Answer:
[tex]y=\frac{1}{10}x + 7[/tex]
Step-by-step explanation:
Hi there!
We are given the points (-20, 5) and (-10, 6)
We want to write the equation of the line in slope-intercept form
Slope-intercept form can be written as y=mx+b, where m is the slope, and b is the y intercept
First, let's find the slope of the line
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex] are points
We have everything we need to find the slope, but let's label the values of the points to avoid confusion and mistakes
[tex]x_1=-20\\y_1=5\\x_2=-10\\y_2=6[/tex]
Substitute these values into the formula to find the slope
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{6-5}{-10--20}[/tex]
Simplify
m=[tex]\frac{1}{-10+20}[/tex]
m=[tex]\frac{1}{10}[/tex]
The slope (m) of the line is 1/10
We can substitute this value into the formula y=mx+b
y = [tex]\frac{1}{10}x[/tex] + b
Now we need to solve for b
As the equation passes through the points (-20, 5) and (-10, 6), we can use either point to solve for b.
Taking (-20, 5) for instance:
Substitute -20 as x and 5 as y:
5=[tex]\frac{1}{10}(-20)[/tex] + b
Multiply
5=-2+b
Add 2 to both sides
7=b
Substitute 7 as b.
y=[tex]\frac{1}{10}x + 7[/tex]
Hope this helps!
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A total of 643 tickets were sold for the school play. They were either adult tickets or student tickets. There were 57 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
350 adult tickets
Step-by-step explanation:
If x is the number of adult tickets sold, then x-57 is the number of student tickets sold (57 fewer). The total number sold is ...
x +(x -57) = 643
2x = 700 . . . . . . . . collect terms, add 57
x = 350 . . . . . . . divide by 2
There were 350 adult tickets sold.
You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 24cm3 . Determine the minimum surface area necessary to construct a box of this volume. Enter an exact answer.
An investment of $1,000 earns an annual interest rate of 2%. How much more interest is earned in Year 5 with compound interest than with simple interest?
An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method.
How to determine money gain by simple interest
Simple interest (C) is the amount of money gained and solely related to the initial capital ([tex]C_{o}[/tex]), in monetary units. The money earned by simple interest is determined by the following formula:
[tex]C = \frac{C_{o}\cdot r\cdot t}{100}[/tex] (1)
Where:
r - Interest rate, in percentaget - Time, in yearsCompound interest (C) takes into account the capital throughout time and its formula is presented below:
[tex]C = C_{o}\cdot \left[\left(1+\frac{r}{100} \right)^{t}-1\right][/tex]
Now we proceed to determine the simple and compound interest: ([tex]C_{o} = 1000[/tex], r = 2, t = 5)
Simple interestC = [(1000) · (2) · (5)]/100
C = $ 100
Compound interestC = (1000) · {[1+(2/100)]⁵-1}
C = $ 104.08
An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method. [tex]\blacksquare[/tex]
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Select the correct answer from each drop-down menu.
The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0.
The equation of this circle in standard form is
. The center of the circle is at the point
, and its radius is
units.
Step-by-step explanation:
[tex](x - 2) {?}^{2} + (y + 3) { = 18} [/tex]
This exercise uses Newton's Law of Cooling.
Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to
cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k - 0.1947, assuming time is measured in hours. Suppose that the
temperature of the surroundings is 60°F.
(a) Find a function TCC) that models the temperature t hours after death.
TL)
х
(6) If the temperature of the body is now 78°F, how long ago was the time of death? (Round your answer to the nearest whole number.)
Xhr
By applying the Newton's law of cooling and performing the neccessary calculations, the time of death of the body is about 4 hours ago.
Newton's law of coolingAccording to the Newton's law of cooling;
T(t) = T(s) + (To - Ts)e^-kt
T(t) = temperature at time t
T(s) = temperature of the surroundings
To = Initial temperature
k = cooling constant
t = time taken
Substituting the values;
T(t) = 60 + (98.6 - 60)e^- 0.1947t
To find the time taken to attian a temperature of 78°F;
78 = 60 + (98.6 - 60)e^- 0.1947t
78= 60 + 38.6e^- 0.1947t
78 - 60 = 38.6e^- 0.1947t
18/38.6 = e^- 0.1947t
0.466 = e^- 0.1947t
ln0.466 = lne^- 0.1947t
ln0.466 =- 0.1947t
t = ln0.466 /- 0.1947
t = 4 hours
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What is the quotient?
