Which of the following equations describes the line shown below? Check allthat apply.(-2,6)(4,3)A. y-3 = -1/2 (x-4)B. y-6 = -1/2 (x+2)C. y-3 = -2 (x-4)D. y-6 = -1/2 (x-2)E. y-4 = -1/2 (x-3)F. y-6 = -2 (x+2)
Answers
To find the equation of the line, we will use the formula;
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_{1)}[/tex]The points given are;
(-2, 6) and (4, 3)
x₁ = -2 y₁=6 x₂=4 y₂=3
Substitute the value into the formula
[tex]y-6=\text{ }\frac{3-6}{4+2}(x+2)[/tex]Evaluate
[tex]y-6=\frac{-3}{6}(x+2)[/tex][tex]y-6=-\frac{1}{2}(x+2)[/tex]The correct option is B
Related Questions
At Jebel Jais in UAE, there is a 40-mile mountain bike trail. Khaled rode ½ of the trail on Saturday and 1/9 of the trail on Sunday. He estimates that he rode more than 22 miles over the two days.What is the estimate of 1/2 + 1/9
Answers
The estimate of 1/2 + 1/9 is 24.444...
Explanation:Given that:
Khaled rode 1/2 of the trail on Saturday, and 1/9 of the trail on Sunday.
Since he estimated that he rode more than 22 miles over the two days.
1/2 of 40 = 1/2 * 40 = 20
1/9 of 40 = 1/9 * 40 = 4.4444...
His total ride was 24.4444...
Find the volume of the following figure.1.5m2.5 m6 m
Answers
Start by dividing the figure into 2 prisms
calculate the volume for both independently.
For the rectangular prism
[tex]V=l\cdot w\cdot h[/tex]then,
[tex]\begin{gathered} V=2\cdot2.5\cdot1.5 \\ V=7.5m^3 \end{gathered}[/tex]For the triangular prism
[tex]V=\frac{1}{2}l\cdot h\cdot w[/tex]then,
[tex]\begin{gathered} V=\frac{1}{2}\cdot1.5\cdot4\cdot2.5 \\ V=7.5m^3 \end{gathered}[/tex]Add both volumes together
[tex]\begin{gathered} V_t=7.5m^3+7.5m^3 \\ V_t=15m^3 \end{gathered}[/tex]A taxi charges a flat rate of S8 plus $2 per mile travelled. Write an equation to represent the total cost of ajourney. (Let d miles - distance travelled)A total cost = 8d + 2B. total cost = 8d + 2dC. total cost = 8 + 2dD. total cost = 812 + d)
Answers
Flat rate: $8
Cost per mile : $2
distance = d (miles)
To find the total cost, we have to add the flat rate (8) and the product of the cost per mile (2) and the distance traveled(d).
Total cost = 8+2d (option C)
what is 2 1/2 ÷ 1/3 ?
Answers
SOLUTION
Given the question in the question tab, the following are the solution steps to get the answer
Step 1: Write the expression
[tex]2\frac{1}{2}\text{ }\frac{.}{.}\text{ }\frac{1}{3}[/tex]Step 2: Solve the expression by following these steps
Convert the mixed fraction to an improper fraction
[tex]2\frac{1}{2}=\frac{(2\times2)+1}{2}=\frac{4+!_{}}{2}=\frac{5}{2}[/tex]Rewrite the expression and perform the division
[tex]\begin{gathered} \frac{5}{2}\text{ }\frac{.}{.}\text{ }\frac{1}{3} \\ \text{Turn the divide to multiplication, this inverts the expression after the division sign} \\ \frac{5}{2}\times\frac{3}{1}=\frac{5\times3}{2}=\frac{15}{2}=7\frac{1}{2} \end{gathered}[/tex]Hence, the solution of the expression is
[tex]\frac{15}{2}\text{ or }7\frac{1}{2}[/tex]find the zeros of the function f( x) equals x squared plus 2X minus 3
Answers
f(x) =x² + 2x - 3
The zeros of the function is the x-value for which the function equals to zero.
