Plot the point the. Make a staircase using the given slope connect the points to form a line. Answer the questions below
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In order to create a staircase with the points, let's find 2 more points of the line.
The slope of -5 indicates that each unitary increase in x causes a decrease of 5 units in y.
So starting from (2, -3), we can add one unit to x and subtract one unit from x:
[tex]\begin{gathered} (2,-3) \\ (2+1,-3-5)=(3,-8) \\ (2-1,-3+5)=(1,2) \end{gathered}[/tex]Graphing these points and the corresponding line, we have:
a)
The line is decreasing (because of the negative slope)
b)
The y-intercept is the point where x = 0. Using the point (1,2) and subtracting one unit to x (therefore adding 5 units to y), we have:
[tex]\begin{gathered} (1,2) \\ (1-1,2+5)=(0,7) \end{gathered}[/tex]So the y-intercept is (0, 7)
c) Using the slope m = -5 and the y-intercept b = 7, the equation is:
[tex]y=-5x+7[/tex]d)
y2 = -5x + 7
e)
Our line is steeper than y = x, since the absolute value of the slope is greater than the slope of y = x (which is 1)
f)
Our line is higher than y = x in the y-axis, because the y-intercept is 7, and the y-intercept of y = x is 0.
g)
We can see the negative value of the slope (-5), indicating that if we increase the value of x, the value of y decreases.
Related Questions
Please see attached picture below to help me pleaseplot 1 1/2 and 2 1/4 on the number line
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The given mixed numbers are:
[tex]1\frac{1}{2},2\frac{1}{4}[/tex]The first thing we need to do is convert it into improper fractions, as follows:
[tex]\begin{gathered} 1\frac{1}{2}=\frac{1\times2}{2}+\frac{1}{2} \\ 1\frac{1}{2}=\frac{2}{2}+\frac{1}{2} \\ 1\frac{1}{2}=\frac{3}{2} \end{gathered}[/tex]Now, continue with 2 1/4:
[tex]\begin{gathered} 2\frac{1}{4}=\frac{2\times4}{4}+\frac{1}{4} \\ 2\frac{1}{4}=\frac{8}{4}+\frac{1}{4} \\ 2\frac{1}{4}=\frac{9}{4} \end{gathered}[/tex]In order to plot them on the number line, for the first fraction 3/2, we need to divide the unity into 2 equal parts, and then count 3 of these divisions, that would be 1 1/2 or 3/2, is the same:
Now for the 2 1/4 or 9/4 (they are the same), we need to divide the unity into 4 equal parts and then count 9 of these divisions, then:
If x = 14 , what value of Y is a solution to this equation ? A. -7 B. -8 C. -10 D. -30
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Given
Graph
Procedure
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
Point 1. (-2,0)
Point 2. (2,-2)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-0}{2--2} \\ m=-\frac{2}{4} \\ m=-\frac{1}{2} \end{gathered}[/tex]y=mx+b
replacing (x,y) with point 1
[tex]\begin{gathered} y=mx+b \\ 0=-\frac{1}{2}(-2)+b \\ 0=1+b_{} \\ b=-1 \end{gathered}[/tex]we obtain the equation:
[tex]y=-\frac{1}{2}x-1[/tex]If x = 14 , what value of Y is a solution to this equation?
[tex]\begin{gathered} y=-\frac{1}{2}(14)-1 \\ y=-7-1 \\ y=-8 \end{gathered}[/tex]The answer is y=-8
16.The least common denominator of 1/2, 1/8, and 1/10 isO A. 10.OB. 80.C. 40.D. 16.nMark for review Awill be biabliabted on the review page)
Answers
Given
The numbers, 1/2, 1/8, and 1/10.
To find: The least common denominator.
Explanation:
It is given that,
1/2, 1/8, and 1/10 .
Then,
Therefore, the LCM is,
[tex]\begin{gathered} LCM=2\times2\times2\times5 \\ =40 \end{gathered}[/tex]Hence, the least common denominator is 40.
