Answer:
y = x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 1 , then
y = x + c ← is the partial equation
To find c substitute (- 2, - 3 ) into the partial equation
- 3 = - 2 + c ⇒ c = - 3 + 2 = - 1
y = x - 1 ← equation of line
How do I verify: tan(x)+cot(x)=(2)/sin(2x)?
I always get stuck after writing out (sin^2x+cos^2x)/sin(x)cos(x)
[tex]sin^2(\theta)+cos^2(\theta)=1\qquad \qquad sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]tan(x)+cot(x)=\cfrac{2}{sin(2x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand-side}}{\cfrac{sin(x)}{cos(x)}+\cfrac{cos(x)}{sin(x)}\implies \cfrac{sin^2(x)+cos^2(x)}{\underset{\textit{using this LCD}}{sin(x)cos(x)}}} \implies \cfrac{1}{sin(x)cos(x)}[/tex]
now, let's recall that anything times 1 is just itself, namely 5*1 =5, 1,000,000 * 1 = 1,000,000, "meow" * 1 = "meow" and so on, so we can write anything as time 1.
let's recall something else, that same/same = 1, so
[tex]\cfrac{cheese}{cheese}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{horse}{horse}\implies \cfrac{butter}{butter}\implies \cfrac{25^7}{25^7}=1[/tex]
therefore
[tex]\cfrac{1}{sin(x)cos(x)}\cdot \cfrac{2}{2}\implies \cfrac{2}{2sin(x)cos(x)}\implies \cfrac{2}{sin(2x)}[/tex]
Find the slope of the line. Describe how one variable changes in relation to the other.
A. 2/3; the amount of water increases by 2 gallons every 3 min
B. -2/3; the amount of water decreases by 2 gallons every 3 min
C. -3/2; the amount of water decreases by 3 gallons every 2 min
D. -1; the amount of water decreases by 1 gallon every minute
Answer:
D. -1 the amount of water decreases by 1 gallon every minute.
Step-by-step explanation:
15, 0 -> 12, 3
3 - 0 = 3
-------
12 - 15 = -3
3/ -3 = -1
Example 8: Over the track-and-field season, the height Fred cleared in the high jump increase from 1.81 m to 1.96 m. a) Find Fred's percent increase in height. W b) What final height would Fred have to clear for a 20% increase in height over the track-and-field season?
Answer:
a. about 8.3%
b. 2.172 m
Step-by-step explanation:
a. 1.81 * x = 1.96
x = 1.083
Percent increase is approximately 8.3%
b. 1.81 * 1.2 = x
x = 2.172 m
Find a polynomial f(x) of degree 4 that has the following zeros. -7, 0, 1, 6
leave your answer in factored form.
please help! its my exam study guide and i need to finish it!
[tex]\begin{cases} x=-7\implies &x+7=0\\ x=0\implies &x=0\\ x=1\implies &x-1=0\\ x=6\implies &x-6=0 \end{cases}\qquad \implies (x+7)(x)(x-1)(x-6)=\stackrel{y}{0} \\\\\\ (x+7)(x)\stackrel{using~\mathbb{FOIL}}{(x^2-7x+6)}=0\implies (x^2+7x)(x^2-7x+6)=0[/tex]
[tex]\begin{array}{llll} x^2-7x+6\\ \qquad \times ~x^2\\\cline{1-1} x^4-7x^3+6x^2 \end{array}\qquad +\qquad \begin{array}{llll} x^2-7x+6\\ \qquad \times ~7x\\\cline{1-1} 7x^3-49x^2+42x \end{array} \\\\\\ (x^4-7x^3+6x^2)+(7x^3-49x^2+42x)=0 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x^4-43x^2+42x=y~\hfill[/tex]
I’ll give u the crown
Ms. Goitia went to 6 Nationals games in 27 days. How many games will she go to in 162 days?
Answer:
She will go to 729 games in 162 days.
