Answers
First, we need to find the equations of the two dotted lines.
One of the lines is parallel to the x-axis and passes through the point (0, 2), then its equation is:
y = 2
The other line has a slope of 1 and intercepts the y-axis at the point (0,0). Using the slope-intercept form with m = 1 and b = 0, its equation is:
y = mx + b
y = 1*x + 0
y = x
Given that the shaded region is below both lines and the lines are not included in the solution, then we need to use a "<" sign in the inequalities. Finally, the system of inequalities is:
y < x
y < 2
Related Questions
Thomas wants to invite Madeline to a party. He has 80% chance of bumping into her at school. Otherwise, he'll call her on the phone. If he talks to her at school, he's 90% likely to ask her to the party. What is the probability of Thomas inviting Madeline to the party over the phone?
Answers
Recall that the probability must add 1, therefore:
[tex]0.6+x=1[/tex]Solving for x, we get:
[tex]\begin{gathered} x=1-0.6 \\ x=0.4 \end{gathered}[/tex]Therefore, the probability of Thomas inviting Madeline to the party over the phone is:
[tex]0.2\cdot0.4=0.08[/tex]or 8%.
Find an equation for the ellipse whose vertices are at (4,-3) and (4,7), and focus is at (4,4).
Answers
The vertices of the ellipse are given as
[tex]\begin{gathered} V_2=(4,-3) \\ V_1=(4,7) \end{gathered}[/tex]The focus of the ellipse is given as
[tex](4,4)[/tex]The equation of an ellipse is given as
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]Where the coordinate of the center is
[tex](h,k)[/tex]To calculate the coordinate of the center, we will use the formula below
[tex]\begin{gathered} \frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2} \\ =\frac{(4+4)}{2},\frac{(-3+7)}{2} \\ =\frac{8}{2},\frac{4}{2} \\ (4,2) \\ (h,k)=(4,2) \end{gathered}[/tex]The formula to calculate the value of a is given below
[tex]\begin{gathered} V_1=(h,k+a) \\ V_2=(h,k-a) \end{gathered}[/tex]By comparing coefficients, we will have
[tex]\begin{gathered} k+a=7\ldots\text{.}(1) \\ k-a=-3\ldots\text{.}(2) \end{gathered}[/tex]By adding equations (1) and (2) and solving simultaneously, we will have
[tex]\begin{gathered} 2k=4 \\ \text{divide both sides by 2,} \\ \frac{2k}{2}=\frac{4}{2} \\ k=2 \end{gathered}[/tex]By substituting hk=2 in equation 1, we will have
[tex]\begin{gathered} k+a=7 \\ 2+a=7 \\ a=7-2 \\ a=5 \end{gathered}[/tex]The coordinate of the focus,is calculated using the formula below
[tex](h,k+c)[/tex]By substituting the values, we will have
[tex]\begin{gathered} k+c=4 \\ 2+c=4 \\ c=4-2 \\ c=2 \end{gathered}[/tex]The value of will be calculated using the formula below
[tex]\begin{gathered} c^2=a^2-b^2 \\ b^2=a^2-c^2 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} b^2=a^2-c^2 \\ b^2=(5)^2-(2^2 \\ b^2=25-4 \\ b^2=21 \end{gathered}[/tex]By substituting the values of a,b,h and k in the equation of an ellipse, we will have
[tex]\begin{gathered} \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1 \\ \frac{(x-4)^2}{21^{}}+\frac{(y-2)^2}{25^{}}=1 \\ \end{gathered}[/tex]Hence,
The equation of the ellipse will be
[tex]\frac{(x-4)^2}{21^{}}+\frac{(y-2)^2}{25^{}}=1[/tex]Solve for the variable x in the equation x + 15 = 62. Question 20 options: A) 47 B) –47 C) 77 D) –77
Answers
Answer:
A) 47
Step-by-step explanation:
x + 15 = 62
x + 15 -15 = 62 -15
x = 47
Identify whether the problem is "Sum of Two Cubes" or "Difference of Cubes". Then, factor the problem.x^3 - 8
Answers
We have in this case the difference of Perfect Cubes since we have:
[tex]x^3-8=x^3-2^3[/tex]We know that this case can be factored as follows:
[tex]a^3-b^3=(a-b)\cdot(a^2+ab+b^2)[/tex]If we have that:
a = x
b = 2
Then, we have:
[tex](x-2)\cdot(x^2_{}+2x+2^2)=(x-2)\cdot(x^2+2x+4)[/tex]Therefore, the factored form of the perfect cube (for difference) is:
[tex]undefined[/tex]Quality control finds on average that 0.026% of the items from a certain factory are detective. One month, 4000 items are checked. How many items are expected to be detective?