Need help finding 2 more points on the line for question # 12(3,8) and (-4,8)Slope:8-8/-4-3 = 0/-7
Answers
ANSWER
The slope between the two points is 0
EXPLANATION
Given that;
(3, 8) and (-4, 8)
Slope is defined as the gradient of a line
The formula for determining slope is given below as
[tex]\text{ Slope = }\frac{\text{ rise}}{\text{ run}}[/tex]Where
rise = y2 - y1
run = x2 - x1
So, we have
[tex]\text{ Slope = }\frac{\text{ y}_2\text{ - y}_1}{\text{ x}_2\text{ - x}_1}[/tex]In the given point, let x1 = 3, y1 = 8, x2 = -4 and y2 = 8
[tex]\begin{gathered} \text{ slope = }\frac{\text{ 8 - 8}}{\text{ -4 - 3}} \\ \\ \text{ slope = }\frac{\text{ 0}}{\text{ -7 }} \\ \text{ slope = 0} \end{gathered}[/tex]Therefore, the slope between the two points is 0
A witch brewed a magical invisibility potion. There is a proportional relationship between the amount of potion the witch drinks (in milliliters), x, and the amount of time she is invisible (in minutes. After drinking 1 milliliter of potion, the witch was invisible for 5 minutes. Write the equatio for the relationship between x and y. y
Answers
x represents the amount of portion in millimeters
y represents the time she was invisible
Write out an equation to show the variation relationship
Since the variation is direct
Then
[tex]\begin{gathered} x\propto y \\ x=k\times y \end{gathered}[/tex]To get the value of k
when x= 1 mm, y = 5 minutes
[tex]\begin{gathered} k\text{ = }\frac{x}{y} \\ =\frac{1}{5}\text{ mm/min} \end{gathered}[/tex]The relationship between x and y will be
[tex]\begin{gathered} \text{substitute k in x=}ky \\ x=\frac{1}{5}\times y \\ x=\frac{y}{5}\text{ (this is the relationship)} \end{gathered}[/tex]Label the median on the trapezoid.Then fill in the in the list
Answers
Given:
The trapezoid ABCD is given.
To find:
Label the median and fill in the blanks.
Explanation:
Let us label the median first.
Here, a line EF is a median.
It connects the midpoint of the legs. (It bisects each leg).
It is always parallel to both BC, and AD.
It is the average of the two parallel legs.
Which of the following functions has a vertical asymptote at x=3, a horizontal asymptote at f(x)=2, and a root at x=5?
Answers
To have a vertical asymptote, is the value in which the denominator is zero, therefore if vertical asymptote x=3, then the denominator must be x-3.
Then we find the root, which is the x-intercepts, let's find them:
[tex]\begin{gathered} \frac{-4}{x-3}+2=0 \\ \text{ }\frac{-4}{x\text{ - 3}}=\text{ - 2} \\ \text{ -4 = - 2\lparen x - 3\rparen} \\ \text{ }\frac{-4}{\text{ -2}}=\text{ x - 3 } \\ \\ 2=x\text{ - 3} \\ x=5 \end{gathered}[/tex]So, the function D has the requirements
The function f(x)=x - 3x2 + 2x rises as x grows very large. O A. True O B. False
Answers
Let's find the limit:
[tex]\lim _{x\to\infty}f(x)=\lim _{x\to\infty}(x^3-3x^2+2x)=\lim _{x\to\infty}x^3=\infty^3=\infty[/tex]Therefore, we can conclude that the function rises as x grows very large.
Answer:
True
Find the greatest common factor of thefollowing monomials:6m3n2 m5 n52mn3
Answers
So we have the following set of terms:
[tex]6m^3n,2m^5n^5,2mn^3[/tex]The greatest common factor (from now on, GCF) is a term that meets the following:
- All the three terms are multiples of it.
- It's the greatest number with the greatest power of each variable that meets the condition above.
One way to find it is looking for the GCFs of the integers, the powers of m and the powers of n separately. For example, the integers present in the set of three terms are 6, 2 and 2. If we factor each of them we get:
[tex]2\cdot3,2,2[/tex]The only number that appears in the 3 factored numbers is 2 so the GCF of the integers is 2.
Then we have to find the GCF among the powers of m. When you look for the GCF of a set of powers of the same variable the result is the power with the smallest exponent so if the powers we have are:
[tex]m^3,m^5,m[/tex]Then the GCF is m because its exponent is 1 whereas the other two exponents 3 and 5 are greater.
If we do the same for the powers of n we have:
[tex]n,n^5,n^3[/tex]Again, the GCF is the power of n with the lowest exponent, in this case n.