Step-by-step explanation:
27÷6 = 4.5
4.5 · 162 = 729
Answer:
729 games in 162 days
Step-by-step explanation:
If she goes to 6 games in 27 days, then you divide 27 by 6, to get the unit rate.
27/6=4.5
Now that you have the unit rate, you multiply 162 by the unite rate, or 4.5, in this case.
162x4.5=729
-hope it helps
40 pts! PLEASE HELP FAST WILL MARK BRAINLIEST
Complete the table below to solve the equation 2.5x - 10.5 = 64(0.5x).
X
f(x) = 2.5x – 10.5
g(x) = 64(0.5x)
2
3
4
5
Answer:
f(2) = 2.5×2-10.5
=5-10.5
=-5.5
g(2) = 64(0.5×2)
= 64×1
=64
f(3)=2.5×3-10.5
=7.5-10.5
=-3
g(3)=64(0.5×3)
=64×1.5
=96
f(4)=2.5×4-10.5
=10-10.5
=-500
g(4)=64(0.5×4)
=64×2
=128
f(5)=2.5×5-10.5
=12.5-10.5
=2
g(5)=64(0.5×5)
=64×2.5
=150
I think it is the processs It will help you
WILL GIVE BRAINLIEST
What decimal is equivalent to -3 3/20?
Answer:
3 3/20 is equal to 3.15 in decimal form.
Step-by-step explanation:
Answer:
A. -3.15
Step-by-step explanation:
this isn't much but i really like math xD hope this helps! :) (please pick as brainlyist)
if the length of a cuboid is 60cm and width 40cm and its surface area is 14800cm² find its height
Please Guyz I Want Full Solved Not Just Answer Please
Answer:
50 cm
Step-by-step explanation:
let x be the heigth we are looking for.
Each rectangle that covers the cuboid is the product of two dimensions [tex](60\cdot40;\ 60x;\ 40x)[/tex]
Since it's a cuboid, we assume opposite sides are equal.
So each rectangle is counted twice:
[tex]Area=2(60\cdot40+60x+40x)=14800[/tex]
Now, we just isolate x:
[tex]60\cdot40+60x+40x=7400\\2400+100x=7400\\100x=5000[/tex]
Answer:50 cm
Serena is driving to the mountains for a summer
camping trip. She is traveling at a constant rate of 45
miles per hour. The graph shows the ratio time:
distance. How far has Serena traveled after 4 hours?
A car travels 18 miles on a gallon of gas. The car used 65 gallons of gas last week.compute the number of miles the car traveled?
Answer: 1170 miles
Work Shown:
(18 miles)/(1 gallon) = (x miles)/(65 gallons)
18/1 = x/65
x/65 = 18
x = 65*18
x = 1170
Answer: 1170 miles
1 gallon of gas --> 18 miles
65 gallon of gas --> 18 * 65 (which is 1170 miles)
When you’re driving and your instructor tells you to do a shoulder check, do you look directly to the right and left or behind your shoulder
Answer:
If you're moving the vehicle to the right, shoulder check by moving your head 90° to the right. Turn your head 90° degrees in the direction you're moving the vehicle. And, if you're moving the vehicle to the left, you shoulder check to the left by turning your head 90° to the left.
What is the difference of the fractions? Use the number line to help find the answer.
1/5-3/4
○ -19/20
○ -11/20
○ 11/20
○ 19/20
Answer:
-11/20
Step-by-step explanation:
[tex]\frac{1}{5} - \frac{3}{4} = \frac{?}{?}[/tex]
first you want to get a common denominator (number on the bottom)
[tex]\frac{4}{20} - \frac{15}{20} = \frac{?}{?}[/tex]
now you can subtract the numerators (number on tope) (also don't touch bottom)
[tex]it ~equals = -\frac{11}{20} ~~because ~4-15 ~is -11[/tex]
Find the value of x need help
Answer:
x=-10
Step-by-step explanation:
since there's a given 120 degrees, and it's a isosceles triangle, we know that the line adds up to 180 (where the 120 degrees is). so 120+x=180, the interior angle measures 60 degrees. That being said, the 3 angles measure 60 degrees also. now there's a right angle mark on top, so we find the angle of the smaller triangle (near angle 2) by doing 90-60=30 degrees.
angle 2 is said to be x+160, and there's a line, which tells us that they must add to 180.. so x+160+30=180
x+190=180
x=-10.
