Learning Log9-11-20Provide a complete written response to the prompts. You must include any graphs or sketchesthat apply1. Explain how the points of intersection of graphs of functions can be determined (orverified) using the multiple representations of a system of equations. Provide examples anda sketch.I
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Previous concepts
We need to take in count that the intersection or the values of x that satisfy a system equations represent the solutions.
We have 3 possible cases when we have a system of equations:
1) One Solution
2) No solutions
3) Infinite solutions
Also we know that if we have one or more solutions then the system would be consistent otherwise would be inconsistent.
Solution
Let's analyze the situation with examples.
1) Case 1: One solution.
We have the following system of equations :
[tex]y=3x+2,y=-2x+1[/tex]We can graph both equations and we can see this:
And as we can see we have an intersection point (-0.2, 1.4) with just one solution for this case.
2) Case 2: No solutions
We have the following system of equations : y = 3x + 2, y = 3x + 1
Related Questions
What is the domain
of the function?
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The domain of the function is found as [-7, 6].
What is termed as the domain?A function is an mathematical object that accepts input, appears to apply a rule to it, and returns the result. A function can be thought of as a machine that requires in a number, performs some operation(s), and then outputs the result. The domain of a function is the collection of all its inputs. Its codomain is the set of possible outputs. The range refers to the outputs which are actually used.For the given question,
The graph of the function is given.
By the definition of the domain, the maximum and minimum values of the graph on x axis are 6 and -7 respectively.
Thus, the domain of the function is found as [-7, 6].
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I need help on 8 please it says find the value of x round each answer to the nearest tenth
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Step 1
Redraw the diagram and use the Pythagoras theorem to find the value of c\x.
Step 2:
Find the value of y from the right-angle triangle of sides: 10, 25 and y using the Pythagoras theorem
Opposite = y
Adjacent = 10
Hypotenuse = 25
[tex]\begin{gathered} \text{Pythagoras theorem} \\ \text{Opposite}^2+adjacent^2=hypotenuse^2 \\ y^2+10^2=25^2 \\ y^2\text{ + 100 = 625} \\ y^2\text{ = 625 - 100} \\ y^2\text{ = 525} \\ y\text{ = }\sqrt[]{525} \\ y\text{ = 5}\sqrt[]{21} \end{gathered}[/tex]Step 3
Next, use the Pythagoras theorem to find x from the triangle with sides
28, x and y
Hypotenuse = 28
Opposite = x
Adjacent = y
[tex]\begin{gathered} x^2+y^2=28^2 \\ x^2\text{ + (5}\sqrt[]{21})^2=28^2 \\ x^2\text{ + 525 = 784} \\ x^2\text{ = 784 - 525} \\ x^2\text{ = 259} \\ \text{ x = }\sqrt[]{259} \\ x\text{ = 16.1} \end{gathered}[/tex]Final answer
x = 16.1
solve for x: 2/3x-1=5
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The given equation is
[tex]\frac{2}{3}x-1=5[/tex]First, we have to sum 1 on each side
[tex]\begin{gathered} \frac{2}{3}x-1+1=5+1 \\ \frac{2}{3}x=6 \end{gathered}[/tex]Now, we multiply the equation by 3/2
[tex]\begin{gathered} \frac{2}{3}x\cdot\frac{3}{2}=6\cdot\frac{3}{2} \\ x=\frac{18}{2} \\ x=9 \end{gathered}[/tex]Therefore, the solution is 9.distribute and simply (x- 2)2+9
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Weare asked to used distributive property and reduce the expression:
(x - 2 ) 2 + 9
so we apply distributive property to eliminate the parenthesis, multiplying the factor of "2" by "x" and by "-2":
2 x - 4 + 9
now combine like terms:
2 x + 5
If the question involved instead the following expression:
(x - 2)^2 + 9 (where the "2" was in fact a power affecting the binomial (x-2), then
A man sold 4 times as many tie dyed T shirts as silk screened shirts. He sold 190 shirts altogether. how many tie dyed shirts did he sell?
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Answer: 152 tie dyed T shirts
Let the number of dyed T shirts be = x
Let the number of silk screened shirts be = y
He sold sold 4 times as many tie dyed T shirt as screened shirts
Since x = Tie dyed T shirt
Therefore, x = 4y
x = 4y ------------------- equation 1
He sold 190 shirts all together
x + y = 190 ------------ equation 2
Substitute the value of x = 4y into equation 2
4y + y = 190
5y = 190
Divide both sides by 5
5y/5 = 190/5
y = 38
Since x = 4y
x = 4(38)
x = 152 tie dyed T shirts
Therefore, 152 tie dyed T shirts was sold
According to the question, the man sold 4 times as many tie dyed T shirt as silk screened shirt
This implies that for 1 silk screen shirt sold, he would also sell 4 tie dyed T shirt
Since, x = tie dyed T shirt and y = silk screened shirts
Then, x= 4 x y
x = 4y
The man sold 190 shirts altogether
This implies that, he sold a total of 190 of both tie dyed T -shirt and silk screened shirts
Mathematically,
x + y = 190
Since x = 4y
Then, 4y + y = 190
This Implies that for 1
which fact below has the same difference as 18-6= ?8-1614-814-716-8
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18-6=12
8-16=-8 not equal 18-6
14-8=6 not equal 18-6
14-7=7 not equal 18-6
16-8=8 not equal 18-6
Hence none of the options has the same difference as 18-6
Find the direction angle of the vector u = -3i+8j. That is, find the angle between 0 and 360° that u makes with the positive x-axis (measured counterclockwise)Do not round any intermediate computations, and round your answer to the nearest whole number.
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we have the vector
u=-3i+8j
see the attached figure, to better understand the problem
we have that
tan(x)=8/3
x=tan^-1(8/3)
x=69.44 degrees
Find out the angle theta
theta=180-x
theta=180-69.44
theta=111 degreeswhat is the answer use the slope intercept form to graph the equation y=7/4x-1
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The equation y = 7/4x - 1 is in slope-intercept form, with a slope of 7/4 and a y-intercept of -1.
To graph it, you need to locate the point (0, -1) - the y-intercept -, and then use the slope to find another point. From (0, -1) you have to move 4 units to the right, and 7 units up, reaching the point (4, 6). Then, you have to draw the line that passes through theses points, as follows:
What is the range of the function f(x)=√x-8 + 6?Of(x) ≥-8O f(x) ≥-6Of(x) ≥ 6O f(x) ≥ 8
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Hello!
We have the function below:
[tex]f(x)=\sqrt{x-8}+6[/tex]Let's analyze the graph of it:
Note that for the domain, it starts when x = 8.
For the range, it starts when y = 6.
So, the range of this function is:
[tex]\begin{gathered} [6,+\infty) \\ \text{ or} \\ \boxed{f(x)\geqslant6} \end{gathered}[/tex]Third alternative.
Use the appropriate form of the percentage formula.What percent of 14.4 is 11.7? Round to the nearest hundredth of a percent.
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Hello there. To solve this question, we'll have to compare the values with two fractions:
To see how much of 14.4 is 11.7, in percentage, we start by considering 14.4 represents 100%, or 100, since we want to find the answer in percent as well.
Then we make:
[tex]\frac{11.7}{x}=\frac{14.4}{100}[/tex]Cross multiply the numbers:
[tex]11.7\cdot100=14.4\cdot x[/tex]Divide both sides of the equation by a factor 14.4
[tex]x=\frac{11.7\cdot100}{14.4}[/tex]Using a calculator, we get that x is equal to:
[tex]81.25[/tex]Therefore, 11.7 is 81.25% of 14.4!
Please help me on my assignment The select is options x and y
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SOLUTION
The domain of f is all the x-values, of the points on the graph, while the range is the corresponding y-values.
