I need help answering this questionThird part: What is the range of the function?
Answers
From the graph we can see that the value of y when x is less than 0 is y = 0. Also we can see that the value of y when x is bigger than 0 is y = 2
The thing we need to look at now is the circles in x = 0. The filled circle is in y = 0, which implies y = 0 for x less or equal than 0.
Thus the answer is:
Option B:
[tex]f(x)=\begin{cases}0,\text{ if }x\le0 \\ 2,\text{ if }x>0\end{cases}[/tex]Please check the solution I gave in the Answer Tab. Do you understand what I did?
Second part of the question:
Since the function is defined for all values of x, the domain are all real numbers. In interval notation,
Option B:
[tex]\text{The domain is }(-\infty,\infty)\text{.}[/tex]Third part of the question:
The range are all the values of y that the function takes. Since the function has only 2 values of y: 0 and 2, the range is:
[tex]\text{The range is }\mleft\lbrace0,2\mright\rbrace[/tex]Related Questions
The total cost, c, of renting a canoe for n hours can be represented by a system of equations. a. Write the system of equations that could be used to find the total cost, c, of renting a canoe for n hours.b. Graph the system of equations.c. When would the total cost for renting a canoe in be the same on both rivers?
Answers
From the given infomation, the cost for river Y is constant, that is,
[tex]\begin{gathered} Y=\text{ \$33+\$13} \\ Y=\text{ \$46} \end{gathered}[/tex]where Y denotes the cost for river Y.
On the other hand, the cost for river Z is given by
[tex]Z=\text{ \$5}\cdot n+\text{ \$13}[/tex]where n denotes the number of hours and Z the cost for river Z.
Therefore, the Total cost (C) will be the sum of the cost for river Y and river Z, that is,
[tex]C=\text{ \$46+\$5}\cdot n+\text{ \$13}[/tex]which gives
[tex]C=\text{ \$5}\cdot n+\text{ \$}59[/tex]the graph below shows the solution set of which inequality?A. √x<-3B. √x>-3C. √x>0D. √x<0There is no equality for the graph. Which one shows no equality?
Answers
Grap A. √x < -3
Graph B. √x > - 3
Graph C. √x > 0
Graph D. √x < 0
LESSON 7 SESSION 1 1 3 The triangle below models a section of the supports you might see in a construction crane. 2 3/60° 4 5 a. What is the sum of the angle measures of the triangle? Show your work.
Answers
EXPLANATION
Since this is a triangle, we can assevere by the alternate interior angles postulate that the angles 4 is of 90 degrees.
Then, by the Triangle Interior Angles Theorem, we know that the sum of the interior angles is equal to 180 degrees.
Thus,
60 + 4 + 2 = 180
As 4= 90
60 + 90 + m∠2 = 180
Isolating m∠2:
m∠2 = 180 - 90 - 60
Subtracting terms:
m∠2 = 30
Then, we know that the angles ∠1, ∠2 and right angle are complementary.
By definition, the sum of complementary angles is equal to 90 degrees.
Thus,
m∠1 + m∠2 = 90
Substituting terms:
m∠1 + 30 = 90
Isolating m∠1:
m∠1 = 90 - 30 = 60
Then, we know that the angles 60 and 3 are supplementary, so their sum is equal to 180°
So,
m∠3 + 60 = 180
Isolating m∠3:
m∠3= 180 - 60 = 120
Finally, we have that the angles 4 and 5 are the same measure because they are supplementary angles.
m∠4=m∠5 = 90
The measure of all the angles are:
m∠1= 60°
m∠2= 30°
m∠3= 120°
m∠4=90°
m∠5=90°
The average walking speed R of a person living in a city of population P is modeled by the function, R(P)=0.37lnP+0.05, where R is in feet per second. The population of Newport News is 162,000. Find the average walking speed of people living in Newport News.