To find such x-value, simply substitute f(x) =0 and the solve forx
x² + 2x - 3 =0
We can solve using the factorization method
Find two numbers such that its product gives -3 and its sum gives 2.
The numbers are : +3 and -1
Replace the coefficient of x by the two numbers
x² + 3x - x - 3 = 0
x(x+ 3) - 1(x+3) = 0
(x+3)(x- 1) = 0
x+3 = 0 and x- 1 = 0
x = -3 and x= 1
Therefore, the zeros of the functions are: D)(-3,0) and (1,0)
Jalme drew a snowflake on graph paper. What is its area in square unit? Show your work
Answers
We can divide the snowflake into a big square and a 2 small squares as:
The big square has side c with measure
[tex]3^2+3^2=c^2[/tex]which was obtained from the following right triangle:
Then, c (the lenght of the square sides) is given by
[tex]\begin{gathered} c=\sqrt[]{3^2+3^2} \\ c=\sqrt[]{9+9} \\ c=\sqrt[]{2\cdot9} \\ c=3\sqrt[]{2} \end{gathered}[/tex]Therefore, the area of the big square is
[tex]\begin{gathered} A_{\text{Big}}=c^2 \\ A_{\text{Big}}=(3\sqrt[]{2})^2 \\ A_{\text{Big}}=9\cdot2 \\ A_{\text{Big}}=18units^2 \end{gathered}[/tex]Now, the sides of the small squares measure 1 unit, then the area of one small square is
[tex]\begin{gathered} A_{\text{small}}=1^2 \\ A_{\text{small}}=1units^2 \end{gathered}[/tex]Finally, the total area is
[tex]A=A_{\text{big}}+4\cdot A_{\text{small}}[/tex]By substituting the last results, we get
[tex]\begin{gathered} A=18+4\cdot1 \\ A=18+4 \\ A=22units^2 \end{gathered}[/tex]that is, the area of the snowflake is 22 units^2.
Find the midpoint of AB. A is at (7,-8) and B is at (-3, 6).
Answers
The midpoint is the average of the x coordinates and the average of the y coordinates given.
Given the 2 pair of points:
A = (7, - 8)
B = (-3, 6)
Let the midpoint have coordinates (x, y).
To find x, we take the average of x-coordinates of A and B, shown below.
[tex]\begin{gathered} x=\frac{7-3}{2} \\ x=\frac{4}{2} \\ x=2 \end{gathered}[/tex]To find y, we take the average of y-coordinates of A and B, shown below.
[tex]\begin{gathered} y=\frac{-8+6}{2} \\ y=-\frac{2}{2} \\ y=-1 \end{gathered}[/tex]The midpoint is (2, -1)Hello, I need help solving this word problem for the dimensions of a rectangle. Thank you so much !
Answers
Let's use the variable L to represent the length and W to represent the width.
If the length is 3 yd less than double the width, we can write the following equation:
[tex]L=2W-3[/tex]If the area is equal to 14 yd², we have this equation:
[tex]L\cdot W=14[/tex]Let's use the value of L from the first equation into the second one, then we solve the resulting equation for W:
[tex]\begin{gathered} (2W-3)\cdot W=14 \\ 2W^2-3W=14 \\ 2W^2-3W-14=0 \\ W=\frac{-(-3)\pm\sqrt[]{(-3)^2-4\cdot2\cdot(-14)}}{2\cdot2} \\ W=\frac{3\pm\sqrt[]{9+112}}{4} \\ W=\frac{3\pm11}{4} \\ W_1=\frac{3+11}{4}=\frac{14}{4}=3.5 \\ W_2=\frac{3-11}{4}=-\frac{8}{4}=-2 \end{gathered}[/tex]Since a negative value for the width is not valid, we have W = 3.5 yd.
Now, calculating the length, we have:
[tex]\begin{gathered} L=2W-3 \\ L=2\cdot3.5-3 \\ L=7-3 \\ L=4\text{ yd} \end{gathered}[/tex]Therefore the length is 4 yards and the width is 3.5 yards.
