MN goes through
(2,3)(-3,2)Slope:-
m=2-3/-3-2=-1/-5=1/5Slope of perpendicular line:-
-5Passes through k(3,-3)
Equation in point slope form
y-y1=m(x-x1)y+3=-5(x-3)y+3=-5x+15y=-5x+12Check one by one
0=-5(-12)+12=60+12=722=-5(2)+12=-10+12=2Yes option B is correct
Answer:
(2, 2)
Step-by-step explanation:
First find the slope of the line MN, using the two given points:
[tex]\sf let\:(x_1,y_1)=(2,3)[/tex]
[tex]\sf let\:(x_2,y_2)=(-3,2)[/tex]
[tex]\implies \sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-3}{-3-2}=\dfrac15[/tex]
If two lines are perpendicular to each other, the product of their slopes will be -1.
Therefore, the slope (m) of the line perpendicular to MN is:
[tex]\implies \dfrac15 \times m=-1[/tex]
[tex]\implies m=-5[/tex]
Using the point-slope form of the linear equation with point K (3, -3), we can construct the linear equation of the line perpendicular to MN:
[tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-(-3)=-5(x-3)[/tex]
[tex]\implies \sf y=-5x+12[/tex]
Now we have the equation of the line perpendicular to MN, we can input the x-values of the solution options to see which once is correct:
[tex]x=0\implies \sf y=-5(0)+12=12\implies (0,12)[/tex]
[tex]x=2\implies \sf y=-5(2)+12=2\implies (2,2)[/tex]
[tex]x=4\implies \sf y=-5(4)+12=12\implies (4,-8)[/tex]
[tex]x=5\implies \sf y=-5(5)+12=-13\implies (5,-13)[/tex]
Therefore, the point that is on the line that is perpendicular to MN and passes through point K is (2, 2)
3sqrt x =x-4
[tex]3 \sqrt{x} = x - 4[/tex]
solve for x
Answer:
x = 16
Step-by-step explanation:
3√x = x - 4
Raise the equation to the second power.
(3√x)² = (x - 4)²
9x = x² - 8x + 16
Rewrite the equation with the values on the left.
-x² + 17x - 16 = 0
x² - 17x + 16 = 0
Factor.
(x - 16)(x - 1) = 0
Set each part equal to 0.
x - 16 = 0
x = 16
x - 1 = 0
x = 1
Your solutions are 16 and 1, but it doesn't end there. Both of these may not satisfy the original equation, so plug them back in.
3√x = x - 4
3√16 = 16 - 4
3(4) = 12
12 = 2
16 is a solution.
3√x = x - 4
3√1 = 1 - 4
3(1) = -3
3 ≠ -3
1 is NOT a solution.
PLEASE HELP!!
it’s multiple choice but i never get any of the answers.
differentiate y=x^(e^x)
We are given the function to differentiate:
[tex]{\quad \qquad \sf \rightarrow y=x^{e^x}}[/tex]
Do take natural log on both sides, then we will be having
[tex]{:\implies \quad \sf ln(y)=ln(x^{e^{x}})}[/tex]
[tex]{:\implies \quad \sf ln(y)=e^{x}ln(x)\quad \qquad \{\because ln(a^b)=bln(a)\}}[/tex]
Now, differentiate both sides by using so called chain rule and the product rule
[tex]{:\implies \quad \sf \dfrac{1}{y}\dfrac{dy}{dx}=e^{x}ln(x)+\dfrac{e^x}{x}}[/tex]
[tex]{:\implies \quad \boxed{\bf{\dfrac{dy}{dx}=x^{e^x}\bigg\{\dfrac{e^x}{x}+ln(x)e^{x}\bigg\}}}}[/tex]
Hence, Option B) is correct
Product rule of differentiation:
[tex]{\boxed{\bf{\dfrac{d}{dx}(uv)=u\dfrac{dv}{dx}+v\dfrac{du}{dx}}}}[/tex]Where, u and v are functions of x
Find the area please!!!
Answer:
32.24
Step-by-step explanation:
To get the height, use Pythagoras theorem on the smaller triangle
8^2=2^2+x^2
x^2=64-4
x=√60=2√15.
then for the base use P.T for the bigger triangle
10^2=y^2+√60^2
y^2=100-60
y=√40=2√10
1/2×(2√10+2)×2√15
=32.24
Need help math problem
Answer:
Question 16: 44 inches
Question 18: 10, 24, 26
Step-by-step explanation:
Question 16:
Pythagoras Theorem: c^2 = a^2 + b^2, where c is the hypotenuse and the longest side.