Answers
Let's begin by identifying key information given to us:
The average working speed of a person is given by:
[tex]R\mleft(P\mright)=0.37\cdot lnP+0.05[/tex]Population (Newport News), P = 162,000
The average walking speed of the people is calculated as shown below:
[tex]\begin{gathered} R\mleft(P\mright)=0.37\cdot lnP+0.05 \\ P=162,000 \\ R(162,000)=0.37\cdot ln(162,000)+0.05_{} \\ R(162,000)=4.438+0.05=4.488\approx4.5 \\ R(162,000)=4.5ft\text{/s} \end{gathered}[/tex]Triangle ABC has the following vertices:A(-4,6)B(6,6)C(1,-3)Is triangle ABC an equilateral triangle, and why?Choose 1 answer:Yes, because AB = BC=AC.Yes, because AB 1 AC.No, because BC is longer than AB.No, because BC is not perpendicular to AB.
Answers
Explanation
We are given the following:
[tex]\begin{gathered} A(-4,6) \\ B(6,6) \\ C(1,-3) \end{gathered}[/tex]We are required to determine whether or not triangle ABC is an equilateral triangle.
We know that an equilateral triangle is a triangle with all sides equal.
We also know that the distance between two points is given as:
[tex]Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]- The distance AB becomes:
[tex]\begin{gathered} A(-4,6)\to(x_1,y_1) \\ B(6,6)\to(x_2,y_2) \\ AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ AB=\sqrt{(6-6)^2+(6-(-4))^2} \\ AB=\sqrt{0^2+10^2}=\sqrt{0+100}=\sqrt{100} \\ AB=10\text{ units } \end{gathered}[/tex]- The distance BC becomes:
[tex]\begin{gathered} B(6,6)\to(x_1,y_1) \\ C(1,-3)\to(x_2,y_2) \\ BC=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ BC=\sqrt{(-3-6)^2+(1-6)^2} \\ BC=\sqrt{(-9)^2+(-5)^2}=\sqrt{81+25}=\sqrt{106} \\ BC\approx10.3\text{ units} \end{gathered}[/tex]Hence, the answer is:
[tex]\text{ No, because BC is longer than AB}[/tex]Option C is correct.
The given function is f(x) = 8x^2 + 3x - 3.Find and simplify the followinga. F(x +1) = b. F(-x) =
Answers
The given function is f(x) = 8x^2 + 3x - 3.
a.
[tex]\begin{gathered} f(x+1)=8(x+1)^2+3(x+1)-3 \\ =8(x^2+2x+1)+3x+3-3 \\ =8x^2+16x+8+3x \\ =8x^2+19x+8 \end{gathered}[/tex]b.
[tex]\begin{gathered} f(-x)=8(-x)^2+3(-x)-3 \\ =8x^2-3x-3 \end{gathered}[/tex]1. Find the value of x when: 7/5 = x/3
Answers
The expression given is:
[tex]\frac{7}{5}=\frac{x}{3}[/tex]And we need to find the value of x.
To solve for x, we need to have the variable x alone on one side of the equation, for this, we multiply both sides of the equation by 3:
[tex]3(\frac{7}{5})=3(\frac{x}{3})[/tex]Solving the left-hand side we have to multiply 3 times 7 and divide that by 5. Since 3*7 is equal to 21:
[tex]\frac{21}{5}=3(\frac{x}{3})[/tex]Continuing with the left-hand side, the division of 21/5 is equal to 4.2:
[tex]4.2=3(\frac{x}{3})[/tex]Finally, solving the right-hand side, we note that 3/3 is 1, thus, we will only be left with x:
[tex]4.2=x[/tex]The value of x is 4.2.
