In this case we have the point (-2,4), since this represents the x and y coordinates of the solution of the system of equations, then:
x= -2
y= 4
Let's create the pair of equations:
1. ax+by=c
2. ex+fy=g
Randomly let's define the values of the coefficients a, b, e and f:
a= 1
b=2
e= -1
f= 4
With these values and the known coordinates of the solution, let's replace into the expressions of the system of equations and solve for c and g, like this:
find the average rate of change of f(x)=x^2 on the interval [1,5]
The function supplied has an average rate of change for the range (1, 5) of -6.
f(x) = 17 - x2 (assumed)
The average f(x) change rate for the time period has to be determined (1, 5)
The function f(x) spanning the range (a, b) changes at an average rate equal to
A and b are valued as 1 and 5, respectively, in this instance.
f(1) = 17 - (1)2
f(1) = 17 - 1
f(1) = 16
f(5) = 17 - (5)2
f(5) = 17 - 25
f(5) = -8
It was determined that f's average rate of change (x)
As a result, the function supplied has an average rate of change for the range (1, 5) of -6.
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Find the rates of change in population for both parks between 2009 and 2014, and determine which park showed faster population growthduring those years.
The table and graph given show the information about two national parks.
It is required to find the rate of change of the population of the two parks between 2009 and 2014, and then determine the park that shows faster population growth during those years.
Notice that the variable x represents the number of years after 2005.
Hence, the years 2009 and 2014 represent, x=4 and x=9, respectively.
The formula for the rate of change of a function f(x) between x=a and x=b is given by the formula:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]Calculate the rate of change for park A:
Substitute a=4 and b=9 into the formula:
[tex]\frac{f(9)-f(4)}{9-4}[/tex]Substitute f(9)=2870 and f(4)=2370 from the table for park A into the expression for the rate of change:
[tex]\frac{2870-2370}{9-4}=\frac{500}{5}=100\text{ swallows per year}[/tex]Calculate the rate of change for park B:
[tex]\frac{f(9)-f(4)}{9-4}[/tex]Substitute f(9)=2800 and f(4)=2200 from the graph of park B:
[tex]\frac{2800-2200}{9-4}=\frac{600}{5}=120\text{ swallows per year}[/tex]Notice that the rate of change in population for park B is higher than that of park A.
Hence, park B showed faster population growth during those years.
Answers:
Rate of change for park A= 100 swallows per year.
Rate of change for park B= 120 swallows per year.
Park B showed faster population growth during those years.
If each quadrilateral below is a trapezoid, find the missing measures.
#5
Applying the definition of the adjacent angles of a trapezoid, the value of x in quadrilateral TUVS is: x = 4.
What are the Adjacent Angles of a Trapezoid?The adjacent angles of a trapezoid are the angles that are found on the same leg of the trapezoid, and they are said to be supplementary to each other because they have a sum of 180 degrees.
Given that quadrilateral TUVS is a trapezoid, where angles SVU and TSV are adjacent angles, therefore:
m∠SVU + m∠TSV = 180°
m∠SVU = 139°
m∠TSV = (14x - 15)°
Substitute
139 + (14x - 15) = 180
139 + 14x - 15 = 180
Combine like terms
124 + 14x = 180
14x = 180 - 124
14x = 56
14x/14 = 56/14
x = 4
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help pls for my freind!!!
Mary and two of her friends shared the cost of gas for a road trip if the total amount that they paid for gas was $546 and they shared it equally what amount did mary pay
Answer:
182
Step-by-step explanation:
It’s literally 546 divided by 3
1. A sum of money is to be shared among three friends Paul, Mark and Anna in the ratio 2: 3: 5 respectively. If Paul received $ 48,000. Determine
a. Anna’s Share
b. Mark’s share.
c. The total sum
a)Sum of money share by Anna is $120000
b)Sum of money share by Mark is $72000
c) The total sum the three friends have is $ 240000
The ratio of the amount of money shared among three friends is 2: 3: 5.
Let's take the common factor to be x.
Sum of money Paul has = 2x
Sum of money Mark has = 3x
Sum of money Anna has = 5x
It is given that Paul receive $48000
So,
2x = 48000
x = 24000
a) Anna's share = 5x
= 5× 24000
= $120000
b) Mark's share = 3x
= 3 × 24000
= $72000
c) The total share = 2x + 3x + 5x
= 10x
= 10 × 24000
= $240000
Therefore the sum of money share by Anna is $120000, Mark is $72000 and the total sum of money is $240000.
