The ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.
How to identify ordered pairs?A set of ordered pairs that defines a function will be the one that has exactly one y-value that assigned to every x-value. This means that none of its x-values can have two corresponding y-values.
All the sets of ordered pairs don't have exactly one y-value that corresponds to each of its x-value except {(0,0),(1,10),(10,4),(-1,-7)}.
Thus, we can say that the ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.
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If c = 16, solve for b
Answer:
Step-by-step explanation:
given
cos(30°) = [tex]\frac{adjacent}{hypotenuse} \\[/tex]
cos(30°) = [tex]\frac{b}{c} \\[/tex]
cos(30°)=[tex]\frac{b}{16}[/tex]
b = 16cos(30°)
b [tex]16(\frac{\sqrt{3} }{2})\\ = 8\sqrt{3}[/tex]
If f(x) = −3x 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true. x =
The value of x for the equation to the true is 2/3
Solution to equationGiven the following functions
f f(x) = −3x + 4 and;
g(x) = 2
If the functions are equal, then;
-3x + 4 = 2
Subtract 4 from both sides
-3x = 2 - 4
-3x = -2
x = 2/3
Hence the value of x for the equation to the true is 2/3
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HELP !!!
A taxi driver uses this formula to work out the price of a journey, in pounds. price of journey = 3 + 2 x distance in miles. Leah has £5, the journey to her home is 2.5 miles. She asks the taxi driver to take her as near to home as possible. How far will she need to walk to arrive home?
The distance Leah would have to walk home is 1.5 miles
Calculating distanceFrom the question, we are to determine the distance Leah will have to walk home
From the given information,
Price of journey in pounds = 3 + 2 × distance in miles
Let the distance be d
Then,
Price of journey in pounds = 3 + 2d
Since Leah has £5, we can write that
5 = 3 + 2d
5 - 3 = 2d
2 = 2d
∴ d = 2/2
d = 1 mile
This means her money can only cover 1 mile
But the journey to her home is 2.5 miles
Therefore, she will have to walk
2.5 mile - 1 mile = 1.5 miles
Hence, the distance Leah would have to walk home is 1.5 miles
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is this correct ?-?
I need to get this done lol
Answer:
6
Explanation:
[tex]\textsf {The range of a data representation refers to difference of the smallest and }\\\textsf {greatest possible values. }[/tex]
[tex]\textsf {Here :}[/tex]
[tex]\textsf {smallest value = 5}\\\textsf {greatest value = 11}[/tex]
[tex]\textsf {Then the range will be :}\\\implies \textsf {greatest value - smallest value}\\\implies \mathsf {11 - 5}\\\implies \mathsf {6}[/tex]
simplify 26a7 + (-25a7)
Answer:
1a7
Step-by-step explanation:
26+-25=1
2. The wind blows the pinwheel below clockwise 180 degrees. What positions would the ribbon labeled A end up in after the wind blows it?
Answer: In between the red and yellow ribbons
Step-by-step explanation:
When something is rotated 180 degrees, you basically just mirror it. Since this pinwheel has an uneven amount of ribbons, there isn't a ribbon opposite of it, so it would be between red and yellow.
4(p+q) /p-q x q+p/8(p+q)
Answer:
[tex]\frac{q+p}{2(p-q)}[/tex]
Step-by-step explanation:
[tex]\frac{4(p+q)}{p-q} *\frac{q+p}{8(p+q)}[/tex]
We will cancel out like terms.
[tex]\frac{4}{p-q} *\frac{q+p}{8}\\=\frac{4(q+p)}{8(p-q)} \\=\frac{q+p}{2(p-q)}[/tex]
1
2
4
10
01:28:2
solve x2 + 12x = -11 by completing the square. which is the solution set of the equation?
be
o {-11, -1}
o {-11, 1}
{11, -1}
o {11, 1}
Answer:
11
Step-by-step explanation:
The figure shows the letter M and four of its transformed images—A, B, C, and D:
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of the letter M is shown on ordered pair 1, 2 and 1, 4 and 2, 3 and 3, 12, and 3, 4. Another image of letter M is shown on ordered pair 4, negative 4 and 4, negative 2 and 5, negative 3 and 6, negative 2 and 6, negative 4. This M is labeled as B. Another image of letter M labeled C is shown on negative 4, negative 4 and negative 4, negative 2 and negative 3, negative 3 and negative 2, negative 2 and negative 2, negative 4. An image of the letter W labeled A is shown on 1, negative 2 and 1, negative 4 and 2, negative 3 and 3, negative 2 and 3, negative 4. Another image of the letter W labeled D is shown on negative 2, 4 and negative 2, 2 and negative 3, 3 and negative 4, 2 and negative 4, 4. The letters A, B, C, D are written towards the bottom left of the respective W and M.