Two artist are mixing up green paint for a mural The first artist Shane mixes 3 parts blue and 2 parts yellow to make a shade of green. The second artist nora mixes 5 parts blue and 3 parts yellow to make another shade of green. Whose green paint mixture will be more yellowish? explain your reasoning
Answers
First artist: (shane)
3 part blue
2 part yellow
Total of 5 part
2 are yellow from 5 parts
That is
2/5 = 0.4 * 100 = 40%
Second artist: (nora)
5 part blue
3 part yellow
Total 8 part
3 are yellow from 8 parts
That is
3/8 = 0.375 * 100 = 37.5%
So,
Shane's mixture will be more yellowish
Mrs. Mazzucco dumps out her change purse and finds that
she has 15 coins, all dimes and quarters, for a total of $2.70.
How many quarters does she have?
Answers
Answer: 10 quarters and 2 dimes.
Step-by-step explanation:
4 quarters = 1 dollar
1 quarter = 25 cents
1 dime = 10 cents
If 4 quarters are 1 dollar then 2 dollars would be 8 quarters.
8 quarters + 2 quarters (50 cents) would be 2.50
You cant add another quarter or that would be 2.75.
Instead you do: 10 quarters + 2 dimes = 2.70
So to sum it all up there are 10 quarters and 2 dimes.
21.A taxi charges a base fee of $3.00 and $0.15 for every mile of the ride. What would be thecost of a 3.4 mile ride?A $0.51B $3.51C $10.20D $10.35
Answers
Given:
Base Charge of the taxi = $3.00
Charge of the ride per mile = $0.15
The base fee here is constant, irrespective of the distance covered.
Therefore, the cost of a 3.4 mile ride will be:
[tex]\begin{gathered} (0.15\ast\text{ 3.4) }+\text{ \$3} \\ =0.51\text{+ \$3 = \$}3.51 \end{gathered}[/tex]Therefore, the cost of a 3.4 mile ride will be $3.51
ANSWER:
$3.51
0 2 20) 5x - (x + 2) >-5(1 + x) + 3 섥놈 SXX2=55*3 x>0 4.x.-25-5x-2 Darsx-23-2 985-272 vhose 22) Name one particular solution to question #20.
Answers
5x - (x + 2) > -5(1 + x) + 3
Removing parentheses and distributing
5x - x - 2 > -5*1 + (-5)*x + 3
4x - 2 > -5 - 5x + 3
4x - 2 > -2 - 5x
5x is subtracting on the right, then it will add on the left
4x -2 + 5x > -2
9x - 2 > -2
2 is subtracting on the left, then it will add on the right
9x > -2 + 2
9x > 0
9 is multiplying on the left, then it will divide on the right
x > 0/9
x > 0
Every x greater than zero is a solution, like for example 1, 2, 10, etc.
Hey I need help with this practice problem Struggling to solve it The subject is trigonometry
Answers
First, let's find the values of:
[tex]\begin{gathered} \sin ^{-1}(-\frac{1}{2})=-30 \\ \cos (\pi)=-1 \end{gathered}[/tex]So:
[tex]\cos (-30)+\tan ^{-1}(-1)=\frac{\sqrt[]{3}}{2}-\frac{\pi}{4}=\frac{4\sqrt[]{3}-2\pi}{8}=\frac{2(2\sqrt[]{3}-\pi)}{2(4)}[/tex]Simplify:
Answer:
[tex]\frac{2\sqrt[]{3}-\pi}{4}[/tex]2) Choose the correct answer.There could besolutions to an inequality.infinitely manytwocommonthree
Answers
Most of the time, an inequality has more than one or even infinity solutions.
For example the inequality
[tex]x>3[/tex]The value of x can be any number greater than 3 up to infinity.