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Scale 15/25 by the factor of 0.2.
Answer:
0.12
Step-by-step explanation:
15/25 as a decimal is 0.6
0.6(0.2) Time 0.6 by the scale factor to get 0.12.
58 Find the missing angle measures: C 42 9 А. 10 B X х В. A 40 4 0 12 S 13 T 14 X 48 57 41 76 SIT 46
Let us first solve the triangle on the right side involving angle x.
Recall that the sum of angles in a triangle must be equal to 180°.
So we can write
[tex]\begin{gathered} 41+78+x=180 \\ 119+x=180 \\ x=180-119 \\ x=61\degree \end{gathered}[/tex]Therefore, the angle x is equal to 61°
Now let us solve the triangle involving angle S and T.
Again applying the property that the sum of angles in a triangle must be equal to 180°
[tex]\begin{gathered} 48+57+S=180 \\ 105+S=180 \\ S=180-105 \\ S=75\degree \end{gathered}[/tex]As you can see, the angle S and T form a straight line angle.
Recall that a straight line angle is equal to 180°
[tex]\begin{gathered} S+T=180 \\ 75+T=180 \\ T=180-75 \\ T=105\degree \end{gathered}[/tex]Therefore, angle S = 75° and angle T = 105°
Now let us solve the remaining figure.
On the right side of the figure, apply the property that the sum of angles in a triangle must be equal to 180°
[tex]\begin{gathered} A+42+40=180 \\ A+82=180 \\ A=180-82 \\ A=98\degree \end{gathered}[/tex]As you can see, the angles A and B are opposite angles.
We know that opposite angles are equal.
[tex]\angle A=\angle B=98\degree[/tex]Now we know the angle B so let us apply the property that the sum of angles in a triangle must be equal to 180°
[tex]\begin{gathered} B+48+C=180 \\ 98+48+C=180 \\ 146+C=180 \\ C=180-146 \\ C=34\degree \end{gathered}[/tex]Therefore, angle A = 98° and angle B = 98° and angle C = 34°
Please Help:What is the median of the data set?9, 3, 10, 12, 4, 5, 12, 2Enter your answer in the box. __
ANSWER
[tex]7[/tex]EXPLANATION
We want to find the median of the data set.
First, we have to arrange the data values in the data set from least to greatest:
[tex]2,3,4,5,9,10,12,12[/tex]Since the number of data values in the data set is even (8), to find the median, find half of the sum of the two middle terms in the ordered dataset i.e. 5 and 9.
That is:
[tex]\begin{gathered} \frac{5+9}{2}=\frac{14}{2} \\ \Rightarrow7 \end{gathered}[/tex]That is the median of the data set.
Help me please its homework and its the last question ;-; . Also hope you have had a good day ;}
The value of the angle x will be equal to 113.5°.
An angle may be defined as the figure which can be formed from two rays joining at a point. The lines will be called as the sides of the angle and the point at which the rays join is called vertex of the angle. There are generally 5 types of angles namely Acute angle, Obtuse angle, Reflex angle, Right angle and Complete angle. The value of a complete angle will be given as 360°. Since, in the question all the angles are measured to the nearest. So, the value of 59° could actually be something between 58.5° and 59.5°. Analogously, 108° is between 107.5° and 108.5°, and 81° is between 80.5° and 81.5°. Now, the summation of all four angles will be equal to 360°.
x + 58.5° + 107.5° + 80.5° = 360°
=> x = 360° - (58.5° + 107.5° + 80.5°)
=> x = 360° - 246.5°
=> x = 113.5° which is the required value.
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What is the value for y in the following expression
when x = 10
y=-2x + 8
Answer:
-12
Step-by-step explanation:
y=-2x + 8
when x = 10
substitute the value of x in the equation
y = -2(10) + 8
y = -20 + 8
y = -12
Working with Law of Sines. I have attached a picture.
..
SOLUTION
[tex]\begin{gathered} Sine\text{ rule is given as;} \\ \frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC} \end{gathered}[/tex][tex]Where\text{ the capital letters represent the angles and the small letters stand for the sides facing each angle.}[/tex]From our question;
[tex]\frac{13}{sin68}=\frac{x}{sin83}[/tex][tex]\begin{gathered} x=\frac{13sin83}{sin68} \\ x=13.9 \end{gathered}[/tex]x = 13.9
How much commission will jack make on the sale of a $160,700 house if he receives 4.7% of the selling price His commission will be …?