WILL GIVE BRAINLIEST
Answer:
the y intercept is 5/3
the y intercept is 3/5
subtract 19/12 - 3/4
[tex] \rm \frac{19}{12} - \frac{3}{4} = \frac{9}{12} - \frac{9}{12} = \frac{9 - 9}{12} = \frac{0}{12} = \bf0 \: \: (done.)[/tex]
Answer:
[tex]\frac{19}{12} - \frac{3}{4}=\frac{5}{6}[/tex]
Step-by-step explanation:
[tex] \frac{19}{12} - \frac{3}{4} [/tex]
[tex] = \frac{19 \times 4}{12 \times 4} - \frac{3 \times 12}{4 \times 12}[/tex]
[tex] = \frac{76}{48} - \frac{36}{48} [/tex]
[tex] = \frac{76 - 36}{48}[/tex]
[tex]= \frac{40}{48} [/tex]
[tex] = \frac{40 \div 8}{48 \div 8} [/tex]
[tex] = \frac{5}{6}[/tex]
How do you factor x2 + 2xy + y2 -2^4
Answer:
try this answer x2 + 2xy + y2 - 16
Answer each question and round your answer to the nearest whole number
A model power plant has a scale of 2 cm: 4 m. If the model power plant is 6 cm tall,
then how tall is the real power plant?
3 m
O 12 m
2 m
O 10 m
Ricky ran 3/4 of a mile in 1/12 of an hour. What was Ricky´s average speed?
Answer: 9
Step-by-step explanation:
3/4mile takes 1/12 hours
so a whole hour is 3/4 / 1/12 = 3/4*12 = 9miles/hour
Answer:
3/2 miles per hour
Step-by-step explanation:
To find his average speed, divide 3/4 mile by 1/2 hour:
3 2
----- * ------ = 3/2 miles per hour
4 1
Write g(x)=40x+4x2 in vertex form
Elijah was six times as old as his son. In twelve years he will be twice as old as his son. How old are they now
To solve this, we need to turn this word problem into a system of linear equations. To do this, let's use x to stand for Mr. Fontana's age, and y to stand for his son's age.
The first sentence states that eight years ago, Mr. Fontana was six times as old as his son.
eight years ago = x - 8
Fontana was six times as old as his son = 6(y - 8). Remember, we need subtract 8 from his son's age, which is why I wrote it as 6(y - 8), and his father was 6 times his son's age 8 years ago, which is why I multiplied 6 by y - 8.
Now, putting this all together gives us our first equation:
x - 8 = 6(y - 8)
We can now rewrite this equation in standard form:
x - 8 = 6y - 48 ----->
x - 6y = -48 + 8 ----->
x - 6y = -40 <----- this is our first linear equation
To find our second, we need to turn the second sentence into an equation. It says that in 12 years, Mr. Fontana will be twice as old as his son:
x + 12 = 2(y + 12)
Now, we need to rewrite this equation in standard form:
x + 12 = 2y + 24 ----->
x - 2y = 24 - 12 ----->
x - 2y = 12 <----- this is our second linear equation. We now have our system of equations:
x - 6y = -40
x - 2y = 12
Now we can find the father's age (x) and his son's age (y). First, multiply the second equation by -1, giving us:
x - 6y = -40
-x + 2y = -12
Now we can add both equations together:
x - x - 6y + 2y = -40 + -12 ----->
-4y = -52
Solve for y, by dividing both sides of the equation by -4, giving us:
y = 13
So, now we know the son's age: 13
To find the father's age, replace y in either the first equation or the second equation, with 13. Let's use the first equation:
x - 6(13) = -40 ----->
x - 78 = -40 ----->
x = 78 - 40 ----->
x = 38
Therefore, Mr. Fontana is 38 years old and his son is 13 years old.
