debt with respect to time = [tex]\frac{difference of credit card debt}{difference of years}[/tex]
average rate = [tex]\frac{5625}{14}[/tex] = $ 401.79 / year
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Ilean works as a welder and
web designer. As a welder, she earns $18 per hour. Last week she
worked x hours as a welder and her friend paid her $75 to design a web page. Write an
expression to represent the total amount llean earned last week.
The expression which can be used to represent the total amount llean earned last week is 75 + 18x
EquationAmount llean earns per hour welding = $18Number of hours worked as welder = xAmount earned as a web page designer = $75An expression to represent the total amount llean earned last week = Amount earned as a web page designer + (Amount llean earns per hour welding × Number of hours worked as welder)
= 75 + (18 × x)
= 75 + 18x
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What is the median of this data set?
22, 37, 49, 15, 12
Answer:
the answer is 22
Step-by-step explanation:
12,15,22,37,49
since 22 is in the middle its the median (make sure you put the #'s from least to greatest)
Answer:
22
Step-by-step explanation:
22, 37, 49, 15, 12
First put the data set from least to greatest.
12, 15, 22, 37, 49
The median is the middle number of the data. In this case, the median is 22.
Hope this helps!
What is piaget's term for cognitive development between the ages of about 2 and 6?
If the hypotenuse has a length 7√2, then both legs have a length
Of what
Answer:
7
Step-by-step explanation:
this is probably a 45-45-90 triangle if its both legs
if you buy a computer game for $54, you have a $5 mail-in rebate, and you pay 8% sales tax, how much does your game cost?
Answer:53.32
Step-by-step explanation:
$54 retail price
sales tax 8%
$54x8%= 4.32
sales tax is $4.32
$54+$4.32= $58.32
total with tax is $58.32
$58.32-$5= 53.32
Shawnice Smith
Agrade
Addition Word Problems
Directions: Solve the following addition word problems.
MATH
1. 100 students participated in a sports card show in the school gym. Brad brought his
entire collection of 2,000 cards to show his friends. He had 700 football cards and 400
basketball cards. If the rest of his cards were baseball cards, how many baseball cards
did he bring with him?
Writing equivalent ratios and ordered pairs Gallons 1 2 3 Quarts 4 8 12 which ordered pairs represents the equivalent ratios in the table? (1,2) (1,4) (2,8) (4,1) (3,12)
Step-by-step explanation:
gallons to quarts have the ratio 1:4.
there are 4 quarts in a gallon (hence the name of quarts by the way).
so, the question is really, which order pair have also a 1:4 ratio between x and y ?
(1, 4)
(2, 8)
(3, 12)
the (4, 1) would represent a 4:1 ratio.
and as you know, 4/1 is different to 1/4.
a ratio is nothing else than a fraction. just the "whole" is different.
the pure fraction 1/4 means that the whole is 4/4, has 4 times 1/4.
a ratio 1:4 (you can also write as 1/4) means that the whole has 5 (1+4) parts.
other than that they are compared and calculated with the same way as normal fractions.
Identify the solutions to the quadratic equation 6x^2+x-1=0
Answer:
1/3 and -1/2
Step-by-step explanation:
You can use the factoring method to identify the solutions of x
6x^2+x-1
2 numbers have to multiply to 6 and subtract to 1 because x is the same as 1x
So, you get 3x and 2x
since you know that -1x1 is -1 you will get
(3x-1)(2x+1)=0
Now, since (3x-1) and (2x+1) multiply to get 0, if either (3x-1) or (2x+1) is 0 the statement will be valid
3(1/3)-1=0
2(-1/2)+1=0
So, your answers are 1/3 and -1/2
Determine the coordinates of the point p on the line y=-x+6 such that p is equidistant from the points a(10,-10) and o(0,0) (that is, so that pa=po). express your answer as an ordered pair (a,b).
Solution,
Let P = ( x, -x + 6) = (x, 6 - x)
We want to solve this
( Distance from P to (0,0) )^2 = (Distance from P to (10, -10) )^2
x^2 + (6 - x)^2 = [ ( x - 10)^2 + ( 6 - x + 10)^2
x^2 + x^2 - 12x + 36 = x^2 - 20x + 100 + x^2 - 32x + 256 simplify
-12x + 36 = -52x + 356
40x = 320
x = 8
And y = -(8) + 6 = -2
So...P = ( 8, -2)
In mathematics, an equation is an equation that expresses two equations by joining them with an equal sign =. Equations in other languages and the word their relatives can have slightly different meanings; for example, in French, an equation is defined as containing one or more variables, but in English, it is an equal sign.
A well-formed expression consisting of two combined equations is an equation, and a variable makes the equation true. The variable for which the equation must be solved is also called the unknown, and the value of the unknown that satisfies the equation is called the solution of the equation. There are two types of equations: identities and constraint equations. The ID applies to all values of the variable. Constraint equations apply only to specific values of variables
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What quadrant does the terminal side of this angle lie in?
A) Quadrant III
B) Quadrant II
OC) Quadrant IV
OD) Quadrant I
Answer:
Quadrant III
Step-by-step explanation:
Top-right quadrant = QI
Top-left quadrant = QII
Bottom-left quadrant = QIII
Bottom-right quadrant = QIV
Triangle \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime is the image of \triangle ABC△ABCtriangle, A, B, C under a rotation about the origin, (0,0)(0,0)left parenthesis, 0, comma, 0, right parenthesis.
From the information given, the rotated triangle is same as the original triangle. This is because, vertices of the rotation remain at the origin - (0,0).
What is the proof the above?Notice that the question states: △A'B'C' is the image of △ABC. Given that the △ without primes is the original and the one with primes depict the rotated triangle,
under a rotation about the origin, (0,0) (0,0) (0, 0), indicating no movement,
△A'B'C' is in the same position with △ABC.
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Answer: D: 60 degrees
Step-by-step explanation:
khan
Draw the graph of the linear equation 2x – y + 1 = 0. From the graph find the values of h and k if the graph passes through the point (h,4) and (1/2 , k)
Answer + Step-by-step explanation:
2x – y + 1 = 0
We know that the graph of a linear equation is a line.
So ,in order to draw it we need to find two points A and B of the line
Afterward, we join A and B to get the graph.
2x – y + 1 = 0
If x = 0 → y = 1 ⇒ A(0 , 1) lie on the line AB (the graph)
If x = 1 → y = 3 ⇒ B(1 , 3) lie on the line AB
Now ,all we have to do is plotting A and B
on the coordinates plane ,then connecting then with a line.
According to the graph (check the attached image) :
If (h,4) ∈ line AB ⇒ h = 3/2
If (1/2 , k) ∈ line AB ⇒ k = 2