The commission of Jack on selling house is $7552.9.
Given that, Jack make on the sale of a $160,700 house if he receives 4.7% of the selling price.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let commission of Jack be x.
Now, x= 4.7% of 160,700
⇒ x = 0.047 × 160,700
⇒ x = 7552.9
Therefore, the commission of Jack on selling house is $7552.9.
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Can someone help please
The maximum displacement is 5, the angular frequency is 2π and the period of the motion is 1.
What are the features of an object under simple harmonic motion?
Kinematically speaking, an object under simple harmonic motion is described by the following equation:
y = A · cos (2π · t / T)
Where:
A - AmplitudeT - PeriodPlease notice that the angular frequency ω, radians per second, is equal to 2π / T. Then, we find that the maximum displacement is 5, the angular frequency is 2π and the period of the motion is 1.
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Analyzing Graphs of Functions
Which graph shows a function where f(2)= 4?
21
12
12y
12ty
8
8
8
8
4
4
4
х
4 8 12
-12-8 -4
4 8 12
-12-8-4
4 8 12
12-48-4
4 8 12
4
-12-84
8-44
-8
-12
8
-8
-12
-12 V
Intro
Done
From the graphs we can conclude:
[tex]undefined[/tex]HELP! Use the graph to determine the behavior of the function between the indicated points.
The behavior of the function is given as follows:
A and B - DecreasingB and C - ConstantC and D - IncreasingD and E - Decreasing.What is a function?A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
End behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. Said differently, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +∞) and the left end of the x-axis (as x approaches -∞).
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The curve of the function for the segments AB, BC, CD, and DE is decreasing, constantly increasing, and decreasing respectively.
Given that,
A graph has been shown the behavior of the graph is to be discussed.
When a function is graphed, the function must show something likewise increasing, decreasing, and contant relationship.
Here
As per the observation, the graph starts from A and seems to be decreasing up to B and further it is Constant up to C and then increases up to D, afterward it is decreasing up to E.
Thus, the curve of function for the segments AB, BC, CD, and DE is decreasing, constantly increasing, and decreasing respectively.
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Part B
? Question
The volume of the rectangular prism is the product of its length, width, and height.
What is the volume of the rectangular prism in simplest terms?
Type the correct answer in the box. Use numerals instead of words.
Answer:
Step-by-step explanation: i really
x2Step 2 of 2: Determine the degree and the leading coefficient of the polynomial.Degree:. Leading Coefficient
Given the following question:
(incomplete question)
To determine the degree of a polynomial we have to find the highest power IN the polynomial.
Example:
[tex]\begin{gathered} 4x^2+5^6-9 \\ \text{Degree of the polynomial is 6 } \end{gathered}[/tex]Since 6 is the highest power in the polynomial.
To find the leading coefficient of a polynomial is the first coefficient (number placed before a variable) in the polynomial.
Example one:
[tex]\begin{gathered} 4x^2+5^6-9 \\ \text{ Leading coefficient is 4} \end{gathered}[/tex]Since 4 is the first coefficient in the polynomial.
Example two:
[tex]\begin{gathered} x^2+3x-7 \\ \text{ Leading coefficient is 3} \end{gathered}[/tex]Since 3 is the first coefficient in the polynomial.
Jonah picked 287 cherry tomatoes from his garden in May and 339 in June.
How many cherry tomatoes did Jonah pick in all?
The estimate by rounding to the nearest hundred. Then solve.
Jonah picked total 626 cherry tomatoes if she licked 287 cherry tomatoes in May and 330 cherry tomatoes in June.
As the mentioned numbers are in hundreds and not in thousands, the number can not be rounded. Now we will need to perform addition to find the total number of cherry tomatoes picked by Jonah combined in May and June.
Total number of cherry tomatoes = 287 + 339
Performing addition to find the total number of cherry tomatoes picked by Jonah
Total number of cherry tomatoes = 626
Therefore, Jonah picked 626 cherry tomatoes combined in May and June.
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Find the 9th term of the geometric sequence whose common ratio is 1/3 and whose first term is 6.
Given: the geometric sequence whose common ratio is 1/3 and whose first term is 6.