Which of the four images was formed by a reflection of the letter M?
A
B
C
D
The image was formed by a reflection of the letter M would be image A in the second quadrant b the reflection on X-axis. The correct option is A.
Explanation of how reflection across axis works?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in the opposite side of the axis as if we're seeing it in a mirror.
If you study it more, you will find that it's symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
Thus, if you're reflecting a point (x,y) along the x-axis, then its x abscissa will stay the same but y coordinates will negate.
Thus (x,y) turns to (x, -y)
Similarly, if you're reflecting a point (x,y) along the y -axis, the resultant image of the point will be (-x,y).
The image was formed by a reflection of the letter M would be image A in the second quadrant b the reflection on X-axis. The correct option is A.
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The reflection of letter M is (A)
What is reflection?A figure is said to be a reflection of the other figure, then every point in a figure is at equidistant from each corresponding point in another figure.
According to the graph the reflection of Of letter M is with same coordinates but with x as positive and y as negative.
Hence the reflection is (A).
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Identify two angles that are marked
congruent to each other on the diagram
below. (Diagram is not to scale.)
Answer:
Angles G and H are congruent.
Step-by-step explanation:
Josie needs to rent a car from SureRide Car Rentals. The cost of renting a car iS a
one-time fee of $80 plus $0.75 per mile. Write and graph an equation to represent
pay tO rent a car a from SureRide.
the cost which Josie must
Answer: y = 0.75x + 80
Step-by-step explanation:
let x = 1 mile
y = 0.75x + 80
A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 1000 bacteria in the initial polulation and the number doubled after the first 30 minutes, how many bacteria will be present after 4 hours
Answer:
256,000
Step-by-step explanation:
If the culture doubles in size every 30 minutes, it doubles 2 times per hour. In 4 hours it will have doubled 2×4 = 8 times. Each doubling multiplies the number by 2, so 8 doublings will multiply the number by 2^8.
The population will be ...
1000×2^8 = 256,000 . . . bacteria present after 4 hours
Horizontal lines n and m are intersected by lines q and p. At the intersection of lines q and n, the uppercase right angle is angle 4. At the intersection of lines q and m, the uppercase left angle is angle 1. At the intersection of lines p and n, the bottom left angle is angle 3. At the intersection of lines p and m, the uppercase left angle is angle 2.
If angle 1 is 110°, what would the other angle measures have to be in order for m || n and
q || p?
Angle 2 = °
Angle 3 = °
Angle 4 =
The values of the angles based on the information will be:
Angle 2 = 110°
Angle 3 = 70°
Angle 4 = 70°
How to calculate the angles?From the information given, angle 1 is 110° and the horizontal lines n and m are intersected by lines q and p.
In this case, it should be noted that vertcally opposite angles are equal. Hence, angle 2 is also 110°.
Angle 3 will be:
= 180° - 110° = 70° (angle on a straight line).
Angle 4 will also be 70° as a vertically opposite angle to angle 3.
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Answer:
The values of the angles based on the information will be:
Angle 2 = 110°
Angle 3 = 70°
Angle 4 = 70°
Step-by-step explanation:
Use the graphs below to answer the following questions: a. g(f(2) b. f(f(1)) c. f(g(2))
Answer:
19-73 19-73 and a very nice little
Step-by-step explanation:
19-73 19-73 and he changed
fill in the blank
83 x 391 - 83 x ____ = 83 x (391 - 15)
Answer:
83 x 391 - 83 x 15 = 83 x (391 - 15)
Step-by-step explanation:
BODMAS is stands for Bracket Of Division Multiplication Addition and Subtraction.
left hand side:
83 × 391 - 83 × ____ = 32453 - 83 × ____
right hand side:
83 × (391 - 15) = 83 × 376 = 31208
equating both sides
32453 - 83 × ____ = 31208
32453 - 31208 = 83 × ____
1245 ÷ 83 = 15
hence the answer is 15.
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Bronze is a mixture of copper and tin.
The copper and tin are in the ratio 9:1.
a) How much tin is there in a bronze bracelet
weighing 260 grams?