Answers
Given that 4000 items are checked in one month, let the number of detective items be represented as y.
Quality control finds on average that 0.026% of the items in the factory are detective. This implies that
[tex]\text{Number of }\det ective\text{ items = }\frac{\text{0.026}}{100}\times\text{Total number of items checked}[/tex]When 4000 items are checked, we have the number of detective items to be evaluated as
[tex]\begin{gathered} \text{Number of }\det ective\text{ items = }\frac{\text{0.026}}{100}\times\text{Total number of items checked} \\ y=\frac{0.026}{100}\times4000 \\ \Rightarrow y=1.04 \end{gathered}[/tex]Hence, the number of detective items is 1.04.
00What is the length of BC?17А A9 units11 unitsO 15 unitsO 16 units8С
Answers
ANSWER:
15 units
STEP-BY-STEP EXPLANATION:
We can determine the BC value we can determine it by means of the Pythagorean theorem, with the hypotenuse 17 and the other side 8, therefore:
[tex]\begin{gathered} h^2=a^2+b^2 \\ \\ \text{ We replacing} \\ \\ 17^2=8^2+b^2 \\ \\ b^2=289-64 \\ \\ b=\sqrt{225} \\ \\ b=15 \end{gathered}[/tex]Therefore, the length of BC is 15 units.
How many units the function y = |x + 7| is translated from the parent function?Moved 7 units left from the originMoved 7 units right from the originMoved 7 units upwards from the originMoved 7 units downwards from the origin
Answers
According to the given information, the correct answer is the first choice Moved 7 units left from the origin.
The parent function would be |x|, and if we have |x+7| all the function values will be moved 7 units left from the origin.
I’ll give branniest to answer
with work shown
The equation is y=8.52x+6.0 estimate the value of y when x=25
Answers
Answer:
y = 219
Step-by-step explanation:
y = 8.52x + 6.0 ← substitute x = 25
y = (8.52 × 25) + 6.0 = 213 + 6 = 219
Answer:
Y= 219 when x =25
Step-by-step explanation:
Substitute for x = 25
Y= 8.52(25) +6.0
=213 +6
=219
Write an equation for the line parallel to the given line that contains C. C(4,7); y = - 2x + 1 (Type your answer in slope-intercept form.)
Answers
Let's begin by listing out the given information:
Equation of line: y = -2x + 1
Point C (x, y) = (4, 7)
[tex]y=-2x+1\Rightarrow m=-2[/tex]Parallel lines have the same slope. As such, the slope of the parallel line must also be -2
Using point slope equation of a straight line, we have:
[tex]\begin{gathered} y-y_1=-2\left(x-x_1\right) \\ at(x,y)=(4,7) \\ y-7=-2(x-4) \\ y-7=-2x+8 \\ y=-2x+8+7 \\ y=-2x+15 \end{gathered}[/tex]80 plus 8 plus 76 plus 5 plus 50 plus 75 plus 100 plus 100
Answers
80 plus 8 plus 76 plus 5 plus 50 plus 75 plus 100 plus 100 in Mathematical equation will be:
[tex]80\text{ + 8 + 76 + 5 + 50 + 75 + 100 +100}[/tex]Let's determine the sum,
[tex]80\text{ + 8 + 76 + 5 + 50 + 75 + 100 +100}[/tex][tex]88\text{ + 76 + 5 + 50 + 75 + 2}00[/tex][tex]164\text{ + 5 + 50 + 2}75[/tex][tex]169\text{ + 3}25[/tex][tex]494[/tex]Therefore, the answer is 494.
Answer:
496
Step-by-step explanation:
80+8+76+5+50+75+100+100
First, Narrow it down a bit: (80+8)=88, (76+5)=81, (50+75)=125, and (100+100)=200.
Now, your equation is: 88+81+125+200.
Now, narrow it down a bit more: (88+81)=169 and (125+200)=325.
Now, your equation is just: 169+325
Lastly, narrow it down to the last number: (169+325)=496.