Answer:
x = 4.2
Please help me on the second portion, writing the first six terms
Answers
EXPLANATION
1)
[tex]a_n=n^2+4[/tex]First term:
[tex]a_1=1^2+4[/tex][tex]a_1=1+4=5[/tex][tex]a_1=5[/tex]Second term:
[tex]a_2=2^2+4[/tex][tex]a_2=4+4[/tex][tex]a_2=8[/tex]Third term:
[tex]a_3=3^2+4[/tex][tex]a_3=9+4[/tex][tex]a_3=13[/tex]Fourth term:
[tex]a_4=4^2+4[/tex][tex]a_4=16+4[/tex][tex]a_4=20[/tex]Fifth term:
[tex]a_5=5^2+4[/tex][tex]a_5=25+4[/tex][tex]a_5=29[/tex]Sixth term:
[tex]a_6=6^2+4[/tex][tex]a_6=36+4=40[/tex][tex]a_6=40[/tex]Use this to find the equation of the tangent line to the parabola
Answers
Applying the sum and difference rules:
[tex]\frac{d}{dx}f(x)=\frac{d}{dx}(4x^2)-\frac{d}{dx}(2x)+\frac{d}{dx}(3)[/tex]Applying the constant multiple rule:
[tex]\frac{d}{dx}f(x)=4\frac{d}{dx}(x^2)-2\frac{d}{dx}(x)+\frac{d}{dx}(3)[/tex]The derivative of a constant is zero, and the derivative of x is one. Applying the power rule:
[tex]\begin{gathered} \frac{d}{dx}f(x)=4(2x^{})-2(1)+0 \\ f^{\prime}(x)=8x^{}-2 \end{gathered}[/tex]Evaluating f'(x) at x = -4:
[tex]\begin{gathered} f^{\prime}(-4)=8(-4)^{}-2 \\ f^{\prime}(-4)=-34 \end{gathered}[/tex]This value is the slope of the tangent line at the point (-4, 75), that is,
[tex]m=-34[/tex]Given the general equation of a line:
[tex]y=mx+b[/tex]Substituting with m = -34 and the point (-4, 75), that is, x = -4, and y = 75, and solving for b:
[tex]\begin{gathered} 75=(-34)(-4)+b \\ 75=136+b \\ 75-136=b \\ -61=b \end{gathered}[/tex]And the equation of the tangent line is:
[tex]y=-34x-61[/tex]1. Natalia is x years old. Sarah is 3 times as old as her. Natalia is 5 years older than Alme a. Find Alma's age in terms of x. b Find Sarah's age in terms of x. c If x= 12. how much older is Sarah than Natalia?
Answers
Part a. Find Alma's age in terms of x.
Since Natalia is x years old and it is also 5 years older than Alma, this means that Alma is 5 years younger than Natalia. We represent this as the age of Natalia "x" minus 5:
[tex]Alma=x-5[/tex]Part b. Find Sarah's age in terms of x.
Sarah is 3 times as old as Natalia, we represent this as follows:
[tex]\text{Sarah}=3x[/tex]The age of Sarah is the result of multiplying 3 times x.
Part c. If x=12 how much older is Sarah than Natalia?
In part b we defined the age of Sarah in terms of x:
[tex]\text{Sarah}=3x[/tex]Substituting x=12:
[tex]\begin{gathered} \text{Sarah}=3(12) \\ \text{Sarah}=36 \end{gathered}[/tex]Sarah is 36 years old. To find the difference, we subtract their ages:
[tex]36-12=24[/tex]Sarah is 24 years older than Natalia.
Answer:
Part a. x-5
Part b. 3x
Part c. 24 years
Sally has a checking account set up with an initial balance of S4200. She pays $600 from the account each month for rent (no otherpayments occur on the account). How many months, m, of paying rent will it take for the account to have $1200 left?0 7 monthsO 5 monthsO 6 months04 months
Answers
Given data:
initial balance in the account :$4200
Each month to be paid for rent =$600
Amount of Balalnce left in the account after paying m months rent =$1200
subract the inital amount from the balance amount.
4200-1200=3000
Thus, the amount paid for the rent is 600 then
[tex]600\times5=3000[/tex]Therefore it takes 5 months of paying rent from the account to have $1200 left.
Find the quotient. ⅚ ÷ 2
Answers
The quotient is the result you get after performing the division function.
