Distance:-
[tex]\\ \rm\Rrightarrow \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{(10-1)^2+(6-4)^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{9^2+2^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{81+4}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{85}[/tex]
[tex]\\ \rm\Rrightarrow 9.22units[/tex]
Find the solution to the equation:
f(x)=x^2-4x+3
Please show work!
Answer:
two solutionsx = 1, 3
Explanation:
[tex]\sf f(x)=x^2-4x+3[/tex]
[tex]\rightarrow \sf x^2-4x+3=0[/tex]
[tex]\rightarrow \sf x^2-3x-x+3=0[/tex]
[tex]\rightarrow \sf x(x-3)-1(x-3)=0[/tex]
[tex]\rightarrow \sf (x-1)(x-3)=0[/tex]
[tex]\rightarrow \sf x-1=0, \ x-3=0[/tex]
[tex]\rightarrow \sf x=1, \ x=3[/tex]
Thus, there are two solutions and the values are 1 and 3
Let's see
[tex]\\ \rm\rightarrowtail f(x)=0[/tex]
[tex]\\ \rm\rightarrowtail x^2-4x+3=0[/tex]
[tex]\\ \rm\rightarrowtail x^2-3x-x+3=0[/tex]
[tex]\\ \rm\rightarrowtail x(x-3)-1(x-3)=0[/tex]
[tex]\\ \rm\rightarrowtail (x-1)(x-3)=0[/tex]
[tex]\\ \rm\rightarrowtail x=1,3[/tex]
which trig ratio
determine which trig ratio to use to solve for x
Answer:
Step-by-step explanation:
1.cos
2.sin
3.cos
4.tan
5.sin
6.tan
Step-by-step explanation:
remember the basic trigonometry setup ?
the norm circle (radius = 1) with a horizontal and a vertical line through the center of the circle.
and then there is an angle at the center indicated by the horizontal line and an inclined (by that angle) radius line connecting the center and the circle arc.
this inclined radius line is then the baseline (Hypotenuse) of a right-angled triangle, and the legs of that triangle are sine and cosine of the angle at the center (sine is the vertical leg, cosine is the vertical leg).
in essence (at least it works for me), when given such right-angled triangle problems, I always try to rotate and/or flip this triangle until it looks like the described situation above.
the only other thing to remember is that for triangles inside circles with a different radius than 1, everything is multiplied by the actual radius (it really happens also for the norm circle, but multiplying by 1 does not really change anything, right ?).
so, now for the given problems :
1)
x is the radius of the circle.
we can make 68° the defining angle of that trigonometric situation. so, the top right vertex would be the center of the circle with radius x.
then
30 = cos(68)×x
x = 30/cos(68)
= 80.08401488...
2)
60 is the radius of the circle.
x is the defining angle.
then
15 = sin(x)×60
sin(x) = 15/60 = 1/4
x = 14.47751219...°
3)
x is the radius of the circle.
22° is the defining angle.
then
14 = cos(22)×x
x = 14/cos(22)
= 15.0994864...
4)
the unnamed side is the radius of the circle. let's call it "s".
54° is the defining angle.
then
47 = cos(54)×s
x = sin(54)×s
x/47 = sin(54)×s / (cos(54)×s) = sin(54)/cos(54) = tan(54)
x = 47×tan(54) or 47×sin(54)/cos(54)
= 64.68995026...
5)
14 is the radius of the circle.
41° is the defining angle.
then
x = sin(41)×14
= 9.184826406...
6)
the unnamed side is the radius of the circle. let's call it "s".
x is the defining angle.
then
57 = cos(x)×s
9 = sin(x)×s
9/57 = sin(x)×s / (cos(x)×s) = sin(x)/cos(x) = tan(x)
x = 8.972626615...°
Please help! : )
What are the two acute angles?
A video posted on the internet is becoming very popular, and the total number of views is increasing by 20% every hour. If the video currently has 71,000 views, how many views will it have in 9 hours?
Answer:198000 maybe
Sorry if it’s wrong
HELP!!
Find the mistake: Use the picture to find the diagonal of
the television. Look at the student’s work and solution.
Identify the error, solve the problem. Then share a
strategy this student could use to prevent this error again.