So the correct answer would be infinitely many
Can you please help me out with a question
Answers
The equation of a circle is given as
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where h,k are the centres and h =2 while k =2} \\ x,\text{ y are the points located at P, so that x = 5 and y = 4} \\ r\text{ = radius} \end{gathered}[/tex]Substituting these values into the equation of a circle yields
[tex]\begin{gathered} (5-2)^2+(4-2)^2=r^2 \\ 3^2+2^2=r^2 \\ r^2=9+4 \\ r^2=\text{ 13} \\ r\text{ =}\sqrt[\square]{13} \\ r\text{ =3.605551275} \\ r\approx3.6\text{ units} \end{gathered}[/tex]Therefore, the answer is option A
find the measure of the two missing sides for each figure below leave answer and rationalized and simplified form
Answers
Let's begin by identifying key information given to us:
We have one known angle & one side
[tex]\begin{gathered} \theta=60^{\circ} \\ adjacent(a)=2\sqrt[]{6} \\ opposite(b)=\text{?} \\ hypotenuse(c)=\text{?} \end{gathered}[/tex]Based on the information we have been provided, we will solve for the missing sides using Trigonometric Ratio (SOHCAHTOA). This is shown below:
[tex]\begin{gathered} TOA\Rightarrow\tan \theta=\frac{opposite}{adjacent} \\ tan\theta=\frac{opposite}{adjacent} \\ tan60^{\circ}=\frac{opposite}{2\sqrt[]{6}} \\ But,tan60^{\circ}=\sqrt[]{3} \\ opposite=2\sqrt[]{6}\text{ x }\sqrt[]{3} \\ opposite=2\sqrt[]{18} \\ \\ CAH\Rightarrow cos\theta=\frac{adjacent}{hypotenuse} \\ cos\theta=\frac{adjacent}{hypotenuse} \\ cos60^{\circ}=\frac{2\sqrt[]{6}}{hypotenuse} \\ But,\cos 60^{\circ}=\frac{1}{2} \\ hypotenuse\text{ x }\cos 60^{\circ}=2\sqrt[]{6} \\ hypotenuse=\frac{2\sqrt[]{6}}{\frac{1}{2}} \\ hypotenuse=\frac{2\cdot2\sqrt[]{6}}{1}=4\sqrt[]{6} \\ hypotenuse=4\sqrt[]{6} \end{gathered}[/tex]Complete the missing parts of thetable for the following function,y = (*)*xlike-2 -1y [?] 70 1[ ] 12131343
Answers
We have to find the missing parts of the table for the function:
[tex]y=(\frac{1}{7})^x[/tex]This will be done by replacing each x-value onto the function.
For x=-2We obtain:
[tex]y=(\frac{1}{7})^{-2}=(\frac{7}{1})^2=7^2=49[/tex]This means that for x=-2, the value of y is 49.
For x=0As every number (except 0) elevated to 0 is 1, we have
[tex]y=(\frac{1}{7})^0=1[/tex]This means that for x=0, the value of y is 1.
For x=2[tex]y=(\frac{1}{7})^2=\frac{1^2}{7^2}=\frac{1}{49}[/tex]This means that for x=2, the value of y is 1/49.
An extra-large rectangular chocolate bar is 4 inches longer than its width. If the perimeter ofthe bar is 16 inches, find the width of the chocolate bar. Round to one decimal place.
Answers
The perimeter of a rectangle is given by the formula
[tex]P=2L+2W[/tex]we have
P=16 in
L=W+4
substitute given values in the formula
[tex]\begin{gathered} 16=2(W+4)+2W \\ solve\text{ for W} \\ 16=2W+8+2W \\ 4W=16-8 \\ 4W=8 \\ W=2\text{ in} \end{gathered}[/tex]Find out the value of L
[tex]\begin{gathered} L=W+4 \\ L=2+4 \\ L=6\text{ in} \end{gathered}[/tex]The width is 2.0 inchesThe University of Texas system consists of 9 campuses and has a budget of $2.4 billion in state funding. If the money were to be allocated equally based on total student enrollment, how much would be appropriated per student, rounded to the nearest cent?