Given:
[tex]⅚\div2[/tex]We have:
[tex]\frac{5}{6}\div\frac{2}{1}[/tex]Flip the fraction on the right and change the division symbol to multiplication
[tex]\frac{5}{6}\ast\frac{1}{2}\text{ = }\frac{5}{12}[/tex]ANSWER:
[tex]\frac{5}{12}[/tex]Picture Perfect a photo company, sells prints in various sizes. The cost of 4x6 prints can be represented by y = 25x = 2. where x is the number of prints ordered Max is going to order between 15 and 20 4x6 prints DO NOT include the 5 in your answer Do include decimals! The range for this situation is
Answers
the given equation is
y = 25x - 2
the minimum value of x is 15
so the minimum cost of the prints that can ordere is,
put x = 15
y = 25* 15 - 2
y = 375-2 = 373
the maximum cost will be,
put x = 20
y = 25 * 20 - 2
y = 500 - 2
y = 448
so the range of cost of the prints is 373 to 448.
solve the following system algebraically enter the solution as an ordered pair. (x, y)
Answers
we have
4x+5y=2 ------> equation A
x+2y=-1
isolate the variable x
x=-1-2y ------> equation B
substitute equation B in equation A
4(-1-2y)+5y=2
solve for y
-4-8y+5y=2
8y-5y=-4-2
3y=-6
y=-2
Find the value of x
x=-1-2y
x=-1-2(-2)
x=-1+4
x=3
answer is
solution is (3,-2)you want to buy a house and can afford a monthly mortgage payment of $850 you plan to take out a 20-year loan. The current available rate is an APR of 3.72% whatever you're more mortgage Lender predicts that the rate could rise to 4.22 % in the near future. If the APr rises from 3.72 % to 4.22 % will the maximum loan amount that you can afford increase or decrease by how many dollars question if the APR rises from 3.72 % to 4.22 % the maximum loan amount that you can afford will decrease by
Answers
Answer:
Explanation:For a payment of 3.72% per month, the amount after 20 years is:
(850 * 20*12) + (0.0372*8500*20*12)
= $211,588.8
This is the amount affordable
For a rate of 4.22%, we have:
If the rate rises from 3.72% to 4.22%, then
(850 * 20*12) + (0.0422*8500*20*12)
= $212,608.8
The amount by which the loan increases is:
$212,608.8 - $211,588.8 = $1020
Figure Q was rotated about the center shown by 270 counterclockwise
Which figure is the image of Q?
Answers
Answer:
b
Step-by-step explanation:
Figure Q was rotated about the center shown by 270 counterclockwise
So, figure B. is the image of Q As rotation doesn't change shape and size.
To solve rotation figure questions when rotating 270 degrees, follow these steps:
Draw the original figure: Begin by drawing the original figure on a piece of paper. This will be the starting position of the shape before any rotation.
Identify the center of rotation: The center of rotation is the point around which the figure will rotate. It could be a vertex, the midpoint of a side, or any other specified point.
Draw a 270-degree rotation: To rotate the figure 270 degrees counterclockwise, draw a new figure that has each point of the original figure rotated 270 degrees counterclockwise around the center of rotation.
Measure the new position: Measure the new position of each point in the rotated figure to compare it with the original.
Analyze the changes: Observe the changes in the shape, angles, and positions of the vertices to understand how the figure has transformed.
To know more about counterclockwise:
https://brainly.com/question/29971286
#SPJ2
a sample of ore is found to be 0.0051% silver and 0.048% diamond what is the percentage of matter in the ore that is neither silver nor diamond
Answers
% silver in the ore = 0.0051%
% diamond in the ore = 0.048%
The percentage of the matter in the ore that is neither silver nor diamond can be calculated below
[tex]\begin{gathered} \text{silver}=\text{ 0.0051\%} \\ \text{diamond}=0.048\text{ \%} \\ \text{neither silver nor diamond = 100-0.0051-0.048 = }99.9469\text{ \%} \end{gathered}[/tex]Find the measure of ∠YOZ by answering the questions.1. Find the measure of ∠WOV. Which angle relationship did you use?2. Now find the measure of ∠YOZ. Which angle relationship did you use?