Answer:
It is actually very simple:
Notice that they don't actually do the square of 49 and 64. For some reason, they do the square root of the values without squaring them. If we were to do it in the right way, the answer would be:
[tex]49^{2} +64^{2} = c^{2}[/tex]⇔ 2401+4096 = [tex]c^{2}[/tex] ⇔ 6497 = [tex]c^{2}[/tex] ⇔ [tex]\sqrt{6497}[/tex] = [tex]\sqrt{c^{2} }[/tex] ⇔ 80,6 ≈ c
I believe this is the answer. I hope I had helped :)
Write the equation of the line that passes through the points (-9,-9)(−9,−9) and (6,-7)(6,−7). Please help me
Answer:
y = (2/15) x -(117/15)
Step-by-step explanation:
To write the equation we should know the slope m and the y-intercept b .
m= (y2-y1)/(x2-x1)
For points (x1 = -9, y1 = -9) and (x2 = 6, y2 = -7)
m = (-7 - - 9)/(6 - - 9) = (-7 + 9)/(6 +9) = 2 / 15
The general equation of a line is
y= mx + b
Our equation is
y = (2/15) x +b
To find b, substitute one of the two points, we know are on the line, in our equation. For example, we can substitute point (-9,-9)
-9 = (2/15) (-9) +b , multiply -9 by 2/15
-9 = - (18/15) +b, add -18/15 on both sides
-9 + (18/15) = b, find common denominator and add
[(-9 ·15) +18]/15 = b , simplify
-117/15 = b
So our equation is:
y = (2/15) x -(117/15)
Do we, as a society, rely on technology too much?
no. the word technology spans every invention ever created. we don't.
Answer:
Yes, We as a society rely too much on technology because it is the new thing that everyone wants or needs. Technology can buy your groceries and food with a single click.
Step-by-step explanation:
Find the Area of the shaded part.
To find the area of the shaded part we have to subtract the rectangle area from the triangle area :
[tex]s = \frac{1}{2} \times (8x + 2)(6x) - (x)(3x + 1) \\ [/tex]
[tex]s = \frac{1}{2} \times (48 {x}^{2} + 12x) - (3 {x}^{2} + x) \\ [/tex]
[tex]s = \frac{48}{2} {x}^{2} + \frac{12}{2} x - 3 {x}^{2} - x \\ [/tex]
[tex]s = 24 {x}^{2} + 6x - 3 {x}^{2} - x[/tex]
[tex]s = 24 {x}^{2} - 3 {x}^{2} + 6x - x[/tex]
[tex]s = 21 {x}^{2} + 5x[/tex]
And we're done
Have a great day ♡
On average, Evie’s chicken lays 3 eggs every 15 days. At this rate, how many days will it take Evie’s chicken to lay 45 eggs?
Answer:
43 ffhfhfhfhfhfhchchchchchc
Answer:
It will take 225 days for Evie's chicken to lay 45 eggs
Step-by-step explanation:
23.-28. In a manner similar to Example 1, (a) identify input and
output consistent with the general proportional model; (b) write
an equation for the model; (c) determine a numerical value for the
constant k; and (d) solve the problem.
23. The maximum distance that you can see from the top of a tall
building is (directly) proportional to the square root of the
height of the building. You can see approximately 41 mi from
the Canadian National Tower lookout level, which is 1,135 ft
tall. How far can you see from the top of the Sears Tower in
Chicago (now the Willis Tower), which is 1,454 ft tall?
23. How far can you see from the top of the sears tower in Chicago, which is 1,454 ft tall?
The distance I can see from the top of the sears tower in Chicago is 46.41 mi.
How far can you see the from the top of the Sears Tower?The equation for direct proportionality = y = b√x
where:
y = dependent variable = distance you can seeb = constantx = independent variable = square root of the height of the building.b = y /√x
41 / √1135
b = 1.217
y = 1.217√1454
y = 46.41 mi
To learn more about direct proportion, please check: https://brainly.com/question/13742765
Which statement describes the behavior of the function f (x) = startfraction 2 x over 1 minus x squared endfraction?
The statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity
How to find the value of the function as x approaches infinity (+ve or -ve)?If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.
