The point-slope formula is
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope of a line passing through the point (x₁, y₁).
Also, the slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this problem, the line passes through points (4, -3) and (-2, 5). Thus, we have:
x₁ = 4
y₁ = -3
x₂ = -2
y₂ = 5
Then, the slope is
[tex]m=\frac{5-(-3)}{-2-4}=\frac{5+3}{-6}=\frac{8}{-6}=-\frac{4}{3}[/tex]And the equation in point-slope form is
[tex]y-(-3)=-\frac{4}{3}(x-4)[/tex]Now, we need to rewrite this equation in slope-intercept form. The slope-intercept equation of a line with slope m and y-intercept b is
[tex]y=mx+b[/tex]Thus, we need to isolate y on the left side of the equation to obtain the slope-intercept form, as follows:
[tex]\begin{gathered} y+3=-\frac{4}{3}x-\frac{4}{3}(-4)\text{ using the distributive property of multiplication over addition} \\ \\ y+3=-\frac{4}{3}x+\frac{16}{3} \\ \\ y+3-3=-\frac{4}{3}x+\frac{16}{3}-3 \\ \\ y=-\frac{4}{3}x+\frac{16}{3}-\frac{9}{3} \\ \\ y=-\frac{4}{3}x+\frac{7}{3} \end{gathered}[/tex]Therefore, the slope-intercept form of that linear equation is
[tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]A small regional carrier accepted 23 reservations for a particular flight with 20 seats. 14 reservations went to regular customers who will arrive for the flight. each of the remaining passengers will arrive for the flight with a 50 % chance ,independently of each other. Find the probability that overbooking occurs find the probability that the flight has empty seats
Answer:
P(Overbooking) = 0.0898
P(Empty seats) = 0.7461
Explanation:
The probability that overbooking occurs is the probability that arrives more than 6 passengers from the 9 that remain.
This probability can be calculated as:
[tex]P(x)=\frac{n!}{x!(n-x)!}\cdot p^x\cdot(1-p)^{n-x}[/tex]Where n is the total number of remaining passengers, and p is the probability that a passenger will arrive for the flight. So, the probability that x people arrive is:
[tex]P(x)=\frac{9!}{x!(9-x)!}\cdot0.5^x\cdot(1-0.5)^{9-x}[/tex]So, the probability that arrives 7, 8, or 9 people is:
[tex]\begin{gathered} P(7)=\frac{9!}{7!(9-7)!}\cdot0.5^7\cdot(1-0.5)^{9-7}=0.0703 \\ P(8)=\frac{9!}{8!(9-8)!}\cdot0.5^8\cdot(1-0.5)^{9-8}=0.0176 \\ P(9)=\frac{9!}{9!(9-9)!}\cdot0.5^9\cdot(1-0.5)^{9-9}=0.002 \end{gathered}[/tex]Therefore, the probability that overbooking occurs is:
[tex]\begin{gathered} P(\text{Overbooking)}=P(7)+P(8)+P(9) \\ P(\text{Overbooking)}=0.0898 \end{gathered}[/tex]On the other hand, the probability that the flight has empty seats is the probability that arrives fewer than 6 people for the flight.
So, using the same equation for P(x), we get that the probability that the flight has empty sats is:
[tex]\begin{gathered} P(\text{Empty seats)=P(0) +P(1) + P(2) + P(3) +P(4) + P(5)} \\ P(\text{Empty seats) = 0.7461} \end{gathered}[/tex]Therefore, the answers are:
P(Overbooking) = 0.0898
P(Empty seats) = 0.7461
2(x+9)=2x+18What is the Name of the property listed above -commutative property of addition-commutative property of multiplication -Associative property of addition -Associative property of multiplication -Distributive property -additive identity -Multiplication identity -Zero property of multiplication-Multiplication property of -1 -none of the above.