-3/8 ÷ -1/4
-1 1/2
-3/32
3/32
1 1/2
Answer:
1 1/2
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Louise measured the perimeter of her rectangular scrapbook to be 154 cm. If the scrapbook is 37 cm wide, how long is the scrapbook?
Answer: 40 cm.
Step-by-step explanation: Perimeter involves adding all the sides of a shape to get the perimeter. So far, two sides of the scrapbook have been given, which are both 37 cm. 37 x 2 = 74, so that leaves us with two sides left, which are the lengths of the scrapbook. The total perimeter is 154, so if we subtract 74 from 154, we get 80. However, we have to split the 80 in half because we have two sides left. Therefore, the scrapbook's length is 40 cm for one side. I hope this isn't too confusing.
Have a great day! :)
f ( x ) = x 2 + 6 x and g ( x ) = x − 8 , calculate. f ( g ( − 5 ) ) =
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
First we have to calculate g (-5) :
[tex]\qquad \tt \dashrightarrow \:x - 8[/tex]
[tex]\qquad \tt \dashrightarrow \: - 5 - 8[/tex]
[tex]\qquad \tt \dashrightarrow \: - 13[/tex]
Now, let's find f (g (-5)) :
[tex]\qquad \tt \dashrightarrow \: {x}^{2} + 6x[/tex]
[tex]\qquad \tt \dashrightarrow \:( - 13) {}^{2} + (6 \times - 13)[/tex]
[tex]\qquad \tt \dashrightarrow \:169 + ( - 78)[/tex]
[tex]\qquad \tt \dashrightarrow \:169 - 78[/tex]
[tex]\qquad \tt \dashrightarrow \:91[/tex]
The graph shows the vertical position of a ball attached to a spring oscillating between a low point and a high point as a function of time.
Select all statements that describe the graph.
The amplitude is 24 cm.
The ball travels 24 cm in 1 s.
It takes the ball 2 s to complete a cycle.
The midline is at f(x)=0.
Step-by-step explanation:
The statements that describe the graph are,
The ball travels 24 cm in 1s.
It takes the ball 2s to complete a cycle
The midline is at f(x)=0
I hope it helped you
Help help help help math
Answer:
x = 6
Step-by-step explanation:
(4x - 3) × 2 = 3(x + 8)
8x - 6 = 3x + 24
8x - 3x = 24 + 6
5x = 30
x = 6
For each of the following expressions, identify the base and the exponent. 2× ,10² , x×
Answer:
2 is the base, 10 is the base, and x is the base. X is the exponent of 2, x is the exponent of 10, and x is the exponent of x.
Step-by-step explanation:
The cost of a barrel of beans, b, fluctuates (changes) by 17% in both
directions during a three-month period.
Match the verbal description of the high cost of a barrel of beans with all equivalent expressions for b is increased by 17%.
A. b + 0.17b
B. b - 0.17b
C. b - 1.17b
D. -0.17b
E. 0.83b
F. 1.17b
Answer:
b increased by 17% =b + 17% of b =b + 0.17b =1.17bCorrect ones A and F
------------------------------------------
b decreased by 17% =b - 17% of b =b - 0.17b =0.83bCorrect ones H and K
What is value of x?
Enter your answer in the box.
X=
Answer: 10
Step-by-step explanation:
X + 10 <14
thank you!
Answer:
x < 4
Step-by-step explanation:
Subtract 10 from both sides.
x + 10 - 10 < 14 - 10
Simplify the arithmetic:
x < 14 - 10
Simplify again..
and then u get x < 4
hope this helps <33
PLEASE HELP PLEASE PLEASE
Answer:
4 degrees is the closest thing i could think of while looking at this.
find the value of angle BAC
Answer:
The value of angle BAC = 75°
Step-by-step explanation:
=> Angle BAC + 105° = 180°
=> Angle BAC = 180° - 105°
=> Angle BAC = 75°
If you drive 23 miles south, make a turn and drive 39 miles east, how far are you, in a straight line, from
your starting point? Round your answer to the nearest tenth of a mile.