For the considered case, the function is:
[tex]f(x) = \dfrac{2x}{1-x^2}[/tex]
The missing options are:
The graph approaches –2 as x approaches infinity.The graph approaches 0 as x approaches infinity.The graph approaches 1 as x approaches infinity.The graph approaches 2 as x approaches infinity.So we need to find the limit of the function as x approaches infinity.
[tex]lim_{x\rightarrow \infty}f(x) = lim_{x\rightarrow \infty}\dfrac{2x}{1-x^2} = lim_{x\rightarrow \infty}\dfrac{2x/x^2}{1/x^2 - 1} = lim_{x\rightarrow \infty}\dfrac{2/x}{1/x^2 - 1}\\\\lim_{x\rightarrow \infty}f(x) = \dfrac{lim_{x\rightarrow \infty}(2/x^2)}{lim_{x\rightarrow \infty}(1/x^2 - 1)} = \dfrac{0}{0-1} = \dfrac{0}{-1} = 0[/tex]
Since the value of the function approaches 0 as x approaches infinity, so as its graph will do.
Thus, the statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity
Learn more about limits of a function here:
https://brainly.com/question/13146225
Why are fractions 2/4 and 5/10 equivalent
Answer:
They both equal 20 when you do the butterfly method. They are all factors of 20.
Step-by-step explanation:
2/4 5/10
2x10=20
4x5=20
Make Sense and Persevere Ben walked from
the restaurant to the bus stop. Then, he took
the bus to the stadium. If he took the shortest
route, how many blocks did Ben travel? Note
that Ben can only travel along the grid lines.
Step-by-step explanation:
for the trip restaurant to the bus stop he had to go 2 blocks down and 3 blocks to the left - in total 5 blocks.
for the trip from the bus stop to the stadium he had to go 3 blocks to the left and then 8 blocks up. in total 11 blocks.
so, the whole trip took 5 + 11 = 16 blocks.
If the circumference is 50 cm what is radius of the circle?
Answer:
7.96
Step-by-step explanation:
C=2πr undo it
R=C/2π=50/2×π≈7.5775 rounded is 7.96
Hope this helps!
Have a nice day!! :D
The radius of the circle is 7.96 cm.
What is the radius of the circle?The radius of a circle is the distance from the center of the circle to any point on its circumference. It is usually denoted by ‘R’ or ‘r’.
The circumference of the circle is given by;
[tex]\rm Circumference = 2\pi r[/tex]
Where r is the radius of the circle.
Substitute all the values in the formula
[tex]\rm Circumference = 2\pi r\\\\50 = 2\pi r\\\\r = \dfrac{50}{2\times 3.14}\\\\r=7.96[/tex]
Hence, the radius of the circle is 7.96 cm.
To know more about the radius of the circle click the link given below.
https://brainly.com/question/11137975
Suppose a charity received a donation of $22.2 million. If this represents 34% of the charity’s donated funds, what is the total amount of its donated funds?
Answer:
ok so lets make this into a algrebra equation
22.2(mil)=0.34x
divide by 0.34
65294117.6471=x
x=65294118
Hope This Helps!!!
The height of a building in a drawing is 15 inches if the actual height of the building is 165 feet find the scale factor of the Drawing
Answer:
The scale is 11 feet per one inch.
Step-by-step explanation:
[tex]\frac{165feet}{15inches} = 11feet / inch[/tex]
[tex] { \alpha }^{2} \beta + \alpha { \beta }^{2} [/tex]
Please solve this
A puppy weighs 4 pounds. How many ounces does the puppy weigh?
Answer:
64 ounces
Step-by-step explanation:
Since 1 lb = 16 oz, just do 4 × 16 = 64
If puppy weighs 4 pounds then the weigh in ounces is 64 ounces.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
There are 16 ounces in a pound.
1 pound= 16 ounces.
Given that puppy weighs 4 pounds.
We have to find the wight in ounces.
To convert pounds to ounces, we need to multiply the weight in pounds by 16.
The puppy weighs 4 pounds x 16 ounces/pound
= 64 ounces
Hence, if puppy weighs 4 pounds then the weigh in ounces is 64 ounces.