Answers
1.-First, notice that angle WOV and angle WOX are complementary, this means that we have the following equation:
[tex]\measuredangle WOV+\measuredangle WOX=90[/tex]since the measure of angle WOX is 30 degrees, we have the following:
[tex]\begin{gathered} \measuredangle WOV+30=90 \\ \Rightarrow\measuredangle WOV=90-30=60 \\ \measuredangle WOV=60\degree \end{gathered}[/tex]2.- To find the measure of angle YOZ, we can see that it is vertical with angle WOV, thus, we have:
[tex]\begin{gathered} \measuredangle YOZ=\measuredangle WOV=60\degree \\ \Rightarrow\measuredangle YOZ=60\degree \end{gathered}[/tex]therefore, the measure of angle YOZ is 60 degrees since it is vertical with angle WOV
write an equation of the parabola that has the same shape as the graph of f(x)=4x²,but with the point (-6,-2) as the vertex.
Answers
The graph must have the same shape as
[tex]f(x)=4x^2[/tex]but with the vertex at (-6,-2).
In general, the equation of the parabola in vertex form is
[tex]y=a(x-h)^2+k[/tex]where (h,k)=(-6,-2) in our case. By comparing both equations, we can see that the searched equation must be
[tex]y=4(x+6)^2-2[/tex]What is the missing reason for the second step in the proof below?RGiven: Tis the midpoint of QRU is the midpoint of RSTUProve: AQRS - ATRUQSREASONSGiven?Substitution and simplificationSTATEMENTS1. Tis the midpoint of ORU is the midpoint of RS2.TR =ỘT TR+QT = QRRU US, RU-US - RS3. OR - QT +TR-TR+TR = 2TRRS = RU +US RU + RU=2RUOR 2RT RT2RU RUOR RTRU6. ZORSE ZTRU7AORSATRU4. RSDivision property of equality,simplificationProperty of proportion fromInterchangeabilityReflexive propertySAS similarity postulate5. RS
Answers
The second statement in the given proof is
[tex]\begin{gathered} \bar{TR}\cong\bar{QT},\: \bar{TR}+\bar{QT}\bar{=QR} \\ \bar{RU}\cong\bar{US},\: \bar{RU}+\bar{US}\bar{=RS} \end{gathered}[/tex]Since we are given that T is the midpoint of QR which makes TR equal to QT and the sum of TR and QT must be equal to QR as per the definition of a midpoint
Similarly, we are given that U is the midpoint of RS which makes RU equal to US and the sum of RS and US must be equal to RS as per the definition of a midpoint
Therefore, the correct answer is "definition of a midpoint"
Find the slope of the line that is parallel to the line that passes through the following pair of points: (4, -2) and (16,0)
Answers
Answer
Slope = (1/6) = 0.1667
Explanation
Twol parallel lines normally have their slopes equal to each other.
So, to find the required slope, we can just find the slope of the line that is parallel to it.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (4, -2) and (16, 0)
x₁ = 4
y₁ = -2
x₂ = 16
y₂ = 0
[tex]\text{Slope = }\frac{0-(-2)}{16-4}=\frac{0+2}{12}=\frac{2}{12}=\frac{1}{6}=0.1667[/tex]Hope this Helps!!!
A motorboat takes four hours to travel 128 km going upstream the return trip takes two hours going down stream. what is the rate of the boat in a still? water what is the rate of the current?
Answers
The rate of the boat in still water is 48 km/h
The rate of current is 16 km/h
Explanation:Let the rate of the current be represented by c
Let the rate of the boat in still water be represented by r
The distance traveled by the boat, d = 128 km
Time taken by the boat to travel upstream, t₁ = 4 hours
The speed of the boat upstream, v₁ = d/t₁
The speed of the boat upstream, v₁ = 128/4
The speed of the boat upstream, v₁ = 32 km/h
Rate of the boat in still water - Rate of current = The speed of the boat upstream
r - c = v₁
r - c = 32...............................(1)
The time taken by the boat to travel downstream, t₂ = 2 hours
The speed of the boat downstream, v₂ = d/t₂
The speed of the boat downstream, v₂ = 128/2
The speed of the boat downstream, v₂ = 64 km/h
Rate of the boat in still water - Rate of current = The speed of the boat downstream
r + c = v₂
r + c = 64......................(2)
Subtract equation (1) from equation (2)
2c = 64 - 32
2c = 32
c = 32/2
c = 16 km/h
Substitute c = 16 into equation (1)
r - c = 32
r - 16 = 32
r = 32 + 16
r = 48 km/h
The rate of the boat in still water is 48 km/h
The rate of current is 16 km/h
Write the simplest polynomial function with integral coefficients that had the given zeros. 7,-7i
Answers
To find to polynomial from zeros.