Answer:
45.27 miles
Step-by-step explanation:
Pythagorean theorem
23^2 + 39^2 = d ^ 2
d = 45.27 miles
If a person drives 23 miles south and make a turn to east and drive 39 miles then the distance between starting point and person is 45.27 miles.
What is pythagoras theorem?Pythagoras theorem applies in a right angled triangle. It says that in a right angled triangle the square of hypotenuse is equal to sum of squares of perpendicular and base of that triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex]
How to find distance?When person drives towards south and then east , it forms a right angled triangle. We have to find the distance of person from the starting point. If we see the figure then we will come to know that we are require to find hypotenuse of triangle.
H=[tex]\sqrt{P^{2} +B^{2} }[/tex]
Distance=[tex]\sqrt{23^{2} +39^{2} }[/tex]
=[tex]\sqrt{1521+529}[/tex]
=[tex]\sqrt{2050}[/tex]
=45.27
Hence the distance of person from starting point is 45.27 miles.
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Help will give thanks to the first to answer
our number is x
we add seven (+7) to x
x+7
Use ABC to find the value of sin A
12/35
35/37
37/12
12/37
Answer:
The correct answer is 12/37
Willie runs 4 miles in 44 minutes. If Willie runs at the same rate, how many miles can he run in 66 minutes?
Answer:
6 miles in 66 mins
Step-by-step explanation:
4 miles = 44 mins
simplify to the lowest point
1 mile = 11 mins
? = 66 mins
? = 1 x 6
you can run 6 miles in 66 mins
Answer:
Step-by-step explanation:
4/44= 0.0909090909...*66=6
find the propotunate value by dividing each initial value and multiply it by the listed secondary value
The ratio of Wei Ling's age to Wei Xuan's age 5 years ago was 2: 5. In 9 years
time, the ratio of Welling's age to Wel Xuan's age will be 3:4 How old is Wei
Xuan now?
Answer:
15 years old
Step-by-step explanation:
Start by defining the variables that we are going to use throughout our working:
Let the current age of Wei Ling and Wei Xuan be L and X years old respectively.
Next, form equations using the given information.
5 years ago
Wei Ling: (L -5) years old
Wei Xuan: (X -5) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan's is 2: 5,
[tex] \frac{ L - 5}{X - 5} = \frac{2}{5} [/tex]
Cross multiply:
2(X -5)= 5(L -5)
Expand:
2X -10= 5L -25
2X= 5L -25 +10
2X= 5L -15 -----(1)
9 years time
Wei Ling: (L +9) years old
Wei Xuan: (X +9) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan is 3: 4,
[tex] \frac{L + 9}{X + 9} = \frac{3}{4} [/tex]
Cross multiply:
3(X +9)= 4(L +9)
Expand:
3X +27= 4L +36
3X= 4L +36 -27
3X= 4L +9 -----(2)
Let's solve using the elimination method.
(1) ×3:
6X= 15L -45 -----(3)
(2) ×2:
6X= 8L +18 -----(4)
(3) -(4):
6X -6X= 15L -45 -(8L +18)
0= 15L -45 -8L -18
0= 7L -63
7L= 63
L= 63 ÷7
L= 9
Substitute L= 9 into (1):
2X= 5(9) -15
2X= 45 -15
2X= 30
X= 30 ÷2
X= 15
Thus, Wei Xuan is 15 years old now.
SOLVE FOR X IN THE FOLLOWING EQUATION :-- -3(2X+3)+4X=4/3X+11
Answer:
-6
Step-by-step explanation:
-2x - 9 = 4/3x+11
-
-6x-27=4x+33
-
-6x-27-4x=33
-
=6x-4x=33+27
-
10x=33+27
-
-10x=60
-
x= -6
Yan had 5 trading cards, and then his friend gave him more cards. Now he has 16 trading cards. Let t represent the number of cards his friend gave him. Write both an addition equation and a subtraction equation to model the problem.