Answers
Step 1:
Given data
Total number of campuses = 9
Total budget = $2.4 billion
Total students
= 33629 + 52359 + 8912 + 21493 + 23049 + 20353 + 5431 + 28923 + 7776
= 231925
Step 2
Convert $2.4 billion to cent, multiply $2.4 billion by 100.
[tex]2.4\text{ b}illion\text{ dollars = 2400000000 dollars = 240000000000 cent}[/tex]Step 3:
Divide the total budget in cent by total number of students
[tex]\begin{gathered} \text{Money appropriated per student = }\frac{240000000000}{231925} \\ =\text{ 1034817.29} \\ =\text{ 1034817 cent} \end{gathered}[/tex]Final answer
1034817 cent
The populations of two towns, town A and town B, are being compared. The population of town A is 8 x 104 and the population of B is 4 x 105 How many times greater is the population of town B than town A? A.5 B.50 C.500 D.5000
Answers
The population of town A is 8 x 10^4
The population of town B is 4 x 10^5
it is required to find,
How many times greater is the population of town B than town A ?
So, divide the population of B by the population of A
So,
[tex]\frac{4\cdot10^5}{8\cdot10^4}=\frac{4\cdot10\cdot10^4}{8\cdot10^4}=\frac{4\cdot10}{8}=\frac{40}{8}=5[/tex]so, the answer is option A. 5
I need help to find the indicated operation:h(t)= 2t-1g(t)= t^3+2Find (h×g)(t)
Answers
(h o g)(t) is 2t^3+3.
Given:
[tex]\begin{gathered} h(t)=2t-1 \\ g(t)=t^3+2 \end{gathered}[/tex]The objective is to find composite functions, (h o g)(t).
The composite function can be calculated as,
[tex]\begin{gathered} (h\circ g)(t)=h(g(t)) \\ =h(t^3+2) \\ =2(t^3+2)-1 \\ =2t^3+2(2)-1 \\ =2t^3+4-1 \\ =2t^3+3 \end{gathered}[/tex]Hence, the composite functions, (h o g)(t) is 2t^3+3.
Joe solved the equation 3 + = 10 and justified each step as shown.Identify Joe's error and fix his mistake.StepJustification3+ = 10Given equationX = 7Multiplication Property of EqualityX= 14Subtraction Property of EqualityAnswer:
Answers
The justification of the second and third step are wrong,
the justification he gave for the second step should be the justification of step 3. And the justification of step 3 should be the justification for step 2
Solve the inequalities|x| < 8
Answers
Given the following inequality:
[tex]|x|<8[/tex]According to the rules of the absolute values, the given inequality will be written as follows:
[tex]-8So, the answer will be:[tex]x=(-8,8)[/tex]The solution on the number line will be as follows:
please help me with parts a, b, and c of thos problem!!
Answers
We have the following:
The formula that corresponds to the calculation of the population is as follows
[tex]P=A\cdot(1+r)^t[/tex]Where A is the population of 952 108 000 inhabitants, r is the growth rate and t is the time elapsed
a.
2000
[tex]\begin{gathered} t=2000-1996=4 \\ P=952,108,000\cdot(1+0.013)^4=1002591447.8\cong1,002,600,000 \end{gathered}[/tex]2010
[tex]\begin{gathered} t=2010-1996=14 \\ P=952,108,000\cdot(1+0.013)^{14}=1140823475.4\cong1,140,800,000 \end{gathered}[/tex]b.
In this case what we must do is replace by 10, which is the equivalent in years of a decade in the part of the equation that corresponds to growth
[tex]\begin{gathered} (1+0.013)^{10}=1.13787 \\ 1.13787-1=0.1378 \end{gathered}[/tex]That is, the growth is approximately 13.78%
c.