Work out the value of (2 cubed) squared
Answers
Answer: 64
Step-by-step explanation:
2 cubed is 8 8 squared is 64 and that is the answer
Walk me through step by step for the third question
Answers
The First Question:
√8
Prime factorization of 8: 2³
= √2³
Apply radical rule: a^b+c = a^b * a^c
2³ = 2² * 2
=√2² * 2
Apply radical rule: √ab = √a√b, a ≥ 0, b ≥ 0
√2² * 2 = √2² √2
Apply radical rule: √a² = a, a ≥ 0
√2² = 2
2√2
The Third question:
√-8
Let's apply radical rule:
√-a = √-1 √
A small business owner is determining her profit for one month. Her expenses were$230.21 for utilities, $2,679.82 for rent, and $3,975.00 for employee salaries. Shehad $11,449.27 in sales for the month. What is her profit?a. $4,550.00b. $4,564.24C. $4,794.45d. $5,034.66
Answers
Answer:
B) $4,564.24
Explanation:
We are given the following information:
Expenses:
Utilities = $230.21
Rent = $2,679.82
Employee Salaries = $3,975.00
Sales = $11,449.27
The profit is obtained by the difference between Sales and Expenses as shown below:
[tex]\begin{gathered} Profit=Sales-Expenses \\ Profit=11,449.27-(230.21+2,679.82+3,975.00) \\ Profit=11,449.27-6885.03 \\ Profit=4564.24 \\ \\ \therefore Profit=\text{\$}4564.24\text{ } \end{gathered}[/tex]Therefore, the correct option is B
witch conversion factor would you use to convert from meters to feel ?
Answers
The conversion factor = 0.3048
Explanations:The conversion from meters to feet is given by the formula:
1 foot = 0.3048 meters
Therfore, to convert a measurement from meters to feet, it has to be multiplied by 0.3048.
The conversion factor = 0.3048
-18. Graph the functions Y, = 0.6* and Y, = 0.3.4 on a graphing calculator.Use a viewing window from -5 to 5 for x and from –2 to 8 for y, witha scale of 1 for both. Sketch the curves.How does the graph of Y, compare with the graph of Y ? Discuss howthe graphs rise or fall and the y-intercepts.
Answers
The Solution:
The given functions are:
[tex]\begin{gathered} y_1=0.6^x \\ y_2=0.3^x \\ \text{for } \\ -5\leq x\leq5,-2\leq y\leq8 \end{gathered}[/tex]From the graphing calculator, we have
Comparing the two graphs:
Both graphs are decreasing simultaneously and rises together. But
[tex]\begin{gathered} y_2=0.3^x\text{ is decreasing faster than } \\ y_1=0.6^x\text{ when decaying. But rises faster when increasing.} \end{gathered}[/tex]They both have the same intercept at point (0,1)
Use the following sample Epworth Sleepiness Scores for the problems below;6, 4, 3, 5, 4, 2, 4, 5, 4, 6, 1, 4, 5, 2Sample variance=Sample Standard Deviation=
Answers
Given:
The data are,
[tex]6,4,3,5,4,2,4,5,4,6,1,4,5,2[/tex]To find:
Sample variance and the Sample Standard Deviation
Explanation:
Using the formula,
Multiply 3/4 × 16/9 O A. 2/4O B. 3/4O C. 64/27O D. 4/3
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given question
[tex]\frac{3}{4}\times\frac{16}{9}[/tex]STEP 2: Find the product
[tex]\begin{gathered} \frac{3}{4}\times\frac{16}{9} \\ Muliply\text{ the numerators and also the denominators} \\ =\frac{3\times16}{4\times9}=\frac{48}{36} \\ \\ Divide\text{ by the common factors} \\ \frac{48}{36}=\frac{12\times4}{12\times3}=\frac{4}{3} \end{gathered}[/tex]Hence, the result is 4/3
Is the vertex of the quadratic function below a maximum or minimum?
Answers
A quadratic equation is of the form below:
[tex]ax^2+bx+c=y[/tex]The vertex of the quadratic equation is the value of y where the curve cut the y-axis.
To find the vertex, we would first first find the x-coordinate of the equation using
[tex]x=-\frac{b}{2a}[/tex]To find the vertex, we would substitute for x in the equation to get y.
Given the quadratic function below
[tex]f(x)=-3x^2-4x+7[/tex]It can be observed that
[tex]a=-3;b=-4,c=7[/tex]The x-coordinate of the vertex is as shown below:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=\frac{--4}{2(-3)} \\ x=\frac{4}{-6} \\ x=-\frac{2}{3} \end{gathered}[/tex]The vertex would be
[tex]\begin{gathered} f(-\frac{2}{3})=-3(-\frac{2}{3})^2-4(-\frac{2}{3})+7 \\ f(-\frac{2}{3})=-3(\frac{4}{9})+\frac{8}{3}+7 \\ f(-\frac{2}{3})=-\frac{4}{3}+\frac{8}{3}+7 \\ f(-\frac{2}{3})=\frac{-4+8}{3}+7 \\ f(-\frac{2}{3})=\frac{4}{3}+7 \\ f(-\frac{2}{3})=1\frac{1}{3}+7=8\frac{1}{3}=\frac{25}{3} \end{gathered}[/tex]Hence, the vertex of the quadratic function is (-2/3,25/3)
It should be noted that when a is positive, the quadratic graph opens upward and the vertex is minimum but when a is negative, the quadratic curve opens downward, and the vertex would be maximum
The graph of the quafratic function given is shown below
It can be observed that the vertex is maximum
Given the set of data below, which measure(s) will change if the outlier is removed? (Check all that apply.)1, 6, 8, 8, 8meanrangemedianmode
Answers
Answer
mean
range
Step-by-step explanation
An outlier is an observation that lies an abnormal distance from the other values.