Now that we have found the GCFs of the integers, the powers of m and the powers of n we can find the GCF of all the terms. This is given by the product of those 3. Then the answer is:
[tex]2mn[/tex]Translate the following into an inequality:What number divided by five, is less than 8?m ÷ 5 < 85 ÷ m ≤ 8m ÷ 5 > 85 ÷ m > 8
Answers
The phrase "number divided by five" can be expressed as
[tex]m\div5[/tex]"is less than 8" is expressed as
[tex]<8[/tex]Putting it together, the inequality is
[tex]m\div5<8[/tex]Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $600 interest. The same amount invested in the other fund earns $800. Find the lower rate of interest (in percent). %
Answers
Given:
The first fund earns $600 and the second fund earns $800.
Let x% be the lower rate of interest.
And x+4% be the higher rate of interest.
The difference between the amounts is,
[tex]800-600=200[/tex]It means,
[tex]\begin{gathered} 4\text{ percent of n =200} \\ \text{Where n is the amount invested. } \\ \frac{4}{100}\times n=200 \\ n=\frac{200\times100}{4} \\ n=5000 \\ It\text{ gives } \\ \text{x percent of }5000=600 \\ \frac{x}{100}\times5000=600 \\ x=\frac{600}{50} \\ x=12 \\ \text{Same way,} \\ \text{x percent of }5000=800 \\ \frac{x}{100}\times5000=800 \\ x=\frac{800}{50} \\ x=16 \end{gathered}[/tex]Alternative way,
For the first fund. let a be the lower rate and a+4 be the higher rate.
[tex]ax=600[/tex]For second fund,
[tex]\begin{gathered} x(a+4)=800 \\ ax+4x=800 \\ 600+4x=800 \\ 4x=800-600 \\ x=\frac{200}{4} \\ x=50 \end{gathered}[/tex]So,
[tex]\begin{gathered} ax=600 \\ 50a=600 \\ a=\frac{600}{50} \\ a=12 \\ \Rightarrow a+4=12+4=16 \end{gathered}[/tex]Answer: The lower rate of interest is 12%
Consider the functionfIWhich graph is the graph of function ??
Answers
Answer:
Explanation:
Given:
[tex]f(x)\text{ = }\frac{x^2-3x}{x-9}[/tex]To find:
the graph that represents the function f
To determine the graph, we need to check if the expression can be simplified:
[tex]\begin{gathered} x^2-\text{ 3x = x\lparen x - 3\rparen} \\ x^2\text{ - 9 is a differenc of two squares} \\ x^2\text{ - 9 = \lparen x - 3\rparen\lparen x + 3\rparen} \end{gathered}[/tex][tex]\begin{gathered} f(x)\text{ = }\frac{x(x\text{ - 3\rparen}}{(x\text{ - 3\rparen\lparen x + 3\rparen}} \\ \\ f(x)\text{ = }\frac{x}{x\text{ + 3}} \\ \\ After\text{ simplifying, we still have a rational function} \\ We\text{ need to get the vertical asymptote} \end{gathered}[/tex][tex]\begin{gathered} vertical\text{ asymptote is the value of x when the denominator is equated to zero:} \\ x\text{ + 3 = 0} \\ x\text{ = -3} \\ This\text{ means at x = -3, there is no domain and the graph will not pass through this point} \\ There\text{ will be a vertical dashed line at this point} \end{gathered}[/tex]We will check the options for the graph that satisfies the above:
Only option B has a vertical dased line at x = -3. Also the graph doesn't pass t
find X if on angle is 65 and the other is (3y+2)
Answers
The angle opposite to equal sides are equal. So two angle are equal to 65 degree each and one angle is (3y + 2).
Determine the value of varaible y, by using angle sum property of triangle.
[tex]\begin{gathered} 3y+2+65+65=180 \\ 3y=180-132 \\ =48 \\ y=\frac{48}{3} \\ =16 \end{gathered}[/tex]So value of y is 16.
solve the following equation for G. be sure to take into account whether a letter is capitalized or not .H-3q=qr
Answers
H - 3q = gr
make g the subject of the relation.
H - 3q = gr
divide through by r
[tex]\begin{gathered} H\text{ - 3q = gr} \\ \frac{H}{r}\text{ - }\frac{3q}{r}\text{ = g} \end{gathered}[/tex]Final answer
[tex]g\text{ = }\frac{H}{r}\text{ - }\frac{3q}{r}\text{ or g = }\frac{H\text{ - 3q}}{r}[/tex]identify the function as exponential growth or exponential decay. then identify the growth factor or decay factor. y=9(1/2)^r
Answers
We have the function:
[tex]y=9\cdot(\frac{1}{2})^r[/tex]The growth/decay factor is the number that is the base of the exponent. For this function, the value of this factor is 1/2.