In this case, we must calculate until 2000 with the percentage of 1.3% and then from 2000 until 2010 calculate with the new growth rate
A then would be the population calculated in part a, that is, 1,002,600,000 and t would be 10 (2010 - 2000)
replacing
[tex]P=1,002,600,000\cdot(1+0.01)^{10}=1107494142.9\cong1,107,500,000[/tex]Therefore with the new growth rate the population in India in 2010 would be 1,107,500,000
Dora has to pick a number between 400 and 500 Dora is thinking of a number between 500 and 600. When she divides it by a 1 digit number it has a remainder of 4. What could be Dora’s number
Answers
Given:
When Dora divides the number between 500 and 600 by a 1 digit number gives the remainder 4.
Let x be the one-digit number that divides the number between 500 and 600. It gives the remainder 4.
[tex]\begin{gathered} 500+(10\times n)+i \\ n=0,1,2,..\ldots\text{.}.9 \\ \text{For i=4,9} \end{gathered}[/tex]It gives the remainder 4.
Therefore,
[tex]\begin{gathered} 500+10n+4\text{ and 500+10n+9 divided by 5 will give the remainder 4} \\ n=0,1,2,\ldots9 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} 504+10n \\ 509+10n \\ n=0,1,2,\ldots.9 \\ \text{Divided by 5} \end{gathered}[/tex]Which point would map onto itself after a reflection across the line y = -x? (-4, 4) (-4, 0) (0, -4) (4,4)
Answers
Answer:
The point that would map onto itself after a reflection across the line is (-4, 0)
Explanation:
Given the points:
(-4, 4), (-4, 0), (0, -4) and (4, 4)
The point that would map onto itself after a reflection across the line:
y = -x
is (-4, 0)
because it is the point in the line y = -x
You want to buy a car. The loan amount will be $35,000. The company is offering a 5% interest rate for 36 months (3years). What will your monthly payments be?
Answers
Given that:
[tex]\begin{gathered} \text{Loan amount, P}_0=35000 \\ \text{Annual interst rate, r = }5\%=0.05 \\ \text{Number of compounding periods in one year, k =12} \\ L\text{ength of loan(in years), N = 3} \end{gathered}[/tex]Find the monthly payment, d.
The formula to find the monthly payment is
[tex]P_0=\frac{d(1-(1+\frac{r}{k})^{-Nk})}{(\frac{r}{k})}[/tex]Plug the given values into the formula.
[tex]\begin{gathered} 35000=\frac{d(1-(1+\frac{0.05}{12})^{-3\cdot12})}{(\frac{0.05}{12})} \\ =33.3657d \\ d=\frac{35000}{33.3657} \\ =1048.98 \end{gathered}[/tex]The monthly payment is $1049 approximately.
draw a model to support your solution 3/5 thought of juice is poured equally into 6 glasses how much juice is in each glass.
Answers
We have to divide 3/5 by 6. The picture above represents 3/5.
Drawing 5 vertical lines, we divide the whole block into 6 equal parts.
Now we have a total of 5*6 = 30 little squares. Dividing 3/5 into 6 equal parts we shade 3 out of 30 little squares. Then, 3/5 ÷ 6 = 3/30 = 1/10 (simplifying)
Monique is paid an hourly rate of $17.63 for regular-time work. What will be her double-time hourly pay rate for overtime worK?
Answers
Monique is paid an hourly rate of $17.63 for regular-time work. What will be her double-time hourly pay rate for overtime worK?
In this problem , multiply the hourly rate by 2
so
(17.63)*2=$35.26
therefore
the answer is
$35.26
Area of faces = 5 units2 or 6 units2From the image,Four of the faces each have an area of 6 units²Two faces each have areas of 5 units²Surface area = _____ units2
Answers
Answer
Option C is correct.
Surface area = 34 units²
Explanation
The total surface area of a cuboid or a rectangular prism is the sum total of the area of its faces.
For this question,
Four of the faces each have an area of 6 units²
Two faces each have areas of 5 units²
Total surface area
= 4 (6) + 2 (5)
= 24 + 10
= 34 units²
Hope this Helps!!!