In the set of data:
[tex]1,6,8,8,8[/tex]the outlier is 1.
Given that the mean is the average between all values in the dataset, then if the outlier is removed, the mean changes.
The range is calculated as follows:
[tex]range=maximum-minimum[/tex]If 1 is removed, the minimum changes, and in consequence, the range also changes.
The median is the middle number in a sequence of numbers. In this case, we have:
The median is 8 in both cases.
The mode is the value that appears most often in a set of data values. The mode of the original dataset is 8, and if the outlier is removed, the median remains the same.
Can someone help me I’ve been stuck on this for like hours now
Answers
We are given the inequality p>4
We want to find any numbers greater than 4
Any negative numbers are less than 4
1, or any numbers starting with 3 are less than 4
4 is equal to 4
Numbers greater than 4
4.001
4.01
4.1
5
7
9
12
If LW = 5x + 2 and LJ = 11x + 2 in the parallelogram below. Find LW.
Answers
Recall that in a parallelogram, the diagonals bisect each other. That means they divide each other in exactly equal parts.
that means that if LW = 5 x + 2 , and LJ = 11 x + 2,
since LJ is the full diagonal segment, and LW is half of it, we can say:
LJ = 2 times LW
In mathematical terms:
LJ = 2 * (LW)
11 x + 2 = 2 * (5 x + 2)
use distributive property
11 x + 2 = 10 x + 4
subtract 10 x from both sides
11 x - 10 x + 2 = 4
x + 2 = 4
subtract 2 from both sides to isolate x completely on the left
x = 4 - 2
x = 2
Then now that we know the value of x, we can use it in the formula for LW:
LW = 5 x + 2 = 5 * 2 + 2 = 10 + 2 = 12
Then LW = 12
Then answer option A is the correct one.
an architect designed a mountain lodge with special viewing windows on the top floor. how many square yards of glass will it take to make in large window?
Answers
Explanation
to find the area of the glass, we can divide the shape into 2 more known shapes, a triangle and a rectangle
so
total area= area of the rectangle(green)+area of the triangle(yellow)
the area of a rectagle is given by:
[tex]\text{Area}_{rectangle}=base\cdot heigth[/tex]and for the triangle, the area is
[tex]\text{Area}_{triangle}=\frac{1}{2}base\cdot height[/tex]then replace
[tex]\begin{gathered} \text{total area=(2 yd }\cdot1\text{ yd)+}\frac{\text{(2 yd }\cdot\text{ 2 yd)}}{2} \\ \text{total area=2 yd}^2+2yd^2 \\ \text{total area=}4yd^2 \end{gathered}[/tex]so, the answer is
[tex]4yd^2[/tex]I hope this helps you
The data points show the amount of money y (in dollars) in an account after a time x (in years).Each figure has the same data points.However, each figure has a different curve fitting the data.The equation for each curve is also shown.Answer the questions that follow.
Answers
SOLUTION
(a) From the slope of the graph, we can see that this is an exponential function
So, the function that best fits the graph is
[tex]y=601(1.05)^x[/tex]Hence the answer to (a) is Figure 1
(b) From the graph of the function we selected, where y represents the amount of money and x the number of years. To get the amount of money, we will substitute x for 18 into the quatiomn, we have
[tex]\begin{gathered} y=601(1.05)^x \\ y=601(1.05)^{18} \\ y=601\times2.406619234 \\ y=1,446.378159448 \end{gathered}[/tex]Hence the answer is $1,446.38
4) Which of the following numbers is an integer?- 9.1,-10,20/3
Answers
Given:
[tex]-9.1,-10,\frac{20}{3}[/tex]-10 is an integer.