The domain of this function is all real numbers, hence the domain f is the interval
[tex](-\infty,\infty)[/tex]The range of f is from negative infinity to 7. Hence the range of f is interval
[tex](-\infty,7\rbrack[/tex]Which expression does not belong? 2^3 8 3^2 2^2*2^1
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in a class of students the following data table summarizes how many students pass a test and completed the homework due the day of the test what is the possibility that a student chosen randomly from the class failed the test
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From the table,
Total number of students that failed the test = 2 + 7 = 9
The total number of students that participated = 10 + 3 + 2 + 7 = 22
The possibility that a student chosen randomly from the class failed the test = Total number of students that failed the test divided by the total number of students that participated
= 9/22
Hence, the possibility that a student chosen randomly from the class failed the test is 9/22
numbe
Please help find the x
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Value of x is 28.
Define parallelogram.A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees. A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal. First, it is important to understand that a parallelogram's inner angles add up to 360 degrees (sum of internal angles = 180(n-2) where n is the number of sides in the image).
Given Data
89°, (5x -8)° , (3x+4)° , 51°
As we know, the sum of angles of parallelogram is 360°.
So,
89 + 5x-8 +3x + 4 + 51 = 360
5x + 3x = 360 - 136
8x = 224
x = 28
Value of x is 28.
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3. Lake City Jr. High Students:*** 12 out of every 18 ride a bus to school*** 9 out of every 15 live in Lake City*** 160 ride a bus to schoolHow many of the Jr. High students do not live in Lake City?
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Let
x ----> total number of students Lake City Jr. High Students
we have that
12 out of every 18 rides a bus to school
160 ride a bus to school
Applying proportion
18/12=x/160
solve for x
x=(18/12)*160
x=240 total students
so
9 out of every 15 live in Lake City
that means
6 out of every 15 does not live in Lake City
Applying proportion
y -----> students that not live in Lake City
6/15=y/240
solve for y
y=(6/15)*240
y=96
therefore
96 students do not live in Lake CityIt is an equation containg atleast one fraction whose numerator and deniminator are polynomials.A.rational functionB.rational equationC.ratuonal inequalityD.irrational equation
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In a equation, if we have polynomials in the numerator and denominator, this equation is considered a rational equation, similar to the case where fractions are considered rational numbers.
So the correct option is B.
true or false?17. The focci of an ellipse are located at 1/3 the length of the major axis from both sides of the center.
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To solve this problem and find if the statement is true, we can start by remembering the general equation for an ellipse:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]where a and b are the major axis and the minor axis for the ellipse, as shown in the following diagram:
The foci of an ellipse, are the focal points of the ellipse, for reference, we show them in the diagram:
The foci can be found using the following equation:
[tex]f=\sqrt[]{a^2-b^2}[/tex]To prove if the foci f is really 1/3 of the length of the major axis (in this case the major axis is a) we can give random values to a and b.
Values for a and b:
a=6
b=4
If the foci of the ellipse were located at 1/3 of the length of the major axis, we should find that the foci "f" is 1/3 of 6, thus, we should find that f=2, let's see if that is true by substituting a and b into the formula for f:
[tex]f=\sqrt[]{a^2-b^2}[/tex][tex]f=\sqrt[]{6^2-4^2^{}}[/tex][tex]\begin{gathered} f=\sqrt[]{36-16} \\ f=\sqrt[]{20} \end{gathered}[/tex]solving the square root we find the value of f:
[tex]f=4.47[/tex]Instead of 2 (which would have been 1/3 of the major axis), we find that f is 4.47, thus the statement "The foci of an ellipse are located at 1/3 the length of the major axis from both sides of the center." Is NOT TRUE.
Answer: False
Instructions: Select all of the methods that will find both real andimaginary solutions.Select one or more:Quadratic FormulaCompleting the SquareFactoringSquare RootsCheck
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Let's begin by identifying key information given to us:
Imaginary solutions
Find the side length of the square given the area
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The area of square is given 72 sq.ft.
ExplanationTo determine the side of square.
Use the formula for area of square.
