Answer:
[tex]T = (20,25)[/tex]
Step-by-step explanation:
Given
[tex]S = (-5,0)[/tex]
[tex]M = (10,15)[/tex]
[tex]Ratio = 3:2[/tex]
Required
Determine the coordinate of T
Line division by ratio is calculated using:
[tex]M(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where:
[tex](x_1,y_1) = (-5,0)[/tex]
[tex](x,y) = (10,15)[/tex]
[tex]m:n = 3:2[/tex]
So, we have:
[tex](10,15) = (\frac{3 * x_2 + 2 * -5}{3+2},\frac{3 * y_2 + 2 * 0}{3+2})[/tex]
[tex](10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5})[/tex]
Multiply through by 5
[tex]5 * (10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5}) * 5[/tex]
[tex](50,75) = (3x_2 -10,3y_2)[/tex]
By comparison:
[tex]3x_2 - 10 = 50[/tex]
[tex]3y_2 = 75[/tex]
[tex]3x_2 - 10 = 50[/tex]
[tex]3x_2 = 50 + 10[/tex]
[tex]3x_2 = 60[/tex] --- Divide through by 3
[tex]x_2 = 20[/tex]
[tex]3y_2 = 75[/tex]
[tex]y_2 =75/3[/tex] --- Divide through by 3
[tex]y_2 =25[/tex]
Hence:
The coordinates of T is
[tex]T = (20,25)[/tex]
Which statement describes the inverse of m(x) = x^2 – 17x?
a. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
b. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
c. The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
d.The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
Given:
The function is
[tex]m(x)=x^2-17x[/tex]
To find:
The inverse of the given function.
Solution:
We have,
[tex]m(x)=x^2-17x[/tex]
Substitute m(x)=y.
[tex]y=x^2-17x[/tex]
Interchange x and y.
[tex]x=y^2-17y[/tex]
Add square of half of coefficient of y , i.e., [tex]\left(\dfrac{-17}{2}\right)^2[/tex] on both sides,
[tex]x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
Taking square root on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}[/tex]
Add [tex]\dfrac{17}{2}[/tex] on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y[/tex]
Substitute [tex]y=m^{-1}(x)[/tex].
[tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex]
We know that, negative term inside the root is not real number. So,
[tex]x+\left(\dfrac{17}{2}\right)^2\geq 0[/tex]
[tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex]
Therefore, the restricted domain is [tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex] and the inverse function is [tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex].
Hence, option D is correct.
Note: In all the options square of [tex]\dfrac{17}{2}[/tex] is missing in restricted domain.
Answer:
C on edu
Step-by-step explanation:
To solve the problem -9 + 18 what is the first step?
a. KCO (keep change fli[p)
b. Subtract 18 - 9
c. Subtract 9 - 18
d. Add 9 + 18
Answer:
Step-by-step explanation:
How do you solve this? Without going into anything to complicated as this should be Year 10 maths
Given : ABCD is a square with each side 5cm .
To Find : The area of the shaded region .
Solution : On observing the figure we can see two quadrants , quadrant ADC & quadrant ABC .
If we join A to C , then it will be common for triangles ADC & ABC . And they will be congruent by SSS congruence condition.
Therefore the area of both quadrants will also be equal . Now we can find area of quadrant as ;
[tex]\large\boxed{\red{\bf Area_{quadrant}=\dfrac{\pi r^2}{4}}}[/tex]
Here radius will be equal to 5cm .
⇒ Area = πr² / 4 .
⇒ Area = π (5cm)² / 4 .
⇒ Area = 22/7 × 25 × 4 cm².
⇒ Area = 19.64 cm² .
So , total area of both quadrants = 39.28 cm² .
Also , area of square will be :
[tex]\large\boxed{\bf{\red{Area_{square}=(side)^2}}}[/tex]
⇒ Area = 5cm × 5cm .
⇒ Area = 25 cm².
Now , subtract area of one quadrant from the area of square = 25cm² - 19.64 cm² = 5.36 cm².
Similarly area of other white region = 5.36cm² .
And the areas sum will be = 5.36cm² × 2 = 10.72cm² .
Now , from the figure it's clear that ,
⇒ Area of unshaded region + Area of shaded region = 25cm².
⇒ 10.72cm² + ar( Shaded region ) = 25cm².
⇒ ar ( Shaded region ) = 25cm² - 10.72cm².
⇒ ar ( Shaded region ) = 14.28 cm².
Hence the area of shaded region is 14.28 cm².
[tex]\large\boxed{\red{\bf Answer = 14.28cm^2}}[/tex]
Pls Help :( 15 points
108 students went on a field trip. Three buses were filled and 27 students traveled in cars. How many students were in each bus?
Please include algebraic equation please.
Answer:
(108-27)/3 =27
Each bus has 27 students, because 108-27=81, 81/3=27
Step-by-step explanation:
Hope this helps! <3
How is 5 represented in 6.75
Answer:
5 is in the hundreths place :))
Step-by-step explanation:
Answer:
0.05
Step-by-step explanation:
since the place value of the five is beyond the decimal point, and it is the second number beyond the decimal point, so it is in the hundredths place.
someone help please!!
Answer:
1
Step-by-step explanation:
5 1/5- 1 3/4 fractions
Answer:
3 9/20
Step-by-step explanation:
first find a common demonator and change the denomators and what ever you did to the bottom you do to the top, then subtract them.
variation does not depend on that of another.