6
Answer:
26 gm
Step-by-step explanation:
Tin is 1 out of (9+1) = 1/10 th
1/10th * 260 gm = 26 gm
please help, performance task: trigonometric identities
The solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)
How to solve the trigonometric equations?Equation 1: 1 - cos(x) = 2 - 2sin²(x) from (-π, π)
The equation can be split as follows:
y = 1 - cos(x)
y = 2 - 2sin²(x)
Next, we plot the graph of the above equations (see graph 1)
Under the domain interval (-π, π), the curves of the equations intersect at:
(-π/3, 0.5) and (π/3, 0.5)
Hence, the solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)
Equation 2: 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π)
The equation can be split as follows:
y = 4cos⁴(x) - 5cos²(x) + 1
y = o
Next, we plot the graph of the above equations (see graph 2)
Under the domain interval [0, 2π), the curves of the equations intersect at:
(π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)
Hence, the solutions to 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π) are (π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)
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A local candy shop sells boxes of chocolate for $3.45 each. If a customer purchases five or more boxes, the cost is only $3 per box, plus the customer has an additional $1 fee per order. If C(x) represents the total cost and x represents the number of boxes, which of the following functions best models this scenario?
C of x equals 3.45 times x if x is less than 5 and 3.00x plus 1 if x is greater than or equal to 5.
C of x equals 3.45 times x if x is less than 5 and 3.00 plus x if x is greater than 5.
C of x equals 3.45 times x if x is less than or equal to 4 and 3.00x minus 1 if x is greater than 5.
C of x equals 3.45 times x if x is less than 4 and 3.00x minus 1 if x is greater than or equal to 5
The function that best models the scenario is as follows;
x < 5 : C(x) = 3.45x + 1
x ≥ 5 : C(x) = 3x + 1
How to find an equation?A local candy shop sells boxes of chocolate for $3.45 each.
This is when the consumer purchase less than 5 boxes of chocolates.
Therefore,
x = number of boxes
when x < 5
C(x) = 3.45x + 1
If a customer purchases five or more boxes, the cost is only $3 per box. Therefore,
when x ≥ 5
C(x) = 3x + 1
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write the faction in the simplest form 28/36
Answer:
7/9
Step-by-step explanation:
Divide the numerator and denominator by 4.
28/36 = 7/9
Answer:
7/9
Step-by-step explanation:
28 and 36 are both divisible by 4.
28÷4 is 7 and
36÷4 is 9
28/36 = 7/9
can someone please help me
Answer:
Domain: All real numbers
Range: y≤4
Question 3 of 10
Evaluate: (4/5) 1/2
O A. 2/25
O B. 2/5
O C.4:5
O D.4/25
Answer:
2/5
Step-by-step explanation:
Round 38.856 to the nearest tenth
Answer:38.9
Step-by-step explanation:
Which of the following is the solution to 3I x-1 I≥ 12?
A. x≤ -3 or x≥ 5
B. x≤ -3 and x≥ 5
C. x≥ 5
D. x≥ -3 or x≥ 5
The solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
For the given inequality the solution can be found as,
When the value of x is negative,3|x-1| ≥ 12
x-1 ≥ 4
x ≥ 5
When the value of x is positive,3|x-1| ≥ 12
- x + 1 ≥ 4
-x ≥ 3
x ≤ -3
Hence, the solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.
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Can I have the solution with steps
Answer:
1/6
Step-by-step explanation:
As usual in trigonometry, there are so many relationships between the trigonometric functions, there is bound to be more than one method to arrive at the answer.
Knowing values for the sine and cosine function for certain angles on the unit circle proves to be quite helpful. In general, I recommend 0°, 30°, 45°, 60°, and 90° at a minimum.
Recall the following 6 things:
[tex]\cos(30^o)=\frac{\sqrt{3}}{2}[/tex][tex]\cos(60^o)=\frac{1}{2}[/tex][tex]\sin(30^o)=\frac{1}{2}[/tex][tex]\sin(60^o)=\frac{\sqrt{3}}{2}[/tex][tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex][tex]\tan^2(\theta)=\tan(\theta)\tan(\theta)[/tex]Knowing these 6 things (4 things from the unit circle, a way to write the tangent function in terms of sine and cosine, and the definition of a squared trig function), we can simplify the given expression down to a single number:
The definition of the tangent squared function is that the output of the tangent function is squared...
[tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1-(\tan(30^o))^2}{1+(\tan(60^o))^2}[/tex]
Using fact 5, and turning the tangent function into sines and cosines...
[tex]=\dfrac{1-\left(\frac{\sin(30^o)}{\cos(30^o)}\right)^2}{1+\left(\frac{\sin(60^o)}{\cos(60^o)}\right)^2}[/tex]
Using facts 1-4, and substituting known values for sines and cosines...
[tex]=\dfrac{1-\left(\frac{(\frac{1}{2})}{(\frac{\sqrt{3}}{2})}\right)^2}{1+\left(\frac{(\frac{\sqrt{3}}{2})}{(\frac{1}{2})}\right)^2}[/tex]
Division is multiplication by the reciprocal...
[tex]=\dfrac{1-\left(\frac{1}{2}*\frac{2}{\sqrt{3}}\right)^2}{1+\left(\frac{\sqrt{3}}{2}*\frac{2}{1}\right)^2}[/tex]
Reducing/simplifying common factors of 2...