Distributive property
Explanation:Given:
[tex]2(x+9)\text{ = 2x + 18}[/tex]To find:
the name of the property stated
[tex]\begin{gathered} 2(x\text{ + 9\rparen = 2\lparen x\rparen + 2\lparen9\rparen} \\ \\ The\text{ form above is the same as:} \\ a(b\text{ + c\rparen = }a(b)\text{ + a\lparen c\rparen} \\ This\text{ is known as distributive property.} \end{gathered}[/tex][tex]\begin{gathered} 2(x)\text{ + 2\lparen9\rparen = 2x + 18} \\ \\ Hence,\text{ 2\lparen x + 9\rparen = 2x + 18 is a distributive property} \end{gathered}[/tex]please see image, use this information to solve the problem.
The coordinates of the point B is,
[tex](56,7)[/tex]Can I find a tutor to help me with this answer?
Explanation:
We have the equation of a quadratic function:
[tex]f(x)=(x-2)^2+2[/tex]And we need to find and plot the vertex of the equation.
We start by remembering that a quadratic equation is represented by a parabola and that the vertex is the point where the parabola changes direction, usually represented by (h, k) as shown in the following example:
• How do we find the vertex using the given equation?
We find it by comparing our equation with the general vertex form of the quadratic equation:
[tex]f(x)=a(x-h)^2+k[/tex]where
[tex](h,k)[/tex]is the vertex, and a is a constant.
Using the given equation, we find the h and k values:
[tex]\begin{gathered} f(x)=(x-2)^{2}+2 \\ \downarrow \\ h=2 \\ k=2 \end{gathered}[/tex]Therefore, the vertex is at (2, 2).
Answer:
The point (2,2) representing the vertex is shown in the image:
State the domain and range of the relation. Then determine whether the relation is a function, write yes or no.
Solution:
The domain is the set of independent values of a relationfor which the reltion is valid.
The range is the set of dependent values of a relation for which he relation is valid and real
Given:
From the above image, we have
[tex]\begin{gathered} Domain:\text{ -2, 3} \\ Range:\text{ 4, -2, 0, 2} \end{gathered}[/tex]For a relation to be a function, for every value of x there is only one corresponding value for y.
Since the value of domain in the above figure outputs more than one value, the relation is not a function.
Hence, the correct answer is NO
In the cost function below, C(x) is the cost of producing x items. Find the average cost per item when the required number of items is produced. C(x) = 4.1% +9,500 a. 200 items b. 2000 itemsC. 5000 items What is the average cost per item when 200, 2000, and 5000 items ?
Since the function of the cost is
[tex]C(x)=4.1x+9500[/tex]Where x is the number of the items
a) There were 200 items
x = 200
[tex]\begin{gathered} C(x)=4.1(200)+9500 \\ C(x)=820+9500 \\ C(x)=10320 \end{gathered}[/tex]To find the average cost per item, find
[tex]\begin{gathered} \text{Ave. =}\frac{C(x)}{x} \\ \text{Ave. = }\frac{10320}{200} \\ \text{Ave. =51.6} \end{gathered}[/tex]b) There were 2000 items
[tex]x=2000[/tex][tex]\begin{gathered} C(2000)=4.1\times2000+9500 \\ C(2000)=17700 \end{gathered}[/tex]Find the average as the same above
[tex]\begin{gathered} \text{Ave. = }\frac{17700}{2000} \\ \text{Ave. = 8.85} \end{gathered}[/tex]c) There were 5000 items
[tex]x=5000[/tex][tex]\begin{gathered} C(5000)=4.1(5000)+9500 \\ C(5000)=30000 \end{gathered}[/tex]Divide it by 5000 to find the average
[tex]\begin{gathered} \text{Ave. = }\frac{30000}{5000} \\ \text{Ave. = 6} \end{gathered}[/tex]Which of the following division problems CANNOT be completed?