[tex]A=side^2[/tex]Substitute the values.
[tex]\begin{gathered} 72=side^2 \\ side=\sqrt{72} \\ side=\sqrt{2\times2\times2\times3\times3} \\ side=6\sqrt{2} \end{gathered}[/tex]AnswerHence the side length of square is
[tex]6\sqrt{2}ft[/tex]A lock on a fence door has a 3 digit combination. Each digit can be any number between 1 – 8. The combinations 123, 456, and 789 are invalid. How many combinations are possible?
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There are a total of 8 possible numbers for each digit and there are 3 digits for the password. Since the problem didn't state that the numbers can't be repeated, then we can apply the following formula:
[tex]C_{n,m}\text{ = }\frac{n!}{m!(n\text{ - m)!}}[/tex]Where "n" is the range of possibilities for each number and "m" is the number of digits we want to arrange them. So applying the data from the problem gives us:
[tex]undefined[/tex]Nazir was given 5over7 of the fruit basket what fraction of the fruit basket was left over?
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The fraction of the fruit basket is 2/7.
What is fraction?
Fraction represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator.
Total fraction = 1 or can be written as 7/7
Nazir given 5/7 of the fruit basket
1-5/7 = 7-5/7
= 2/7
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so I have couple question I need help on I could send an image of the work I need help on
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Explanation:
1) (-3.4)^0
Note: anything raised to the power of zero is 1
Hence, (-3.4)^0 = 1
3)
Find the greatest common factor of the following monomials2b^4 32b^6 22b^5
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The answer is
[tex]2b^4[/tex]First let's see the divider of the coeficient:
2 is a prime
32 = 2^5 = 2*2*2*2*2
22 = 11*2
The GCD of all is 2
Now, we have b to the 4, 5 and 6. We can write it:
[tex]\begin{gathered} b^6=b^4\cdot b^2 \\ b^5=b^4\cdot b \end{gathered}[/tex]Now we have all to get the answer:
[tex]\begin{gathered} 32b^6=2^4b^2\cdot(2b^4) \\ 22b^5=11b\cdot(2b^4) \end{gathered}[/tex]And the remaining is 2b^4. As you can see, all the monomyals can be divided by 2b^4 and that's the greatest common factor
Given the equation 2(n + 7) - 5 = 29. What two steps are needed to simplify the left side of the equals? Choose the two that apply. *Add 5 to both sidesDistribute the 2Divide both sides by 2Combine like termsSubtract 7 from both sides
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In order to simplify the left side of the equation, the first two steps are:
1) Distribute the 2:
[tex]\begin{gathered} 2\mleft(n+7\mright)-5=29 \\ 2n+14-5=29 \end{gathered}[/tex]2) Combine like terms:
[tex]\begin{gathered} 2n+14-5=29 \\ 2n+9=29 \end{gathered}[/tex]So the correct options are Distribute the 2 and Combine like terms.
Question: solve ABC below using either the law of sines or law of cosines. Round to the nearest tenth.