[tex]=\dfrac{1-\left(\frac{1}{\sqrt{3}}\right)^2}{1+(\sqrt{3})^2}[/tex]
Squaring a square root...
[tex]=\dfrac{1-\left(\frac{1}{3}\right)}{1+(3)}[/tex]
Finding a common denominator...
[tex]=\dfrac{\frac{3}{3}-\frac{1}{3}}{4}[/tex]
Definition of subtracting fractions...
[tex]=\dfrac{\frac{3-1}{3}}{4}[/tex]
Arithmetic...
[tex]=\dfrac{\frac{2}{3}}{4}[/tex]
Division is multiplication by a reciprocal...
[tex]=\dfrac{2}{3}*\dfrac{1}{4}[/tex]
Simplification and reducing the fraction...
[tex]=\dfrac{1}{6}[/tex]
So, [tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1}{6}[/tex]
A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
Answer:
The first statement is true so Shannon is incorrect.
Step-by-step explanation:
Volume of the pyramid with base 20 and h = 6
= 1/3 * base area * height
= 1/3 * 20 * 6
= 40 unit^3.
Please please help what is equivalent to this??
The correct option is Option A: [tex]16^{3x/4}[/tex] is equivalent to the expression [tex](\sqrt[4]{16})^{3x[/tex].
The rules of the exponent are
(a) [tex]a^m*a^n=a^{m+n[/tex]
(b)[tex]a^m/a^n=a^{m-n[/tex]
(c)[tex](a^b)^c=a^{bc}[/tex]
(d) [tex]\sqrt[n]{a}=a^{1/n[/tex]
here the given expression is [tex]16^{3x/4}[/tex]
we can rewrite the expression as
[tex]16^{3x/4}[/tex]
as we know by the rule of the exponent that [tex](a^b)^c=a^{bc}[/tex]
=[tex](16^{1/4})^{3x[/tex]
as we know by the rule of the exponent [tex]\sqrt[n]{a}=a^{1/n[/tex]
=[tex](\sqrt[4]{16})^{3x[/tex]
Therefore the correct option is Option A: [tex](\sqrt[4]{16})^{3x[/tex]
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two ships leave a port sailing 18km/h and 26 km/h. Their angle between their directions of travel from the port is 39 °. How far part are the skips to the nearest km after 2 hours
PLEASE HELP 20 POINTS
Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about point P.
A -105
B -75
C 75
D 105
Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about point P at; D: 105°
How to Interpret Rotation of objects?From the given image, If we connect points C of the blue quadrilateral to point C' of the rotated quadrilateral using the center of rotation P, then we will notice that ∠CPC' will be greater than 90°.
Now, the rotation is counterclockwise and it therefore means that the angle of rotation is will be positive and since ∠CPC' is greater than 90°, then we can say that the only correct option is Option D which is 105°
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For each expression below, select the letter that corresponds to the equivalent expression from the given list.
is equivalent to expression
is equivalent to expression
is equivalent to expression
Option 1 corresponds to Part B , Option 2 corresponds to Part D , Option 3 corresponds to Part A , Option 4 corresponds to Part C
The complete question is attached in the image
What is an Expression ?An expression corresponds to the mathematical statement that consists of variables , Constants and mathematical operators simultaneously.
Solving the given option will give us the answer.
(x²+15x+65)+(2x-5)*(3x+8)
(x²+15x+65)+(6x²+16x-15x-40)
(7x²+16x+25)
Option 1 corresponds to Part B
(4x+1)*(3x-4)-(5x²-10x-12)
(4x+1)*(3x-4)-(5x²-10x-12)
(12x²-16x+3x-4)-(5x²-10x-12)
(7x²-3x+8)
Option 2 corresponds to Part D
(8x²+19x+4)+(3x+2)*(x-5)
(8x²+19x+4)+(3x²-15x+2x-10)
(11x²+6x-6)
Option 3 corresponds to Part A
(6x+1)*(3x-7)-(7x²-34x-20)
(18x²-42x+3x-7)-(7x²-34x-20)
(11x²-5x+13)
Option 4 corresponds to Part C
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Convert 0.50 sen /g to RM/kg
the conversion is:
0.50 sen /g = 5 RM/kg
How to change the units?
First, we know that
1sen = 0.01RM
Then we can change:
0.50 sen /g = 0.50*(0.01 RM) /g = 0.005 RM/g
Now we use the relation:
1g = 0.001kg
So we can rewrite:
0.005 RM/g = 0.005 RM/(0.001kg) = 5 RM/kg
So the conversion is:
0.50 sen /g = 5 RM/kg
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