125^2 = 117^2 + b^2
15,625 = 13,689 + b^2
15,625 - 13689 = b^2
1936 = b^2
√1936 = b
44 = b
Question 18:
Pythagoras Theorem: c^2 = a^2 + b^2, where c is the hypotenuse and the longest side. You have to try all the possibilities. The ones that match are the lengths.
The answers are 10, 24, 26
c^2 = a^2 + b^2
26^2 = 10^2 + 24^2
676 = 100 + 576
676 = 676
Sorry if the photo is bad :)
So, before solving further, let's recall that, a deck of card have 52 cards, with 26 black cards, and 26 red cards, out of which, let's first consider red cards,so 13 of 26 are heart, and the other 13 out of 26 is diamond, now let's consider the black cards, so 13 of 26 black cards are spades and the other 13 out of 26 black cards are clubs, every type have an ace card, and 9 cards numbering from 2-10 and three face cards naming, queen, king and Jack. And the probability of any event is defined as the ratio of no. of favourable outcomes to Total no. of possible outcomes, so let's stary solving all the parts one by one :
7) [tex]{:\implies \quad \sf P(Red\:\:card)=\dfrac{26}{52}}[/tex]
[tex]{:\implies \quad \boxed{\bf{P(Red\:\:card)=\dfrac12}}}[/tex]
8) [tex]{:\implies \quad \sf P(Jack\:\:of\:\:diamonds)=\dfrac{1}{52}}[/tex]
[tex]{:\implies \quad \boxed{\bf{P(Jack\:\:of\:\:diamonds)=\dfrac{1}{52}}}}[/tex]
9) [tex]{:\implies \quad \sf P(Ace)=\dfrac{4}{52}}[/tex]
[tex]{:\implies \quad \boxed{\bf{P(Ace)=\dfrac{1}{13}}}}[/tex]
10) [tex]{:\implies \quad \sf P(A\:\:black\:\:10)=\dfrac{2}{52}}[/tex]
[tex]{:\implies \quad \boxed{\bf{P(A\:\:black\:\:10)=\dfrac{1}{26}}}}[/tex]
11) [tex]{:\implies \quad \sf P(A\:\:heart)=\dfrac{13}{52}}[/tex]
[tex]{:\implies \quad \boxed{\bf{P(A\:\:heart)=\dfrac14}}}[/tex]
12) [tex]{:\implies \quad \sf P(Not\:\:a\:\:club)=\dfrac{39}{52}}[/tex]
[tex]{:\implies \quad \boxed{\bf{P(Not\:\:a\:\:club)=\dfrac34}}}[/tex]
Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x 1 out of a larger piece of paper. which expression can be used to find the perimeter of the rectangle and what is the perimeter if x = 4? (5x−2) (3x 1); 31 centimeters (5x−2) (3x 1); 36 centimeters 2(5x−2) 2(3x 1); 62 centimeters 2(5x−2) 2(3x 1); 70 centimeters
The expression that can be used to find the perimeter of the rectangle is 62 centimeters 2(5x−2)+2(3x+1).
What is the perimeter of the rectangle?The perimeter of the rectangle is equal to the 2 times sum of the length and width of the rectangle.
Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper.
The expression that can be used to find the perimeter of the rectangle is given by;
[tex]\rm Perimeter \ of \ rectangle = 2 (length +width)\\\\\rm Perimeter \ of \ rectangle = 2 (5x-2+3x+1)\\\\ \rm Perimeter \ of \ rectangle = 2 (7x-1)\\\\ \rm Perimeter \ of \ rectangle = 16x-2\\\\When , x\ =\ 4\\\\ \rm Perimeter \ of \ rectangle = 14x-2\ = 16(4)-2\ =\ 64-2\ =\ 62\\[/tex]
Hence, the expression that can be used to find the perimeter of the rectangle is 62 centimeters 2(5x−2)+2(3x+1).
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A jar contains nine black buttons and four brown buttons. If nine buttons are picked
at random, what is the probability that all of them are black?
Answer:
9/13
Step-by-step explanation:
Total = 9 + 4
= 13
Probability: 9/13
pls help the question is here (12points) DUE TO DAY
Answer:
[tex]\bf Area= 90\;in[/tex]
Step-by-step explanation:
Area of ABCD = L * W
[tex]\bf 6\times 12[/tex]
[tex]\bf 72 \;in^2[/tex]
Area of EFGC:- L * W
[tex]\bf 6 \times 3[/tex]
[tex]\bf 18\; in^2[/tex]
Now, the area of the combind rectangles:-
ABCD + EFGC
[tex]\bf 72+18[/tex]
[tex]\boxed{\bf 90\; in}[/tex]
Trevor has an investment worth $6,774.50. he made his only deposit in it 22 years ago. given that the investment yields 2.7% simple interest annually, how big was the initial deposit? a. $2,524.50 b. $4,024.03 c. $4,250.00 d. $11,404.88 please select the best answer from the choices provided a b c d
Answer:
c. 4,250.00
Step-by-step explanation:
The initial deposit amount is $4,250.00.