Answers
SOLUTION:
First we calculate for a with cosines rule
[tex]\begin{gathered} a^2=b^2+c^2-2bcCosA \\ b=\text{ 29yd, c= 23yd, A= 99}\degree \\ a^2=(29)^2+(23)^2-2(29)(23)Cos(99) \\ a^2=841^{}+529^{}-1334\times(-0.1564) \\ a^2=841^{}+529^{}-1334\times(-0.1564) \\ a^2=841^{}+529^{}+208.68 \\ a^2=1578.686 \\ a=\text{ }\sqrt[]{1578.686} \\ a=\text{ 39.73} \end{gathered}[/tex]Then we calculate angle B with sine rule
[tex]\begin{gathered} \frac{a}{\sin A}=\text{ }\frac{b}{\sin B} \\ A=\text{ 99}\degree,\text{ a= 39.73 yd, b= 29 yd} \\ \frac{39.73}{\sin 99}=\text{ }\frac{29}{\sin B} \\ \text{Cross multiplying} \\ \sin \text{ B= }\frac{29\sin 99}{39.73} \\ \sin \text{ B= }\frac{29\times0.987}{39.73} \\ \sin \text{ B= 0.720} \\ B=\text{ }\sin ^{-1}(0.720) \\ B=\text{ 46.05}\degree \end{gathered}[/tex]Then we find the last angle C
[tex]\begin{gathered} A\text{ + B + C= 180}\degree \\ 99\text{ + 46.05}\degree\text{ + C= 180}\degree \\ C=\text{ 180}\degree-\text{ 99}\degree-\text{ 46.05}\degree \\ C=\text{ 34.95}\degree \end{gathered}[/tex]Final answers:
Side
a= 39.7 yd (nearest tenth)
Angles
B= 46.1 degrees (nearest tenth)
C= 35.0 degrees (nearest tenth)
witch of these ordered pairs is a solution to the inequality y - 2x < 3y - 2x < -3 (2,4)(-2,3)(3,4)(1,-1)
Answers
Explanation:
y - 2x < 3
To determine if the ordered [pair is a solution, we would insert the values into the inequality to confirm if the statement will be true.
a) (2,4) = (x, y)
4 - 2(2) < 3
4 - 4 <3
0 < 3
This is false
b) (-2, 3) = (x, y)
3 - 2(-2) < 3
3 + 4 <3
7 < 3
This is false
c) (3, 4) = (x, y)
4 - 2(3) < 3
4 - 6 < 3
-2 < 3
This is true
d) (1, -1) = (x, y)
-1 -2(1) < 3
-1 - 2 < 3
-3 < 3
the volume of the prism below is 264 in3. what is the height of the prism
Answers
The volume of any prism = base area x height
Given Volume = 264 in^3
The prism is triangular based
Therefore, its base area = 1/2 x base x height
The base of the triangle= 8in
Height of the triangle = 6in
[tex]\begin{gathered} \text{ Base area = }\frac{1}{2}\text{ x 8 x 6} \\ \text{Base area= 24in}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{ Recall, Volume = Base area x height} \\ H\text{eight = }\frac{\text{Volume}}{\text{Base area}} \\ \text{ Height=}\frac{264in^3}{24in^2} \\ \\ \text{Height}=11\text{ in} \end{gathered}[/tex]The height of the prism is 11 in.
Write down all the numbers that are between 30 and 60 and have a difference of 4 between their digits.
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Answer:
The whole numbers that are between 30 and 60 and have a difference of 4 are 31, 35, 39, 43, 47, 51, 55 and 59
Step-by-step explanation:
Hope this helps!!!
b=3 y-intercept br Find the slope and y-intercept of the line represented by each table. 3. 0 3 6 9 0 2 х 12 10 19 28 2 37 у у A 4 6 8 x 3 4 5 slope m = slope m= y-intercept br y-intercept
Answers
The slope can be obtained using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]and the y intercept is the value of y when x is equal to zero.
3. We can choose the points (3,10) and (6,19), then
[tex]m=\frac{19-10}{6-3}=\frac{9}{3}=3[/tex]From this, we can use the slope-point form of the line equation to obtain the y intercept
[tex]\begin{gathered} y-10=3(x-3) \\ y=3x-9+10 \\ y=3x+1 \end{gathered}[/tex]Then,
slope =3, y-intercept=1.
4. We choose the points (2,2), (4,3)
[tex]m=\frac{3-2}{4-2}=\frac{1}{2}[/tex][tex]\begin{gathered} y-2=\frac{1}{2}(x-2) \\ y=\frac{1}{2}x-1+2 \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]Then,
slope = 1/2, y-intercept =1
Kyra multiplied 0.27 by a power of ten and got 2.7. What power of ten did she multiply by? Responses
Answers
The power of ten that she multiplied by is 1.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Since Kyra multiplied 0.27 by a power of ten and got 2.7. This will be illustrated as:
= 0.27 × 10¹
= 2.7
Therefore, the power is 1.
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