#6 THE SOLUTION FOR F(X) = 3X + 2 WHEN F(X) IS 2 IS
Answer:
0
*see below incase you worded it wrong
Step-by-step explanation:
then we substitute 2 for f(x)
2 = 3x + 2
0 = 3x
x = 0
UNLESS you mean f(2) is what then that is:
f(2) = 3(2) + 2 = 8
hope that helps!
Help me please!!..,,
Answer:
A.
Step-by-step explanation:
1.5 x 0.1 = 0.15
0.15 inches
Dont know if this is for sure right. Hope it is.
What’s the value of y in this picture
Answer: A 83
Step-by-step explanation:
Add 46 to 51 then subtract from 180 to get the correct answer(83)
Somebody please answer this question I’m begging you
Answer: The answer is A, the y value increases by 1.5 as the x value increases by 1. Therefore A does not describe the graph.
Eight more than.twice an number is four less than the same number
Answer:
2x+8=x-4
Step-by-step explanation:
I think that's right, let me know if it's wrong and I'll delete
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
OA. VE2
✓ B. 1: 13
C. 5 : 13
OD. 2.5: 6
E. 1: 2
OF. : 3
Answer:1 squad 3
2 squad 3 :6
Step-by-step explanation:
Determine whether each equation is true or false.
-5/-1 = 5
(0/-4) = 0
-3/1 = -3
- 8/0 = 0
Step-by-step explanation:
1.False
2.True
3.True
4.False
G
Which fraction is equivalent to 6?
12 / 2
3
2 2+1 3
7, because
6 6+17
mo
2 1 1 3
because 6 - 3 and
39
2 /
3
12
2 1
because =
6 3 and
2
nd 3 -
3
12
2 1
8.
because 6 2
2+1 3
6+28
Answer:
what is the question
Step-by-step explanation:
i don't understand what you're trying to say
Kenya went to the convenience store to buy some candy bars for her friends. She spent a total of $6.00 on candy bars. Each candy bar cost $1.50.
How many candy bars did Kenya buy?
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
PLEASE HELP PLEASE!!
Complete the following statement to estimate the root of 75 to the nearest tenth. Use numbers that are closest to the root of 75
The regular price of a bathing suit is $89.99. Estimate the sale price of the 25 points
bathing suit at 70% off regular price.
$27.00
$82.99
$19.99
Here is a set of signed numbers: 7, -3, 1/2, -0.8, 0.8, -1/10, -2
Order the numbers from least to greatest.
first gets brainllest
Answer:
7, 0.8, 1/2, -0.8, -1/10, -2, -3,
Step-by-step explanation:
accidently put greatest to least just flip it i still want brainliest tho
CHECK PHOTO Intercepts of the graph BE SURE TO BE CORRECT PLEASE no work needed
Answer:
y= (0, .7)
x= (-1.2, 0)
Step-by-step explanation:
r u taking a test?
Please look at the pic and help it got marked wrong
Answer:
although it is true that could be -(1/4)^4
if you multiply the answer can also be -1/256
Heya!!
your answer is!
-1/256
2. What is the measure of the missing angle? *
C-120
B-95
A-85
What is D?
Answer:
60
Step-by-step explanation:
it is because 360-(120+85+95)
Store B sells a set for $27.00 and offers a 20% discount
Answer:
22.50
and you can pleasent do 22.50
Step-by-step explanation:
Which shows another way to write 9.54?
O 0.5 + 0.04
O 9+ 0.4 + 0.05
O (9 * 1) + (5 x 0.1) + (4 x 0.01)
O (9 x 0.1) + (5 x 0.01) + (4 x 0.001)
Answer:
It would be C
Step-by-step explanation:
The following are a list of variables that will almost certainly vary across students in a large undergraduate introductory statistics course.
(a) Favorite beverage
(b) Year of birth
(c) Typing speed
(d) Handedness (e.g., left or right handed)
(e) Age
(f) Occupation
(g) Self-report of Assertiveness
For questions 1a to 1d that follow choose the variable or variables that best represent the level of measurement.
a) Which variables would typically be measured on a nominal scale of measurement?
b) Which variable would likely be measured on an interval, but not a ratio scale?c) Which two variables are most likely to be measured on a ratio scale?d) As typically measured, which variable represents at least an ordinal scale of measurement, but probably not a true interval scale?
Step-by-step explanation:
a. nominal scales
occupation
Favorite beverage
b. Interval but not ratio.
Typing speed
c. ratio scale.
age
Handedness (e.g., left or right handed)
d. Ordinal scale of measurement but not a true interval scale.
Self-report of Assertiveness
year of birth
Please help with question plaaseeee
Answer:
Yes it is.Step-by-step explanation:
The graph is proportional because
it is in a straight line in the graph.
Hope this helps! <3
help with this immediately
Answer:
c
Step-by-step explanation:
%gggggyyhhttbu6gnmk8tg
Help the pic is right here
Answer:
i think its C
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
its just division tbh
Which two numbers have a product of −18 and a sum of −7?
Answer:
2 and -9
Step-by-step explanation:
2 times -9 is -18
2 plus -9 is -7
Hope this helped!
Find the equation of the line passing through the points (-2,-4) and (7,23)
Answer:
y=−5.4x
Step-by-step explanation:
Slope -5.4
Intercept -14.80