As this value is smaller than 1, the factor is a decay factor.
Answer: the decay factor is 1/2.
Using the vertex point(-2.5, -6.25), write the equation of this function in vertex form.
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Form of the parabola:
Standard form:
y = ax² + bx + c
Vertex form:
y = a(x-h)² + k
The vertex is a point, V(h,k), on the parabola. Where:
h = -b/(2a) ; k = (4ac-b²)/4a
If the vertex point is :
V(h,k) = (-2.5, -6.25)
the equation of this function in vertex form is:
y = a(x - (-2.5))² + (-6.25)
y = a(x + 2.5)² - 6.25
Complete the statements to describe the outcomes of operations with the following numbers. Q and b are non-zero rational numbers. x and y are Irrational numbers. Select the word that best completes each statement. To select a word, click the menu and then click the desired word. To choose a different word, click the menu and click the new word. a + b is-Select an Answer- rational. Xy is Select an Answer- Irrational. a + x is-Select an Answer- rational. b.xis -Select an Answer- Irrational.
Answers
a + b is ALWAYS rational
a + x is SOMETIMES rational
x.y is SOMETIMES irrational
b.x is ALWAYS irrational
How to simplify 2a x a x 3a +b x4b
Answers
Answer
6a³ + 4b²
Step-by-step explanation
Given the expression:
[tex]2a\times a\times3a+b\times4b[/tex]Combining similar terms (terms with the same variable):
[tex]\begin{gathered} (2a\times a\times3a)+(b\times4b)= \\ =\lbrack(2\times3)(a\operatorname{\times}a\operatorname{\times}a)\rbrack+\lbrack4(b\operatorname{\times}b)\rbrack= \\ =6a^3+4b^2 \end{gathered}[/tex]Find the sum.(2x + 3y) + (4x + 9y)
Answers
Given the expression:
[tex](2x+3y)+(4x+9y)[/tex]To find the sum, we can group the similar terms and then do the addition:
[tex]\begin{gathered} (2x+3y)+(4x+9y)=2x+3y+4x+9y \\ =2x+4x+3y+9y=6x+12y \end{gathered}[/tex]therefore, the sum is 6x+12y
For the following relation, give the domain and range, and indicate whether it is a function.{(a, 9), (j, 6), (b, 5), (h, 2)}Domain: {Range:{Is it a function?✓ Select an answerNoYes
Answers
Domain = all the possible x values
Range = set of possible y values.
(x,y)
Domain = { a , j , b , h }
Range = { 9 , 6 , 5 , 2 }
Since each input value has one output value, it is a function.
quar OT rate in die table below Number of Pizzas 1 Number of Students 4. 8 12 16 2 3 4 Multiply the number of pizzas by 8 to find the number of students. Multiply the number of pizzas by 4 to find the number of students. Multiply the number of students by 4 to find the number of pizzas. Multiply the number of students by 8 to find the number of pizzas.
Answers
From the given table,
1 Pizza corresponds to 4 students
2 Pizza corresponds to 8 students
3 Pizza corresponds to 12 students
4 Pizza corresponds to 16 students
As you notice, for every pizza there are 4 students,
so the multiplier is 4.
2 pizza x 4 = 8 students
3 pizza x 4 = 12 students
4 pizza x 4 = 16 students
The answer is Option B. Multiply the number of pizza by 4 to find the number of students
I have no idea how to do this I need to get this paper done tonight
Answers
Given:
[tex]\sin\theta=0.47[/tex][tex]0<\theta<90[/tex]Find-:
The value of
[tex]\cos\theta[/tex]Explanation-:
Use trignomertic formula:
[tex]\sin^2\theta+\cos^2\theta=1[/tex]So the value is:
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=1 \\ \\ \cos^2\theta=1-\sin^2\theta \\ \\ \cos\theta=\sqrt{1-\sin^2\theta} \end{gathered}[/tex]Given value of sin is:
[tex]\begin{gathered} \sin\theta=0.47 \\ \\ \sin^2\theta=(0.47)^2 \\ \\ \sin^2\theta=0.2209 \end{gathered}[/tex]So, the value is:
[tex]\begin{gathered} \cos\theta=\sqrt{1-\sin^2\theta} \\ \\ \cos\theta=\sqrt{1-0.2209} \\ \\ \cos\theta=\sqrt{0.7791} \\ \\ \cos\theta=0.883 \end{gathered}[/tex]So, the value is 0.883
The graph of F(x), shown below has the same shape as the graph of G(x)=x^3 -2 but it is shifted to the left 2 units. What is its equation?