What is the value of 3^2x+1, if 3^x=a
Guys HELPPPPP
Step-by-step explanation:
We use the power rule a^(x+y) = a^x * a^y:
3^(2x+1) = 3^(2x) * 3
We can re-write 3^(2x) as (3^x)^2, and we know that 3^x = a, so:
3a^2 is the final answer. There is not exact value, it's all just about re-writing.
[tex]3a^2 [/tex] is a required answer.
Answer:
solution given:
[tex]3^{2x+1}=? [/tex]
if [tex] 3^x=a[/tex]
By using power rule, we can write
[tex]3^{2x+1}[/tex] as
[tex]3^{2x+1}=(3^x)^2*3^1 [/tex]
[tex]a^2*3=3a^2 [/tex]
PLEASE HELP WILL MARK BRAINIEST!!!!!
Answer:
The bisector of a given angle
Step-by-step explanation:
Because, the given picture shows an acute angle and the markings on it are of which you can see when a bisector is being searched for.
Help help help help help math math
Step-by-step explanation:
again, a line cutting through 2 parallel lines must have the exact same angles with both of them. otherwise they would not be parallel.
therefore, both angles must be identical
3x + 2 = 2x + 6
x = 4
A bag of skittles contains 7 purple, 4 red, 6 yellow, and 5 green skittles. Randomly I will grab a skittle, eat it and then grab another to eat. What is the probability that I will get a purple and then red?
Answer:
The probability will be [tex]\frac{1}{2}[/tex], since there are a total of 11 purple and red Skittles and an overall total of 22 Skittles in the bag.
Use the distance to find the distance between the points A (-3,7 and B (-2,5).
Step-by-step explanation:
1 2 3 4 5
wa
Which of the following equations could be the equation to represent the given graph? Make sure you explain your answer thoroughly.
Unit 7 Algebra 2a sample work connections academy
The equation that represents the function is [tex]y = 2(\frac 12)^x[/tex]
The graph is an exponential function, and it passes through the points:
[tex](x,y) = (1,1)\ (0,2)[/tex]
An exponential function is represented with:
[tex]y = ab^x[/tex]
At (0,2), we have:
[tex]ab^0 = 2[/tex]
This gives
[tex]a(1) = 2[/tex]
[tex]a = 2[/tex]
At (1,1), we have:
[tex]ab^1 = 1[/tex]
[tex]ab = 1[/tex]
Substitute 2 for (a)
[tex]2b = 1[/tex]
Divide both sides by 2
[tex]b = \frac 12[/tex]
Substitute values for a and b in [tex]y = ab^x[/tex]
[tex]y = 2(\frac 12)^x[/tex]
Hence, the equation that represents the function is [tex]y = 2(\frac 12)^x[/tex]
Read more about exponential functions at:
https://brainly.com/question/19704059
A car traveling at 48 mph overtakes a cyclist who is riding at 16mph had a 3 hour head start how far from the starting point does the car overtake the cyclist?
The car overtakes the cyclist at a distance of 72 miles from the starting point.
,Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let the car overtake the cyclist at distance d and time t.
For the car:
48 = d / t
d = 48t
For the cyclist:
16 = d / (t + 3)
d = 16t + 48
48t = 16t + 48
32t = 48
t = 1.5 hours
d = 48(1.5) = 72 miles
The car overtakes the cyclist at a distance of 72 miles from the starting point.
Find out more on speed at: https://brainly.com/question/3004254
The perimeter of the equilateral triangle drawn below is 9b + 12.
The shape below is made of four of these triangles.
Find a simplified expression for its perimeter.
Help please, help please
Answer:
i think the perimeter is 60
Step-by-step explanation:
9²+12² = x²
15 = x
perimeter = 15×4 = 60
Dose anyone know questions 2 and 3?
Answer:
Step-by-step explanation:
1.6 / 0.2 = 8 x 10⁽⁵⁻²⁾ = 8 x 10³
The cost increases by $1.50 for each additional toothbrush made.