PLEASE ANSWER IN THE NEXT 1 MINUTE.
What is the greatest common factor of 36 and 90 ?
A 6
B 18
C 36
D 180
Answer:
B
Step-by-step explanation:
It's 18! Obviously it's not 180 because it's too big. It can't be 36 because 36 doesn't go evenly into 90. 6 is too small, so the answer is 18.
Circle A has a center of (2,3) and a radius of 5, and circle B has a center of (1,4) and a radius of 10. What steps will help show that circle A is similar to circle B?
-Dilate circle A by scale factor of 2
- Translate circle A using the rule (x+1, y-1)
-Rotate circle A 180 degrees about the center.
-Reflect circle A over the Y axis
Answer:
-Dilate circle A by scale factor of 2
Got it right on the test (see picture)
Circle A is translated using the rule (x + 1, y - 1). Then the correct option is B.
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Circle A has a center of (2,3) and a radius of 5, and circle B has a center of (1,4) and a radius of 10.
Circle B is translated as 1 unit leftward in the x-direction and 1 unit upward in the y-direction.
Then circle B is dilated by a factor of 2.
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please help!!!!!!!!!!!!!!!
Answer:
There are 8 oz of soup per can : True
In 8 cans, there are 21 oz of soup : False
There are 2 oz of soup in 16 cans : False
In 1/8 of a can, there is 1 oz of soup : True
Step-by-step explanation:
To start, we know we have 168 oz of soup and 21 cans that are all the same size. To find how much is each can, (We know that they will all have the same amount since it says equally sized cans.) we can simply divide the amount we have of soup in oz by the amount of cans we have.
168 / 21 = 8.
This means that all the cans will be filled with 8 oz of soup. Making the first statement true.
Since there are 8 oz in each can, we can do 8 cans * 8 oz to find how many oz are in 8 cans of soup.
8 * 8 = 64 oz.
There are 64 oz of soup in 8 cans. Making the second statement false.
Now again, since there are 8 oz in each can, we can do 16 cans * 8 oz to find how many oz are in 16 cans of soup.
16 * 8 = 128 oz.
There are 128 oz of soup in 16 cans. Making the third statement false.
For the last question, to find 1/8 of a can of soup, we can take 8 oz (8 oz in one can) and divide it by 8.
8/8 = 1
Meaning 1/8 of a can of soup is 1 oz of soup. Making the fourth statement true.
Work out the this sheet
Answer:
A -- She saves 200₤.
B -- She will have 28₤ after buying presents.
Step-by-step explanation:
If two boxes = 20 then one box will be 10. Now we count all boxes. There are 20 boxes... 20 x 10 = 200, so she saves 200₤. If she spends 172₤ on Christmas presents she will have 28₤. (200 - 172 = 28).
HELPPPPPPPPPPPPPPPPP AGIANNNNNNNNNNNNNNN
The distance between the Earth and the Moon is approximately 1,260,000,000 feet, and a rocket can travel there at a speed of about 1,540,000 ft/min. How long will it take the rocket ship to travel to the moon and back, in minutes? Express your final answer in minutes and round to the nearest minute. Be sure to convert each number to scientific notation first, before performing any operations. show your work.
It will take approximately 169 minutes for a the rocket to travel a distance of 1,260,000,000 feet at 1,540,000 ft/min
Speed, Distance and TimeGiven Data
Distance = 260,000,000 feetSpeed = 1,540,000 ft/minApplying the relationship between speed, distance and time we have
Speed = Distance/Time
Substituting our given data into the expression we have
1,540,000 = 260,000,000/time
Making time subject of formula
time = 260,000,000/1,540,000
time = 169 miniutes
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Given vectors, a= (-2 -3) and b= ( 1 -1 ) find 2a-3b
Answer:
(-10,0)
Step-by-step explanation:
2a =[2(-2) , 2(-3)] = (-4 -6) <--- add them
-3b = [-3(1) . -3(-1)] = (-3 +3) <--- add them
2a - 3b =
[(-4 -6), (-3 +3)] =
(-10,0)