Find: 9th term of the geometric sequence
Explanation:
[tex]\begin{gathered} a_n=a_1(r)^{n-1} \\ a_9=6(\frac{1}{3})^{9-1} \\ a_9=6(\frac{1}{3})^8 \end{gathered}[/tex]Final answer: the required answer is
[tex]\frac{6}{3^8}[/tex]please help with answer
Answer:
16a^2 - 4b = -8Step-by-step explanation:
16a^2 - 4b = ?
16(1/4)^2 - 4(6) = ?
4^2 - 4(6) = ?
16 - 4(6) = ?
16 - 24 = ?
-8 = ?Answer:
[tex]16(1 \div 4) {}^{2} - 4(6) [/tex]
Step-by-step explanation:
16
[tex]16( \frac{1}{16} ) - 24[/tex]
[tex]1 - 24[/tex][tex] - 23[/tex]what are the ratio and decimals for sin a ,cos a,tan a
1. Sin A
[tex]\begin{gathered} \sin A=\frac{15}{21} \\ \sin A=0.714 \end{gathered}[/tex]2. Cos A
[tex]\begin{gathered} \cos A=\frac{16}{21} \\ \cos A=0.761 \end{gathered}[/tex]3. Tan A
[tex]\begin{gathered} \tan A=\frac{15}{16} \\ \tan A=0.937 \end{gathered}[/tex]4. Sin B
[tex]\begin{gathered} \sin B=\frac{16}{21} \\ \sin B=0.761 \end{gathered}[/tex]5. Cos B
[tex]\begin{gathered} \cos B=\frac{15}{21} \\ \cos B=0.714 \end{gathered}[/tex]6. Tan B
[tex]\begin{gathered} \tan B=\frac{16}{15} \\ \tan B=1.066 \end{gathered}[/tex]determine if the table is linear, if so, write an equation for the linear table.
If the table is linear we can find an equation in the form
[tex]y=mx+b[/tex]in which b is the y-intercept and
АD✓32What points in Triangle 2 correspond to points A, B,and C in the original triangle?BSubin7:4610/5
Since the original triangle, which is triangle 1 has points A, B, and C.
The points in triangle 2 that corresponds to points A, B, and C are:
Points C, D, and A
Point C corresponds to point A
Point D corresponds to point B
POint A corresponds to point C
ANSWER:
Points C, D and A
45^2 ÷ 78 = ????????
To solve the problem find the value of (45)^2 at first
[tex](45)^2=2025[/tex][tex]\frac{2025}{78}=25\text{ R75}[/tex]The answer is 25 with the remainder 75
[tex]25\frac{75}{78}[/tex]You can simplify the fraction to be 25/26
[tex]25\frac{25}{26}[/tex]
The wholesale price for a bookcase is $144. A certain furniture store marks up the wholesale price by 23%. Find the price of the bookcase in the furniture store.
Round your answer to the nearest cent, as necessary.
Answer:
177.12
Step-by-step explanation:
multiply 144 by 0.23 = 33.12
add 33.12 to 144
awnser is 177.12
What type of angle is this? A. Straight angleB. Supplementary C. Complementary
Recall that when two angles add to give 90 degrees, they are called "complementary angles" This is the case here where you are adding an unknown angle to one that measures 51 degrees to obtain a right angle (90 degrees)
The unknown angle (?) is called the "complementary angle to the 51 degree one.
Please select the third option :
C. Complementary.
Do you remember how it looks an angle that measures 90 degrees? It looks like the angle formed by a square edge, or by two lines that are perpendicular to each other.
When you have two angles one in contact (adjacent) to the other and the two together complete a right angle , those two angles are called complementary angles. There is nothing profound to derive from that, but that it is simply a definition.
The height of a Ferris wheel in feet can be represented by the function y = 50 cos ((-10)) + 52, with time in seconds. What is the maximum height, and at what interval does the height repeat on the interval 0 <x< 50?
6. If UV bisects XY at point W, which statements must be true?A. UW= WVB. WX = YWC. UV-UW= VWD. W is the midpoint of XYE. U, X, and Yare collinearHC
Answer:
B, C and D.
Explanation:
If UV bisects XY at point W, we have the diagram below:
As can be seen, the point W divides XY into two equal parts: XW and YW.
Therefore:
(B) WX=YW.
Also:
UV = UW+WV
(C)UV-UW=WV
Finally, since W bisects XY, W is the midpoint of XY.
The correct options are B, C, and D.
List the common factors of 4, 36, 58, and 1000.