155 ÷ (-3)
10 ÷ 0
0 ÷ 5
⅔ ÷ ¼
Answer:
I think the first one
but if it's a multiple choice answer then the second and third
Step-by-step explanation:
I was gonna say 0 and 5 because since in algebra you can't divide anything with 0 and you can divide the last one
Which equation does the following grid represent? X X XX X XX X X XX X X XX X X A 0.92 - 0.19 = 0.73 OB. 0.73 +0.19 = 0.92 O C. 1.00 - 0.19 = 0.81 O D. 1.00 +0.73 = 1.73
In the Diagram,
We have a box
Total squares: 100
In Red we have= 92 squares
The blank squares= 8
"X" squares = 19
2) Then, Dividing each by 100:
0.92 red -0.19x =0.73 the amount of red squares not marked with an x
Identify the vertex and sketch the graph.f (x) = -2x 2 - 24x - 72
ANSWER
Vertex = (-6, 0) Option B
Graph:
EXPLANATION
Given:
[tex]f(x)=-2x^2-24x-72[/tex]Desired Outcome:
Vertex and graph
Rewrite the equation in vertex form
[tex]y=a(x-h)^2+k[/tex]where:
(h, k) is the vertex.
Now, determine the vertex of the equation
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-(-24)}{2(-2)} \\ h=\frac{24}{-4} \\ h=-6 \end{gathered}[/tex][tex]k=-\frac{D}{4a}[/tex]Let's determine the value of D
[tex]\begin{gathered} D=b^2-4ac \\ D=(-24)^2-4(-2)(-72) \\ D=576-576 \\ D=0 \end{gathered}[/tex]Now,
[tex]\begin{gathered} k=-\frac{D}{4a} \\ k=-\frac{0}{4(-2)} \\ k=\frac{0}{8} \\ k=0 \end{gathered}[/tex]Therefore, the vertex (h, k) = (-6, 0) and when we plot this on a graph, we have:
Hence, the correct option is B.
Help me with this math and explaining the question solution and quickly and explain it
To find the distance between V1 and the aquarium we can use the formula of the distance between two points in the plane, that is,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Where }(x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates of the points} \end{gathered}[/tex]So, in this case, we have
[tex]\begin{gathered} V1(-6,5) \\ AQ(5,5) \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(5-(-6))^2+(5-5)^2} \\ d=\sqrt[]{(5+6)^2+(5-5)^2} \\ d=\sqrt[]{(11)^2+(0)^2} \\ d=\sqrt[]{(11)^2} \\ d=11 \end{gathered}[/tex]Therefore, the distance between v1 and the aquarium is 11 units.
Math help with problems Is this line linear or nonlinear
Answer:
[tex]It\text{ is linear}[/tex]Explanation:
Here, we want to check if the given line is linear or not
From the image shown, the line connects two points on the axes
This connection is in the form of a line segment
Thus, we can confirm that the line is linear
In the figure below, ∠APE and ∠EPD are congruent. What is the arc measure of major arc BAD on circle P in degrees?
You need to determine the measure of the arc BAD in the given circle P.
The angle measure of angle ∠BPD with the vertex in the center of the circle P is congruent to the measure of the intercepted arc BAD.
This means that to determine the measure of the arc, you need to determine the measure of the angle.
The measure of ∠BPD is equal to the sum of the measures of the adjacent angles that form it:
[tex]\angle\text{BPD}=\angle\text{BPA}+\angle\text{APE}+\angle\text{EPD}[/tex]∠APE and ∠EPD have an unknown measure but we know that they are equal, and we know that the total angle of a circle is 360º, i.e. the sum of all the angles is 360º
Let "x" represent the measure of angles ∠APE and ∠EPD, we can represent the total angle of the circle as follows:
[tex]360º=\angle\text{APE}+\angle\text{EPD}+\angle\text{DPC}+\angle\text{CPB}+\angle\text{BPA}[/tex]We know that
∠APE=∠EPD=x
∠DPC=42º
∠CPB=74º
∠BPA=136º
[tex]\begin{gathered} 360º=x+x+42+74+136 \\ 360=2x+252 \\ 360-252=2x \\ 2x=108 \\ \frac{2x}{2}=\frac{180}{2} \\ x=54º \end{gathered}[/tex]So ∠APE=∠EPD=54º
Now that we know the measure of these angles we can calculate the measure of ∠BPD
[tex]\begin{gathered} \angle\text{BPD}=\angle\text{BPA}+\angle\text{APE}+\angle\text{EPD} \\ \angle\text{BPD}=136+54+54 \\ \angle\text{BPD}=244º \end{gathered}[/tex]∠BPD=244º and, as mentioned before the measure of the intercepted arc is the same as the measure of the central angle, then its intercepted arc BAD = 244º as well.
The figure below shows a juice box in the shape for a rectangular prism
(a)
Given the dimensions of the rectangular prism l = 7 cm, w = 2 cm, h = 8 cm, the surface area of a rectangular prism can be computed using the equation
[tex]SA=2(wl+hl+hw)[/tex]Substitute the values on the equation above and compute, we get
[tex]SA=2\lbrack(2cm\times7cm)+(8cm\times7cm)+(8cm\times2cm)\rbrack=172cm^2[/tex]The volume of the rectangular prism can be computed using the equation
[tex]V=l\times w\times h[/tex]Plug in the values on the equation above and compute, we get
[tex]V=(7cm)\times(2cm)\times(8cm)=112cm^3[/tex](b) For the amount of juice inside the rectangular prism, we will use volume.
(c) For the amount of coating of wax for the box, we will use surface area.
The width of a rectangle measures (3u - 4v) centimeters, and its length measures
(10u + 2v) centimeters. Which expression represents the perimeter, in centimeters,
of the rectangle
Answer:
Step-by-step explanation:
Ok lets get rolling
So far as we know, perimeter is the sum of all sides of a figure
in a rectangle opposite sides are equal, therefore we after some machinations we get this equation
P of rectangle = 2(10u+2v) + 2(3u-4v)
P of rectangle = 20u+4v + 6u - 8v
P of rectangle = 26u - 4v
and thats ur answer
hope this helps
_____ ______ ______says that people are able to decide what to buy and how much they are willing and able to pay depending on the satisfaction they receive from the service/product.
Decision makers say that people can decide what to buy and how much they are willing and able to pay depending on the satisfaction they receive from the service/product.
What is meant by decision maker?A decision maker is a person or group in charge of making crucial strategic decisions based on a variety of factors, such as the amount of time available, the resources at hand, the type and quality of information at hand, and the number of interested parties.
According to those who make decisions, consumers can choose what they want to buy and how much they are willing and able to pay based on how satisfied they are with the service or product.
Making decisions is crucial because it allows you to select from a variety of options. It is important to gather all available information and consider the advantages and disadvantages of it before making a decision. It is imperative to concentrate on actions that can assist in making the best decisions.
To learn more about decision maker refer to:
https://brainly.com/question/1249089
#SPJ1
4. [-/12.5 Points]DETAILSAUFEXC4COREQ 13.2.005.MY NOTESASK YOUR TEACHERFind the range, the standard deviation, and the variance for the given samples. Round non-integer results to the nearest tenth.4.3, 4.8, 2.4, 4.1, 2.5, 2.6rangestandard deviationvariance5. [-/12.5 Points]DETAILSAUFEXC4COREQ 13.2.007.MY NOTESASK YOUR TEACHERFind the range, the standard deviation, and the variance for the given samples. Round non-integer results to the nearest tenth.61, 82, 58, 74, 56, 47, 73, 52, 65rangestandard deviationvariance
Range = greatest number - smallest number
Range= 4.8 - 2.4 = 2.4
Mean = 2.4 + 2.5 + 2.6 + 4.1+ 4.3+4.8 = 20.7/6 = 3.45
[tex]\begin{gathered} SD=\sqrt{\frac{\sum_{i=1}^n(x1\text{ - }x)^2}{n\text{ - }1}} \\ SD=\sqrt{\frac{(2.4\text{ - 3.45\rparen}^2+(2.5\text{ - 3.45\rparen}^2+(2.6\text{ - }3.45)^2+(4.1\text{ - }3.45)^2+(4.3\text{ - }3.45)^2+(4.8\text{ -}3.45)^2}{6\text{ - }1}} \\ \\ SD=\sqrt{\frac{(\text{ -1.05\rparen}^2\text{ + \lparen- 0.95\rparen}^2\text{ + \lparen-0.85\rparen}^2\text{ + \lparen0.65\rparen}^2\text{ + \lparen0.85\rparen}^2\text{ + \lparen1.35\rparen}^2}{5}} \\ \\ SD=\text{ }\sqrt[\placeholder{⬚}]{\frac{(1.1025)\text{ + \lparen0.9025\rparen + \lparen0.7225\rparen + \lparen0.4225\rparen + \lparen0.72259\rparen + \lparen1.8225\rparen}}{5}} \\ \\ SD=\text{ }\sqrt[\placeholder{⬚}]{\frac{5.6954}{5}} \\ \\ SD=\sqrt[\placeholder{⬚}]{1.13908} \\ \\ SD=\text{ 1.067} \\ \\ Variance=\text{ }\sqrt[\placeholder{⬚}]{SD} \\ V=\text{ 1.13908} \end{gathered}[/tex]Rounding to the nearest tenth:
Standard deviation: 1.1
Variance: 1.1
Range: 2.4
Jerry attended a computer software conference.He pause $12.00 for admission.He spent $11.50 for lunch. He paid $1.50 for each workshop tickets. If jerry had a total of $35.00 to spend at the conference which inequalities could be used to determine n, the maximum number of workshop tickets that jerry could have purchased?
Given he spent the following:
Admission = $12.00
Lunch = $11.50
Each workshop ticket = $1.50
Total amount Jerry had = $35.00
Here, the total amount Jerr
The inequality to determine the maximum number of tickets that Jerry could have purchased is:
12.00 + 11.50 + 1.50t ≤ $35.00
the length of one leg of a right triangle is 15 m. The length of the other leg is 9 m shorter than the length of the hypotenuse. Find the length of the hypotenuse.
Let the hypotenuse is x
The length of the other leg is 9 m shorter than the length of the hypotenuse
The length of second leg = Hypotenuse - 9
The length of second leg = x - 9
the length of one leg of a right triangle is 15 m.
The first leg = 15m
Pythagoras Theorem : In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
Apply pythagoras for the value of x :
[tex]\begin{gathered} \text{ Hypotenuse}^2=Base^2+Perpendicular^2 \\ x^2=15^2+(x-9)^2 \\ x^2=225+x^2+81-18x \\ x^2-x^2=225+81-18x \\ 18x=306 \\ x=\frac{306}{18} \\ x=17 \end{gathered}[/tex]as x represent the hypotnuese, SO
Hypotenuse = 17m
find the slope of the line
Slope of a Line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Two clear points are visible in the graph of the figure: (0,1) and (4,0).
Note: I'm assuming each division of the grid has a measure of one unit.
Applying the formula:
[tex]\displaystyle m=\frac{0-1}{4-0}=\frac{-1}{4}=-\frac{1}{4}[/tex]The slope of the line is -1/4.
Jerry bought a $78 table on sale for 20% off. The best estimate for the discount can be found using which expression? 0.2(80) 0.2170)
1) Gathering the data
$78 20% off
2) To find the final price Jerry has paid just multiply
78----20%
3) So, the expression used was 78 x (0.8) and Jerry has paid $62.4 for the table
Choose all that give the correct effect on the linear graph of the parent function ƒ(x).f(x) is replaced with f(x) + 5 shifts the line 5 units upf(x) is replaced with f(x − 8) shifts the line 8 units leftf(x) is replaced with 4f(x) stretch vertically by a factor of 4f(x) is replaced with f(3x) compress horizontally by a factor of 1/3
Since the parent function is f(x), then
f(x) + 5 is the shifted 5 units up of f(x)
Then the first answer is correct
f(x - 8) is shifted 8 units right of f(x)
Then the second answer is wrong
f(x) is replaced by 4f(x) means it stretched vertically by a factor of 4
Then the third answer is correct
f(x) is replaced by f(3x) means it compressed horizontally by a scale factor of 1/3
Then the fourth answer is correct
evaluate the expression [tex]2(2 {}^{5)} [/tex]
64
Explanation
[tex]2(2^5)[/tex]Step 1
operate the exponent,so
[tex]\begin{gathered} 2(2^5) \\ 2(2\cdot2\cdot2\cdot2\cdot2) \\ 2(32) \end{gathered}[/tex]Step 2
now, do the multiplication.
[tex]\begin{gathered} 2(32) \\ 64 \end{gathered}[/tex]so, the answer is 64
I hope this helps you
Analyzing rays and segments which statements are true regarding the diagram check all that apply
It can be observed that point C and point B does not lie on the line n, so CB is not contained in line n.
The point C and point E lie on the line m, so CE is contained on the line m.
The ray BC has start point as B , where as ray CB has start point as C. So ray BC and ray CB are different.
The ray AD and ray AC both has same starting point A, where as end point of both ray AD and AC is collinear. So ray AD is same as ray AC.
The angle EAD is formed by the ray AE and ray AD. The statement angle EAD is created from AE and DA is wrong as ray DA is different from AD.
The angle ECB is created by the ray CE and ray CB with common vertex at C. So statement angle ECB is created from ray CE and CB is correct.
Answer:
Correct statements are,
CE is contained on line m.
Ray AD is same as ray AC.
Angle ECB is created from ray CE and ray CB.
A candy store sells different sized bags of jelly beans. The line plot shows the welghts of ten bags. Weight of Jelly Bean Bags X XXXala x X+CO i colwt inloo - 50 1 Pounds Mikalya bought all of the bags weighing less than 2 pound. How many pounds of jelly beans did Mikalya buy? OA pound pound OB. is pound pound
bags less than 3/8
[tex]\begin{gathered} \frac{1}{4}\longrightarrow2 \\ \\ \frac{1}{8}\longrightarrow1 \end{gathered}[/tex]are 3
to fin the total pounds we multiply each weight by the number of bags
[tex]\begin{gathered} \frac{1}{4}\times2=\frac{1}{2} \\ \\ \frac{1}{8}\times1=\frac{1}{8} \end{gathered}[/tex]now sum
[tex]\begin{gathered} \frac{1}{2}+\frac{1}{8} \\ \\ \frac{(8\times1)+(2\times1)}{8\times2} \\ \\ \frac{8+2}{16} \\ \\ \frac{10}{16}=\frac{5}{8} \end{gathered}[/tex]total weight is 5/8pounds
According to an oil company. In a particular year, a certain country used 15.881,567 barrels of ol a day, and worldwide, people used around 85,993,660 barrels of oil per day. This includes oil used for (among other things) fuel and manufacturingthere were 303 million people in the country for this year, what was the daily consumption rate per person in the country?The daily consumption rate is about barrels per day per person in the country(Round to the nearest hundredth as needed.)
In this case the answer is very simple. .
Step 01:
Data
country = 158,815,67 barrels / day
people = 85,993,660 barrels / day
303,000,000 people in the country
Step 02:
daily consumption per day
[tex]\frac{85993660\text{ barrels/day}}{303000000\text{ people}}[/tex]0.28 barrels/day / people
The answer is:
The daily consumption rate per person in the country is 0.28
a) y=2xb) y=2x+2c) y= -2x + 2d) y=2x - 2
Answer
Option D is correct.
y = 2x - 2
Explanation
The key to picking the right equation that fits the data in the table is to check each of the options.
Option A
y = 2x
when x = -3,
y = 2x
y = 2(-3)
y = -6
-6 ≠ - 8
Hence, this option is not correct.
Option B
y = 2x + 2
when x = -3,
y = 2x + 2
y = 2(-3) + 2
y = -6 + 2 = -4
-4 ≠ - 8
Hence, this option is not correct.
Option C
y = -2x + 2
when x = -3,
y = -2x + 2
y = -2(-3) + 2 = 6 + 2
y = 8
8 ≠ - 8
Hence, this option is not correct.
Option D
y = 2x - 2
when x = -3
y = 2 (-3) - 2
y = -6 - 2
y = -8
-8 = -8
This is the correct option.
Hope this Helps!!!
What is the sum of a 7-term geometric series if the first term is −11, the last term is −45,056, and the common ratio is −4? A −143,231B −36,047C 144,177D 716,144
the first term is −11
the last term is −45,056
the common ratio is −4
the formula for geometric series is
[tex]\begin{gathered} a+ar+ar2+ar3+\ldots \\ \sum ^n_1a_1r^{n-1} \\ \text{solution formula:} \\ S_n=a_1\frac{1-r^n}{1-r} \end{gathered}[/tex]where
r = -4
a1 = -11
n = 7
therefore,
[tex]S_7=(-11)\frac{1-(-4)^7}{1-(-4)}[/tex]let's simplify
[tex]\begin{gathered} S_7=(-11)\frac{1-(-4)^7}{1-(-4)}=-11\cdot\frac{1-(-16384)}{1+4}=-11\cdot\frac{1+16384}{1+4}=-11\cdot\frac{16385}{5} \\ S_7=-11\cdot\: 3277 \\ S_7=-36047 \end{gathered}[/tex]Thus, the answer is -36047
A truck averages 16 miles per yulion and has a 25 gallon gas tank. What is the furthest distance the truck can travel without stopping for gas?
A truck averages 16 miles per gallon and has a 25 gallon gas tank. What is the furthest distance the truck can travel without stopping for gas?
Apply proportion
16/1=x/25
solve for x
x=16*25
x=400 miles
answer is 400 milesA rectangle is inscribed with its base on the -axis and its upper corners on the parabola y = 7 - x ^ 2 What are the dimensions of such a rectangle with the greatest possible area?
The width = 3.06
The height = 4.66
Explanation:The rectangle is inscribed with its base on the -axis and its upper corners on the parabola
Width = 2x
Height = 7 - x²
Area of the inscribed rectangle:
Area = width x height
A = 2x (7 - x²)
A = 14x - 2x³
Take the derivative of the area (A) and equate to zero
A' = 14 - 6x²
0 = 14 - 6x²
6x² = 14
x² = 14/6
x² = 2.33
x = √2.33
x = 1.53
The width = 2x
The width = 2(1.53)
The width = 3.06
Substitute x = 1.53 into the equation y = 7 - x² to solve for the height
y = 7 - 1.53²
y = 4.66
The height = 4.66
Identify the term that completes the equation. XZ2=(WZ) (?)Please help
Given triangles, XZW and XZY are right-angle triangles.
Using the Pythagorean theorem for XZW, we get
[tex]XZ^2+WZ^2=WX^2[/tex]Using the Pythagorean theorem for XZY, we get
[tex]XZ^2+XY^2=ZY^2[/tex][tex]XZ^2=ZY^2-XY^2[/tex]Using the Pythagorean theorem for WXY, we get
[tex]WX^2+XY^2=WY^2[/tex][tex]undefined[/tex]