Marko originally filled out 8 more applications than Henry. Then each boy filled out 3 additional applications, bringing the total to 28. How many applications did each boy originally fill out?Let m= number of applications Marko originally filled outLet h= number of applications Henry originally filled outWhat equation can we make to represent the relationship between the number of applications Marko and Henry originally filled out? AnswerUse your relationship from the question above to create an equation representing the number of applications after completing 3 more each: AnswerThe equation we can use to find the number of applications Henry and Marko each completed is :AnswerThe number of applications Marko originally filled out is AnswerThe number of applications Henry originally filled out is Answer
Answers
We have the next information
m= number of applicantios Marko originally filled out
h= number of applications Henry originally filled out
We know that Marko originally filled out 8 more applications than Henry
m=h+8
Then each filled out 3 additional applications
m+h+6=28
Already we have a system of equations of two variables
For the question What equation can we make to represent the relationship between the number of applications Marko and Henry originally filled out.
m=h+8
Use your relationship from the equation above to create an equation representing the number of applications after completing 3 more each
(h+8)+h+6=28
The equation we can use to find the number of applications Henry and Marko each completed is
2h+14=28
We can solve the equation above
2h=28-14
2h=14
h=14/2
h=7
m=h+8=15
The number of applications Marko originally filled out is 15
The number of applications Henry originally filled out is 7
Graph the given functions, fand g, in the same rectangular coordinate system Select integers for x, starting with-2 and ending with 2, and describe how the graph of g is related to the graph off.f(x)=x?_g(x)=x² - 3
Answers
Given
The functions,
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=x^2-3 \end{gathered}[/tex]To complete the ordered pairs for f(x)=x².
Explanation:
It is given that,
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=x^2-3 \end{gathered}[/tex]That implies, for x=-2,
[tex]\begin{gathered} f(-2)=(-2)^2 \\ =4 \end{gathered}[/tex]Also, for x=-1.
[tex]\begin{gathered} f(-1)=(-1)^2 \\ =1 \end{gathered}[/tex]For x=0,
[tex]\begin{gathered} f(0)=0^2 \\ =0 \end{gathered}[/tex]For x=1,
[tex]\begin{gathered} f(1)=1^2 \\ =1 \end{gathered}[/tex]For x=2,
[tex]\begin{gathered} f(2)=2^2 \\ =4 \end{gathered}[/tex]Hence, the ordered pairs are,
[tex]\left(-2,4\right),(-1,1),(0,0),(1,1),(1,4).[/tex]I need help. I need to know the measure of
Answers
The figure appears to be a rectangle and its opposite sides are parallel.
With this condition, ∠FDB and ∠EBG should be alternating angles same with ∠BED and ∠DFE. Under the rules of alternate angles, the two angles should be equal.
Therefore, ∠FDB = ∠EBG and ∠FDB = 27°
∠EBG should also be equal to 27°
The answer is 27°
Megan and her friends went to the movies. Megan took $45 with her to spend on her favorite items so she could share with her friends. Megan loves both popcorn and candy. The price for each bag of popcorn was $9. The price of each box of candy is half the price of a bag of popcorn. a). Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bags of popcorn and the other axis to represent the number boxes of candy.b). Explain your graph.
Answers
Solution:
Given that;
Megan and her friends went to the movies.
Megan took $45 with her to spend on her favorite items so she could share with her friends. Megan loves both popcorn and candy
Let x represent the number of bags of popcorn bought
Let y represent the number of boxes of candy bought
The price for each bag of popcorn was $9. The price of each box of candy is half the price of a bag of popcorn, i.e.
The price of a box of candy will be
[tex]=\frac{9}{2}=\text{\$}4.5[/tex]The equation representing the situation is
[tex]9x+4.5y=45[/tex]a) The graph representing the situation is
The intercepts are
[tex]\begin{gathered} x-intercept:\text{ \lparen5,0\rparen} \\ y-intercept:\text{ }(0,10) \end{gathered}[/tex]b) From the graph:
The graph explains that;
Megan bought 5 bags of popcorn and 10 boxes of candy
For a function f(x), you know that f(3) = -8 and f(4) = 3. One zero of f(x) would be located between x= and x=
Answers
Problem Statement
The question tells us that f(3) = -8 and f(4) = 3 and we are asked to find where one of the zeros of the function.
Solution
The function f(x) moves from negative to positive when moves from x = 3 to x = 4. This means that the value of f(x) must cross the x-axis between these two values of x.
Answer
Thus, one zero of the function lies between X = 3 and X = 4
here is a raffle with 500 tickets. One ticket will win a $960 prize, and the rest will win nothing. If you ave a ticket, what is the expected payoff?
Answers
The expected value is a measure of what you should expect to win per game in the long run. Divide the total prize over the number of tickets to find the expected payoff:
[tex]\frac{960}{500}=1.92[/tex]Therefore, the expected payoff is:
[tex]1.92[/tex]