Find the factors. If it is a positive zero, the factor will be (x- zero) If it is a negative zero if is (x+zero)
Multiply the factors together.
Zeros of 7, -7i would be:
Find the factors:
[tex](x-7)(x\pm7i)[/tex]Multiply the factors together: Will start out with FOIL for (x-7)(x+-7i) =
[tex]\begin{gathered} (x-7)(x\pm7i) \\ (x-7)(x+7i)(x-7i) \\ (x-7)(x^2-7ix+7ix-49i^2) \end{gathered}[/tex]Combine like terms. Then multiply by the last factor
[tex]\begin{gathered} x-7(x^2-49(-1)) \\ \text{where i}^2=-1 \\ (x-7)(x^2+49) \\ x^3+49x-7x^2-343 \\ x^3-7x^2+49x-343 \end{gathered}[/tex]Therefore the correct answer from the Option is D
A survey approximates the number of Americans that are age 65 and older and projects that by the year 2050, approximately 82.2 million Americans will be at least 65. The bar graph shows the estimated number of Americans with projected figures for the year 2020 and beyond.A graphing calculator screen displays an exponential function that models the U.S. population age 65 and over, y, in millions,x years after 1899. Use this information to solve (a)-(d) below.ExpRegy = a*b^xClick the icon to view the bar graph.a = 3.4854891603b= 1.022941093a. Explain why an exponential function was used to model the population data.OA. An exponential function was used because exponential functions are always more accurate than linear functions.B. An exponential function was used because the population is always modeled using exponential functions.OC. An exponential function was used because the data in the bar graph is increasing more and more rapidly.
Answers
ANSWER and EXPLANATION
(a) An exponential function was used to model the population data.
We notice that from the bar graph, the population increases very quickly as the number of years after 1899 increases.
This shows that the population data is increasing rapidly; hence, an exponential function was used.
The answer is option C.
(b) The general form of an exponential function is given as:
[tex]y=a*b^x[/tex]where a = initial value; b = exponential factor
We are given the values of a and b, so, to find the function for the population data, substitute the approximated values of a and b into the function:
[tex]y=3.485*(1.023)^x[/tex]That is the function.
(c) To find the number of Americans aged 65 and over in 2010, we have to first find how many years after 1899 2010 is:
[tex]\begin{gathered} 2010-1899 \\ \\ 111 \end{gathered}[/tex]Now, using the model in b, solve for y when x is 111:
[tex]\begin{gathered} y=3.485*(1.023)^{111} \\ \\ y=43.5\text{ million} \end{gathered}[/tex]According to the bar chart, we see that in 2010, it is estimated that there will be 45.3 million people aged 65 and over.
We see that the rounded value obtained above is less than the value displayed by the bar graph by a value of:
[tex]\begin{gathered} 45.3-43.5 \\ \\ 1.8\text{ million} \end{gathered}[/tex]Hence, the rounded value underestimates the 2010 population by 1.8 million.
(d) To find the number of Americans that will be age 65 and over in 2020, first, find how many years after 1899 that 2020 is:
[tex]\begin{gathered} 2020-1899 \\ \\ 121\text{ years} \end{gathered}[/tex]Now, solve for y when x is 121:
[tex]\begin{gathered} y=3.485*(1.023)^{121} \\ \\ y=54.6\text{ million} \end{gathered}[/tex]That is the estimated number of Americans that will be age 65 and over in 2020/
Please help I don’t understand This lesson is called coordinate that makes the rectangle/parallelogram
Answers
The first step is plot the given points A,B,C to visualize the problem and where D is going to be.