Answers
Given that
[tex]G(x)=x^3-x^2[/tex]If this function is then sifted 2 units to the left
Then the new function
[tex]F(x)=(x+2)^3-(x+2)^2[/tex]The graph is shown
THE ANSWER IS OPTION D
Hi there, I need help I'm struggling with my algebra 2 class. sine, cosine.
Answers
Given: A right-angled triangle with AB=30 units, BC=40 units, and AC=50 units.
Required: To find the trigonometric ratio cos(A).
Explanation: The trigonometric ratio cosine is defined as the ratio of the adjacent side to the triangle's hypotenuse.
[tex]cos(\theta)=\frac{adjacent\text{ }side}{hypotenuse}[/tex]Here, in triangle ABC, the adjacent side for angle BAC is AB, and AC is the triangle's hypotenuse.
Hence
[tex]\begin{gathered} cos(A)=\frac{AB}{AC} \\ =\frac{30}{50} \\ =\frac{3}{5} \end{gathered}[/tex]Final Answer:
[tex]cos(A)=\frac{3}{5}[/tex]Katherine is a personal chef. She charges $100 per three-person meal. Her monthly expenses are $3,075. How many three-person meals must she sell in order to make a profit of at least $1,950?
Answers
Given,
Katherine charges for three-person meal is $100.
The monthly expenses of katherine is $3075.
The amount of profit she want is $1950 atleast.
The total amount she have to earned in the month is,
[tex]\begin{gathered} \text{Total earning amount = amount for expenses+amount of profit} \\ =3075+1950 \\ =\text{ \$ 5025 } \end{gathered}[/tex]The number of three-person meals must she sell in order to make a profit of at least $1,950,
[tex]\text{Number of meals = }\frac{total\text{ earning amount}}{\cos t\text{ of one three person meal}}[/tex]Substituting the values then,
[tex]\begin{gathered} \text{Number of meals = }\frac{5025}{100} \\ =50.25 \\ \approx51 \end{gathered}[/tex]Hence, she must sell 51 three person meal to get atleast profit of $1950.
Which of the following statements are true about the graph of f(x) =1/4 cos(x+pi/3)-1 2 answers
Answers
The given function is written in the form of:
[tex]f(x)=a\cos (bx-c)+d[/tex]in which a = 1/4, b = 1, c = -π/3, and d = -1.
The amplitude of the function is A, hence, the amplitude is 1/4. Statement A is true.
In addition, the vertical shift of the function is D, hence, the vertical shift is 1 unit down since d is -1. Statement 2 is false.
In addition, the horizontal shift or phase shift of a cosine function is C. Therefore, the horizontal shift is -π/3 or π/3 to the left. Statement D is true.
In ADEF, the measure of ZF=90°, DE = 52 feet, and FD = 14 feet. Find the measure of D to the nearest degree.
Answers
EXPLANATION
In order to find the measure of
[tex]\cos x=\frac{adjacent\text{ cathetus}}{\text{Hypotenuse}}[/tex][tex]x=\cos ^{-1}(\frac{14}{52})[/tex][tex]x=74.38^o\approx74^o[/tex]The answer is 74 degrees.
use Euler circles to determine if the Argument is valid or invalid
Answers
Let's use Euler circles, to represent the argument.
As you can observe in the diagram above, the given argument is true because it's being proved that all P is R, basically because P is a subset of R.
(-3, 1) and (2, 1) Different quadrants, so add the absolute values.Horizontal distance from (-3, 1) to y-axis: | __ | = ___Horizontal distance from (2, 1) to y-axis: | __ | = ___Distance from (-3, 1) to (2, 1) is ___ + ___ = ___ .
Answers
Here, we want to make additions
Firstly, we want the horizontal distance from (-3,1) to y-axis
We take the x-coordinate into consideration;
[tex]\begin{gathered} =\text{ (-3-0) = }-3 \\ \text{can also be (0-(-3)) = }3 \end{gathered}[/tex]But since we are considering the absolute value, we only take the positive and it is equal to 1
Secondly, we want the horizontal distance from (2,1) to y-axis
This is same as above, considering the x-axis value, we hav
Lstly, we
Write the first 5 terms of the arithmetic sequence. *a =-23 + 17(n + 1)
Answers
Let's determine the first 5 term under the arithmetic sequence formula: