The midpoint (a, b) = (1, -1)
One endpoint, (x₁, y₁) = (3, 8)
The other endpoint, (x₂, y₂) = ?
Using the formula for midpoint and solving for the missing parameters
[tex]\begin{gathered} a=\frac{x_1+x_2}{2} \\ \\ 1=\frac{3+x_2}{2} \\ \\ 2=3+x_2 \\ \\ x_2=2-3 \\ \\ x_2=-1 \end{gathered}[/tex][tex]\begin{gathered} b=\frac{y_1+y_2}{2} \\ \\ -1=\frac{8+y_2}{2} \\ \\ -2=8+y_2 \\ \\ y_2=-2-8 \\ \\ y_2=-10 \end{gathered}[/tex]The coordinates of the other endpoint = (-1, -10)
To adopt a dog from an animal shelter, you must pay $90 for vaccinations, $75 to spay or neuter the dog, and $40 for a wellness exam by a veterinarian. a. Write an expression in simplest form that represents the amount (in dollars) it costs to adopt x dogsb. What does the coefficient of the expression in part (a) represent?
1) Gathering the data
pay $90 for vaccinations,
$75 to spay or neuter the dog,
and $40 for a wellness exam
Let x be the price of the dog.
2) Since all of these expenses represent money out, or less money in your wallet. And all of these prices refer to the adoption of one dog then We can state
C=(90+75+40)x
C= 205x
Solve the equation for the variable. 5.3 = 2 - 2.7 I
We are asked to solve for the variable in the equation:
5.3 = z - 2.7
SO we need to isolate the variable "z" on one side of the equal sign. for that we add 2.7 to both sides:
5.3 + 2.7 = z - 2.7 + 2.7
combining like terms we get:
8 = z + 0
8 = z
Therefore z is 8.
can someone help me with this one ? list the first 15 perfect cubes:
We have the following exercise
What is a cube of a number x?
The answer is to multiply this number or quantity 3 times. For example:
1^3 = 1 x 1 x 1 = 1,
2^3 = 2x 2 x 2 = 8
4^3 = 4x4x4 = 64
and so on.
Equivalently, let represent with a stick a unity 1: so for example
So if we want 2^3, is the same to say:
that is 2^3 = 8
It used to cost $33.00 to buy a case of 23 bottles of Sriracha. Because of the shortage, each case is now $50.00. How MUCH MORE is each bottle of Sriracha?
The amount of money that each bottle of sriracha would cost more would be = $0.82
What is product shortage?Product shortage is definitely as the decrease in the availability of a product in the market or decrease in its production.
The cost of a case of sriracha = $33.00
The amount of a case after the shortage = $50.00
The amount of bottles that is found in case = 23
The amount of each bottle before shortage = 23/33 = $0.70
The amount of each bottle after shortage = 50/33 =
$1.52
The amount of money that each bottle of sriracha would cost more = 1.52 - 0.70 = $0.82
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input is complete.A parallelogram has a base of 9 units and an area of 12 square units. What is the corresponding height for that base? Remember: Area parallelogram = b × h
As written in the Question Tab, the area of the parallelogram can be solved by multiplying the base and the height. Since we already have the base = 9 units and its area which is 12 square units, the first and last thing to do is divide the area by the base to solve the height of the parallelogram. See computation below:
[tex]\begin{gathered} \text{area = base}\times\text{height} \\ 12=9\times h \\ Divide\text{ both sides by 9.} \\ \frac{12}{9}=\frac{9h}{9} \\ \frac{4}{3}or\text{ 1.33 = h} \end{gathered}[/tex]Therefore, the height of the parallelogram is 4/3 or 1.33 units.
QuestionA cylinder has height 6 meters and radius 5 meters. Find the a. volume and b. surface area. Use 3.14 for. Do not round.
Problem: A cylinder has a height 6 meters and a radius 5 meters. Find the a. volume and b. surface area. Use 3.14 for. Do not round.
Solution:
Remember that the volution of cylinder is given by the following equation:
[tex]V\text{ =}\pi\text{r}^2h[/tex]where r is the radius of the cylinder and h is the height of the cylinder. In this case, we have that:
[tex]V\text{ =}\pi\text{r}^2h=\pi5^2\text{ x 6 = 150}\pi\text{ = 471.23}[/tex]So we can conclude that the volume of the cylinder is 471.23
Now, for surface area, remember that the surface area for the cylinder is given by the following equation:
[tex]V=2\pi r^2+\text{ }2\pi rh[/tex]where r is the radius of the cylinder and h is the height of the cylinder. In this case, we have that:
[tex]V=2\pi r^2+\text{ }2\pi rh\text{ = 2}\pi(5)^2\text{ + 2}\pi(5)(6)\text{ = 110}\pi\text{ = 345.57}[/tex]So we can conclude that the surface area for the cylinder is 345.57
An ostrich ran 4,200 meters to the west at a constant velocity. it ran that distance in 1,200 seconds. what was it's velocity?
distance : 4,200 meters
time : 1,200 seconds
To find the velocity we have to apply the next formula:
Velocity = Distance / time
Replacing with the values given:
Velocity = 4,200 m / 1,200 sec = 3.5 meters per second
Velocity = 3.5 m/sec
I need help with a graph problem please that I am stuck on.
Solution:
First we have to derive the equation of the graph plot.
The general equation of an absolute value function is expressed as
[tex]\begin{gathered} y=a|x-h|+k\text{ --- equation 1} \\ \text{where} \\ (h,k)\text{ is the coordinate of the vertex of the function } \end{gathered}[/tex]step 1: Determine the coordinates (h,k) of the vertex of the graph.
The vertex of the function is the point at which the graph changes direction.
In tha above plot, the vertex of the plot is (-3,4).
Thus,
[tex]\begin{gathered} h=-3 \\ k=4 \end{gathered}[/tex]step 2: Substitute the respective values of -3 and 4 for h and k into equation 1.
Thus,
[tex]\begin{gathered} y=a|x-h|+k \\ \Rightarrow y=a|x-(-3)|+4\text{ ---- equation 2} \\ \end{gathered}[/tex]step 3: Select any point (x,y) on the graph plot, to evaluate a.
Thus, using the point (1,0), we have
[tex]\begin{gathered} y=a|x+3|+4 \\ x=1,\text{ y=0} \\ \Rightarrow0=a|1+3|+4 \\ -4=|4|a \\ \Rightarrow a=-1 \end{gathered}[/tex]step 4: Substitute the obatined value of a into equation 2.
Thus,
[tex]y=-|x+3|+4\text{ ----- equation 3}[/tex]Thus, the equatioin of the graph is evaluated to be
[tex]y=-|x+3|+4[/tex]A) Evaluate f(4).
To evaluate f(4), substitute the value of 4 for x into the derived equation.
Thus,
[tex]\begin{gathered} y=-|x+3|+4 \\ x=4 \\ \Rightarrow y=-|4+3|+4 \\ \therefore y=-3 \end{gathered}[/tex][tex]f(4)=-3[/tex]B) Solve for f(x)=2.
To solve, we have
[tex]\begin{gathered} -|x+3|+4=2 \\ \text{subtract 4 from both sides of the equation} \\ -|x+3|+4-4=2-4 \\ -|x+3|=-2 \\ \text{divide both sides by -1} \\ \frac{-|x+3|}{-1}=-\frac{2}{-1} \\ \Rightarrow|x+3|=2 \\ \text{When }x+3=-2 \\ x=-2-3 \\ \Rightarrow x=-5 \\ \text{when }x+3=2 \\ x=2-3 \\ \Rightarrow x=-1 \end{gathered}[/tex]Thus, we have
[tex]x=-5;-1[/tex]During a job interview, Pam Thompson is offered a salary of $32,000. The company gives annual raises a 4%. What will be Pam’s salary during her fifth year on the job? (Round time value factor to three decimal places and final answer to the nearest whole number.)
We will have the following:
First, we construct the equation that describes the scenario:
[tex]P(x)=32000(1+0.04)^x[/tex]Now, we will determine her salary at the 5th year at her job:
[tex]P(x)=32000(1+0.04)^5\Rightarrow P(5)=38932.89288[/tex][tex]\Rightarrow P(5)\approx38932.893[/tex]So, her salary after 5 years would be approximately $38933.
9Find the percentage change from the first quantity to the second quantity:From 60 km/h to 45 km/h.Answer:%
To calculate the percentage change;
From 60km/h to 45km/h is a decrease
So we will calculate the decrease = 60 - 45 =15
Divide 15 by the original value which is 60 and then multiply by 100%
That is;
Percentage change = 15/60 x100%
=25%
The shaded area is 120T cm?, and the radius is 24 cm. Find X.
We will have the following:
[tex]A=(\frac{x}{2})\cdot r^2\Rightarrow120\pi=(\frac{x}{2})(24)^2[/tex][tex]\Rightarrow\frac{x}{2}=\frac{5\pi}{24}\Rightarrow x=\frac{5\pi}{12}[/tex][tex]\Rightarrow x\approx1.31[/tex]So, the value of x is approximately 1.31.
What expression shows 50 + 30 written as a product of 2 factors?
(A)5(10+ 7)
(B)5(10+ 3)
(C)10(5+ 2
(D)10(5+ 3)
need answers fast pleazz
Answer:
D
Step-by-step explanation:
distribute the 10 to (5+3) and you get 50+30
A gets you 50+35
B gets you 50+15
C gets you 50+20
D gets you 50+30
The following is the cost function for natural gas for the city where Greg lives. Greg's natural gas bill last month was $51.54. How many therms did Greg use last month? Round the answer to the nearest tenth of a therm (one decimal place). Only input the number. Do not input any unit. Example: 89.3
Kauro, this is the solution:
This is the cost function for natural gas for the city where Greg lives:
• c (t) = 16.74 + 0.742t
Now we replace c (t) by 51.54 to solve for t, as follows:
51.54 = 16.74 + 0.742t
Subtracting 16.74 at both sides:
51.54 - 16.74 = 16.74 + 0.742t - 16.74
34.8 = 0.742t
Dividing by 0.742 at both sides:
0.742t/0.742 = 34.8/0.742
t = 46.9 therms
The correct answer is 46.9
suppose they are a T V cost in an election between three Canadians then who is Garza and we see to be decided by polarity of the first 55 votes are counted the Titleist are as followed
a) We have the votes for 55 people out of 80.
We have to find the minimum number of votes needed by Donahue to be sure that he will win the election.
There are 80 - 55 = 25 votes remaining.
Donahue has 24 votes already. The second candidate in number of votes has 18 votes, which is a difference of 6 votes.
We can think of a situation where the remaining votes are given to this two candidates and both have the same votes.
This would mean an amount of 24 + 18 + 25 = 67 votes.
Then, they won't have the same votes but we can think of Donahue having 67/2 = 33.5 ≈ 34 votes, and Garza having 33.
Then, this is the most extreme situation where Donahue wins by one vote.
We can then calculate the difference of votes he needs as 34 - 24 = 10 votes.
b) We can think again the same situation, but with Garza having 34 votes and Donahue having 33 votes.
This the extreme situation where Garza wins by the minimum difference.
Then, Garza would have to add 34 - 18 = 16 votes at least to win in this situation.
Answer:
a) Donahue needs 10 more votes to be sure he wins the election.
b) Garza needs at least 16 votes to be sure he wins the election.
Given: _A and B form a linear pair,_B and C are complementary, and m_A = 103°Prove: m C = 13°Statement:Reason:1. _A and B form a linear pair 1. Given2. m A+ m B = 180°2. Postulate3. mA = 103°3. Given4. 103° + m B = 180°4. Substitution5. m2B = 77°5.[?]6. B and C are complementary 6. Given7. m B + m C = 90°7. Definition8. 77° + m2 = 90°8. Substitution9. m C = 13°9.Select the reason that bestsupports Statement 5 in thegiven proof.A. Multiplication Property of EqualityB. Subtraction Property of EqualityC. Division Property of EqualityD. Addition Property of Equality
SOLUTION
Statement 4, states that
[tex]103^o+mJohn was asked to place the numbers shown below in order from greatest to least. 0.2 , -0.3, 1.6, 120%, -2%, 3.8, --33, 3.14 After ordering the numbers from greatest to least, what number would John have in the 3rd position?
Let's begin by listing out the information given to us:
0.2, -0.3, 1.6%, 120%, -2%, 3.8, -33, 3.14
In sorting the numbers from the greatest to the least, we must bear the following in mind:
I. Any number having a negative parenthesis is lower than zero
II. % means 100; any number having % means the real value of the number is multiplied by 100
0.2 = 0.2
-0.3 = -0.3
1.6% = 1.6 * 100 = 160
120% = 120 * 100 = 12000
-2% = -2 * 100 = -200
3.8 = 3.8
-33 = -33
3.14 = 3.14
Rearranging from the greatest to the least, we have it thus:
120%, 1.6%, 3.8, 3.14, 0.2, -0.3, -33, -200
The number in the third position is 3.8
Hello! I got -560 just want to confirm my answer. Thanks!
Explanation
We are given the following series:
[tex]12+4-4-12-20-...[/tex]We are required to determine the sum of the first 14 terms of the given series.
This is achieved thus:
We know that the sum of n terms of a series is given as:
[tex]\begin{gathered} S_n=\frac{n}{2}[2a+(n-1)d] \\ where \\ a=first\text{ term} \\ d=common\text{ difference} \\ n=number\text{ of terms} \end{gathered}[/tex]Therefore, we have:
[tex]\begin{gathered} S_n=\frac{n}{2}[2a+(n-1)d] \\ where \\ a=12 \\ d=4-12=-8 \\ n=14 \\ \\ \therefore S_{14}=\frac{14}{2}[2\cdot12+(14-1)-8] \\ S_{14}=7[24+(13)-8] \\ S_{14}=7(24-104) \\ S_{14}=7\cdot-80 \\ S_{14}=-560 \end{gathered}[/tex]Hence, the answer is:
[tex]S_{14}=-560[/tex]which statement is true?6 is 4 times as many as 26 is 3 times as many as 26 is 2 times as many as 26 is 12 times as many as 2
6 is 3 times as many as 2, because:
[tex]\begin{gathered} 6=3+2 \\ 6=3+3 \end{gathered}[/tex]I have been struggling with this problem for around 2 hours and can’t seem to get it
the quotient rule say:
[tex](\frac{f(x)}{g(x)})^{\prime}=\frac{g(x)\cdot f^{\prime}(x)-f(x)\cdot g^{\prime}(x)}{(g(x))^2}[/tex]now we defined:
[tex]\begin{gathered} f(x)=-4x^2+16 \\ g(x)=(x^2+4)^2 \end{gathered}[/tex]and the derivative:
[tex]\begin{gathered} f^{\prime}(x)=-8x \\ g^{\prime}(x)=2\cdot(x^2+4)\cdot2x \\ g^{\prime}(x)=4x(x^2+4) \end{gathered}[/tex]so now we can replace on the quotient rule:
[tex]\frac{(x^2+4)^2\cdot(-8x)-4x(x^2+4)\cdot(-4x^2+16)}{(x^2+4)^4}[/tex]now we can use properties, like:
[tex](x^2+4)^2=x^4+8x+16[/tex](-4, 6); slope = - 3/4write the linear equation in slope intercept form given
We know the slope = -3/4 and a point = (-4, 6) of a line, and we wnat to find the equation in the slope-intercept form, so:
[tex]\begin{gathered} \text{The general slope-intercept form of a line is:} \\ y=mx+b \\ \text{Where m is the slope and b is the value of y-intercept} \end{gathered}[/tex]In this case, m=-3/4 and evaluating the point (-4, 6) we can find the value of b:
[tex]\begin{gathered} \text{With m=-3/4 and the point (x, y) = (-4, 6):} \\ 6=-\frac{3}{4}(-4)+b \\ 6=3+b \\ b=6-3 \\ b=3 \end{gathered}[/tex]We found that b = 3, so the equation of the line is:
[tex]y=-\frac{3}{4}x+3[/tex]Solve the equation for y in terms of x. In other words, algebraically rearrange the equation so that the y variable is by itself one side of the equation. Type your answer in the form y=mx+b. If you have a value that is not an integer then type it rounded to the nearest hundredth. Do not put spaces between your characters.5x+2y=0y=Answer
we have the equation
5x+2y=0
solve for y
step 1
subtract 5x on both sides
5x+2y-5x=0-5x
simplify
2y=-5x
step 2
Divide by 2 on both sides
2y/2=-5x/2
y=-(5/2)x
y=-2.50xFind the length of AB.6 in A30°BAB = [ ?Round your answer to the nearest hundredth.
Which of the following is the graph of the quadratic function y = x2 - 6x -
Therefore,
From the graph above,
The correct answer is OPTION C
I need help with a math homework0.25kg=______g
We know that 1 kilogram is equivalent to 1,000 grams. This our conversion factor, knowing this, we transform 0.25 kg.
[tex]0.25\operatorname{kg}\cdot\frac{1,000gr}{1\operatorname{kg}}=250gr[/tex]Therefore, the answer is 250 grams.What is the product of 8V 5 and 5/10 in simplest radical form?
Given the numbers:
[tex]8\sqrt[]{5},5\sqrt[]{10}[/tex]The product of the numbers will be:
[tex]\begin{gathered} 8\sqrt[]{5}\times5\sqrt[]{10}=8\times5\sqrt[]{5\times10}=40\sqrt[]{50} \\ \\ 50=25\times2=5^2\times2 \\ \\ 40\sqrt[]{50}=40\sqrt[]{5^2\times2}=40\times5\sqrt[]{2}=200\sqrt[]{2} \end{gathered}[/tex]So, the answer will be:
[tex]200\sqrt[]{2}[/tex]When given two points and asked to find the equation of the line in slope-intercept form, what are the correct steps? Place a number next to the step to put them in order.
Given
given two points and asked to find the equation of the line in slope-intercept form
Find
what are the correct steps? Place a number next to the step to put them in order.
Explanation
to find the equation of the line in slope intercept form form given two points.
step 1 :
find the slope.
step 2
write equation in point slope form
step 3.
pick a point form the given points , substitue it into the point slope form
step 4.
write the equation in slope intercept form by simplifying
Final Answer
Hence , the correct order is 2 , 1 , 4 , 3
Hi i need some help on question 11 b and c. I have already done a
ANSWER:
a. 16.27 cm^3
b. 4.3 cm
c. 325.4 seconds
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the value of the volume, which is the sum of the volume of each part, like this:
[tex]\begin{gathered} V=V_t+V_c+V_s \\ r=\frac{d}{2}=\frac{2.6}{2}=1.3 \\ V_t=A_b\cdot\frac{h}{3}=\pi\cdot(r)^2\cdot\frac{h}{3}=3.14\cdot(1.3)^2\cdot\frac{1.2}{3}=2.12cm^3 \\ V_c=A_b\cdot h=\pi\cdot(r)^2\cdot h=3.14\cdot(1.3)^2\cdot1.8=9.55m^3 \\ V_s=\frac{4}{6}\cdot\pi\cdot r^3=\frac{4}{6}\cdot3.14\cdot(1.3)^3=4.6cm^3 \\ V=V_t+V_c+V_s \\ V=2.12+9.55+4.6 \\ V=16.27cm^3 \end{gathered}[/tex]The volume of the upper container is 16.27 cm^3, and being symmetrical, it is the same for the bottom container.
At the moment that all the sand finishes going to the bottom container, the height will be the sum of the heights in each case.
Then:
[tex]\begin{gathered} h=1.2+1.8+1.3 \\ h=4.3\text{ cm} \end{gathered}[/tex]Therefore, the height is 4.3 centimeters
To reach that height, all the sand had to be passed from one side to the other, therefore, we can calculate the time as follows:
[tex]\begin{gathered} t=\frac{16.27cm^3}{0.05\frac{cm^3}{s}} \\ t=325.4\text{ sec} \end{gathered}[/tex]It would take a time of 325.4 seconds
9) 59 is 93 percent of what?
93 Let the unknown number be X,
( 59/ X ) = 93 /100
Cross - multiply,
59 x 100 = 93 x x
x = ( 59 x100) divided by 93
x= 5900 / 93
x = 63.44 _
Answer:
Step-by-step explanation:
59 = 93%(X)
59 = 93/100*(x)
59*100 = 93(x)
5900/93 = x
63.44 = x
Hence 59 is 93 percent of 63.44
PR = 9x -31 and QR = 43: Find xQ is the midpoint of PR
We can model the situation as:
Since Q is the midpoint of PR, QR and PQ have the same length, so PQ is also equal to 43.
Now, we can formulate the following equation:
PR = PQ + QR
So, replacing PR by 9x-31, PQ by 43 and QR by 43, we get:
9x - 31 = 43 + 43
9x - 31 = 86
Solving for x:
9x - 31 + 31 = 86 + 31
9x = 117
9x/9 = 117/9
x = 13
Answer: x = 13
Write the equation containing the points (-2,4) and (1,10).
Answer:
y=2x+8
Explanation:
Given the two points:
[tex]\begin{gathered} (x_1,y_1)=(-2,4) \\ \mleft(x_2,y_2\mright)=\mleft(1,10\mright) \end{gathered}[/tex]In order to find the equation of the line connecting them, we employ the use of the two-points formula given below:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the values:
[tex]\frac{y-4}{x-(-2)}=\frac{10-4}{1-(-2)}[/tex]Next, simplify:
[tex]\begin{gathered} \frac{y-4}{x+2}=\frac{6}{3}=2 \\ \implies y-4=2(x+2) \\ \implies y=2(x+2)+4 \\ \implies y=2x+4+4 \\ \implies y=2x+8 \end{gathered}[/tex]The equation containing the points (-2,4) and (1,10) is y=2x+8.