Now, given the definition of a parallelogram, the line DC must have the same slope of BA because both lines al parallel. Similarly, the line BC is parallel to AC. Given this information, it can be shown that the x-coordinate difference between D and C must be the same as the x-coordiante difference between B and A.
Given the point B (-9,1) and A (-2,4), the x-coordinate difference is:
[tex]-9-(-2)=-7[/tex]Hence, this -7 is also the x-coordinate difference between C and D. Given C (-1,-5), the x-coordiante of D must be:
[tex]-1-7=-8[/tex]In the same way, the y-coordinate difference between A (-2,4) and B (-9,1) is:
[tex]4-1=3[/tex]And this y-coordinate difference must be the same between C (-1,-5) and D. Hence the y-coordinate of D is:
[tex]-5-3=-8[/tex]ANSWER
Finally, the coordinates of point D are (-8,-8)
Find mZG.EH100°40°FGmZGo
Answers
We have
Find xy when x(-7,10) and y(3,4)
Answers
.
We were given,
X(-7,10)
Y(3,4)
Required to find;
XY
Recall,
XY is the distance between X and Y
Therefore,
XY will be given by
[tex]XY=\sqrt{(x_2-x_1)^2+}(y_2-y_1)^2[/tex]On substitution:
[tex]\begin{gathered} XY=\sqrt{(3--7)^2+(4-10)^2} \\ XY=\sqrt{10^2+6^2} \\ XY=\sqrt{100+36} \\ XY=\sqrt{136} \\ XY=2\sqrt{34} \\ XY=\text{ 11.66} \end{gathered}[/tex]Therefore XY = 11.66 units
y-6 = 1/6 (x-7)what is y
Answers
y - 6 = 1/6(x - 7)
[tex]y-6=\frac{1}{6}\times\mleft(x-7\mright)[/tex][tex]\begin{gathered} y-6=\frac{1}{6}\mleft(x-7\mright) \\ y=\frac{1}{6}\mleft(x-7\mright)+6 \end{gathered}[/tex][tex]y=\frac{x}{6}-\frac{7}{6}+6[/tex][tex]y=\frac{x}{6}-\frac{29}{6}[/tex]or we can write this as
6y = x - 29
A mural is 12 5/6 ft long and is divided into 7 equal length panels. how many ft long is each pannel?
Answers
EXPLANATION:
In the exercise we can see that it is a division of fractions because we need to know exactly how much length corresponds to each panel, for that we must divide the mixed fraction between the 7 panels.
Now to be able to do a correct division of fractions it is necessary that the mixed fraction becomes an improper fraction and the integer 7 must be converted into a fraction.
Now following the steps already mentioned, the exercise will be as follows:
[tex]\begin{gathered} first\text{ convert }mixed\text{ fraction to improper:} \\ 12\frac{5}{6}=\frac{77}{6} \\ \text{Now }we\text{ must convert }the\text{ 7 to a fraction }for\text{ that we }add\text{ the numer 1 } \\ to\text{ the denominator }; \\ \frac{7}{1} \\ Now\text{ we can divide }both\text{ fractions} \\ \frac{77}{6}\colon\frac{7}{1};to\text{ divide the numerator is multiplied }witch\text{ the second denominator} \\ \frac{77}{6}\times\frac{7}{1}=\frac{77}{42}=1.83\text{ }for\text{ each panel} \end{gathered}[/tex]Marlon's TV plan costs $52.48 per month plus $6.29 per first-run movie. How many first-run movies can he watch if he wants to keep his monthly bill to be a maximum of $104?
Answers
If x represents the number of first-run movies
The information can be interpreted as
[tex]52.48+6.29x\le104[/tex]This can be solved as shown below:
[tex]\begin{gathered} 6.29x\le104-52.48 \\ 6.29x\le51.52 \\ x\le\frac{51.52}{6.29} \\ x\le8.19 \\ x\le8 \end{gathered}[/tex]Hence, the number of first-run movies that can be watched is 8