To learn more on Unit of measurement click:
https://brainly.com/question/15402847
#SPJ2
help me plssss ‼️‼️‼️
teddy bears = 80
hope it helps..!!!
Triangle ABC has side lengths 12, 16, and 20. Do
the side lengths form a Pythagorean triple?
Explain.
Answer:
no they dont form a Pythagorean triple
Step-by-step explanation:
a2 + b2 = c2
put the equation below into vertex form.
y=(x+9)(x+25)
Answer:
Step-by-step explanation:
The rent for an apartment is $800 per month. The landlord charges one month's rent as a deposit plus a nonrefundable damage cost of $250.
The expression 800(n + 1) + 250 represents the cost of the renting the apartment for n months. Write the expression in simplified form.
please help me i have a test tmr
Answer:
800n+1050
Step-by-step explanation:
800(n+1)+250 = 800n+800+250 = 800n+1050.
Hope this helps!
Good luck with your test + I hope you do well on it.
Please mark me as brainliest!
2640 yards= ________ miles
complete each conversion
After converting yards to miles:
2640 yards = 1.5 miles
Given,
2640 yards= ________ miles
Now,
To convert to yard to miles the conversion factor is 0.000568182.
So,
1 yard ⇒ 0.000568182 miles
Multiply 2640 on both sides,
2640 yards ⇒ 1.5 miles.
Therefore 2640 yards is equivalent to 1.5 miles.
Know more about unit conversion,
https://brainly.com/question/14614674
#SPJ6
Rob goes to the gym 3 times a week work out how many times he goes to the gym in
a• four weeks
b• one year
Answer:
a=12 times
b=156 times
Step-by-step explanation:
4 weeks=month
4*3=12
52 weeks=1 year
52*3=156
Therefore he goes 12 times a month, and 156 times a year.
Given one of the interior angles of the hanger, find the measures of angles A and B.
Answer:
A= 130
B= 25
Step-by-step explanation:
A is 130 because the amount of degrees that are in a triangle is 180 degrees. From that we can substract 25 from 180 and get 155.
Since B is congruent with 25, B is also 25 degrees. Therefore, A is 130 because 180 - 50 is 130.
Hope this helps.
There are 777 students in a class: 222 boys and 555 girls. If the teacher picks a group of 333 at random, what is the probability that everyone in the group is a girl?
The probability is 0.1429.
The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:
5/7(4/6)(3/5)(2/4) = 120/840 = 0.1429.
The probability that everyone in the group is a girl is 2/7.
What is probability?Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.
Total number of students in a class = 7
Number of boys students = 2
Number of girls students = 5
The probability that everyone in the group is a girl is;
[tex]\rm Probability =\dfrac{Total \ number \ of \ girls}{Total \ number \ of \ boys}\\\\Probability=\dfrac{2}{7}[/tex]
Hence, the probability that everyone in the group is a girl is 2/7.
Learn more about probability here;
https://brainly.com/question/14461856
#SPJ4
PLEASE HELP! DUE TODAY! TY!
Use the diagram to find the value of x and the measure of Arc MR. (MR) =(3x+19)° and (LK) =189°
Work:
x =
(MR) =
Answer: x=12, (MR)=55
Step-by-step explanation:
In creating a new scale for the mercury thermometer, Anders Celsius initially set the boiling point of water at _____. A. 0° b. 32° c. 100° d. 273°.
The thermometer is a device that is used to measure the temperature gradient. Anders needs to set the boiling point of water at 100° C.
What is a thermometer?
The thermometer is a device that is used to measure the temperature gradient or the temperature of a body/object.
The boiling point of water is 100°C, therefore, Anders needs to set the boiling point of water at 100° C.
Thus, Anders needs to set the boiling point of water at 100° C.
Learn more about Thermometers:
https://brainly.com/question/24189042
If and , which expression is equivalent to ?
A.
B.
C.
D.
What is the constant term in the expression 8xy − 9x2 y − 5x 6
Answer: 6
Step-by-step explanation:
I assume you meant to write 8xy − 9x2y − 5x + 6. The constant term in an expression is defined as a number by itself that contains no variables. Therefore, the answer is 6.