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that,
The worth of an investment is $6774.50
The time period is 22 years.
The rate of interest is 2.7%.
Now, Based on the above information, the calculation is as follows:
We know that;
SI = P x r x t
SI = P x 2.7% x 22
SI = 0.594P
Now,
Investment worth = P + SI
= P + 0.594P
= 1.594P
So, we get;
1.594P = 6774.50
P = $4,250
Therefore, we can conclude that the initial deposit amount is,
⇒ $4,250.00
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Please help me asap with my grade 11 trigonometry math! I'll give brainliest, please help, thank you. *URGENT*
Answer:
Around 295m
Step-by-step explanation:
Answer:
295.44 m to the neaest hundredth
Step-by-step explanation:
A line drawn from the kite perpendicular to the ground forms 2 right triangles. Let this line be x m.
Also let y be the distance from Allison to the bottom of the line.
Consider 'Alison' triangle
cos 70 = y/150
y = 51.303 m
sin 70 = x/150
x = 150 sin 70 = 140.954 m
Consider 'Marcs' triangle
tan 30 = x / (AM - y)
tan 30 = 140.954 / (AM - 51.303)
AM - 51.303 = 140.954/tan 30
AM = 140.954/tan 30 + 51.303
AM = 295.442 m
HELP NEEDED NOW/ASAP PLS NO LINKS AND NO JOCKING.
AND PLS SHOW UR WORK IF POSSIBLE
evaluate (-3 1/3)^2
[tex]\\ \rm\Rrightarrow (-3\dfrac{1}{3})^2[/tex]
[tex]\\ \rm\Rrightarrow (\dfrac{-10}{3})^2[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{(-10)^2}{3^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{100}{9}[/tex]
[tex]\\ \rm\Rrightarrow 11\dfrac{1}{9}[/tex]
Answer:
100/9 (or) 11 1/9
Step-by-step explanation:
Q) (-3 1/3)² = ?
→ (-3 1/3)²
→ (-10/3)²
→ 100/9
→ [ 11 1/9 ]
Hence, the solution is 11 1/9.
NEED HELP PLEASE!!!!
The expressions are equivalent.
[tex] \sqrt{ \frac{2x}{9} } = \frac{ \sqrt{2x} }{ \sqrt{9} } = \frac{ \sqrt{2x} }{3} = \frac{1}{3} \sqrt{2x} \\ [/tex]
the graphs of the functions f(x)=|x-3| + 1 and G(x)=2x + 1 are drawn. which statement about these functions is true?
A: The solution to f(x)=g(x) is 3
B: The solution to f(x)=g(x) is 1
C: The graphs intersect when Y=1
D: The graphs intersect when X=3
The only true statement that compares the two functions is:
B: The solution to f(x)=g(x) is 1
Which statements are correct?Here we have the functions:
f(x) = |x - 3| + 1
g(x) = 2x + 1
First, let's find the solution for:
f(x) = g(x)
|x - 3| + 1 = 2x + 1
|x - 3| = 2x
Notice that we have two options, x = 3:
|3 - 3| = 2*3
0 = 6 (x = 3 is not a solution)
And x = 1:
|1 - 3| = 2*1
2 = 2 (x = 1 is a solution).
Now to get the y-value where the graphs intersect, we just evaluate one of the functions in the solution we found above;
f(1) = |1 - 3| + 1 = 2 + 1 = 3
The graphs intersect when y = 3.
Then we conclude that the only true statement is:
B: The solution to f(x)=g(x) is 1
If you want to learn more about systems of equations, you can read:
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A landscaping company uses a mixture of 20 pounds of grass seed and 356 pounds of fertilizer when reseeding a customer's lawn.
How many pounds of fertilizer will the company need for each pound of grass seed?
O A. 20
O B. 5. 6
O C. 16. 0
D. 17. 8
Answer:
D
Step-by-step explanation:
for 20 pounds of grass seed, we need 356 pounds of fertilizer
20 pounds of grass seed : 356 pounds of fertilizer
divide both sides by 20 to get 1 pound of grass seed on one side, as we want to figure out the corresponding amount of fertilizer for 1 pound of grass seed
20 pounds of grass seed/20 : 356 pounds of fertilizer/20
1 pound of grass seed: 17.8 pounds of fertilizer
If you borrow $500 at 5% for two years, how much will you pay backboy the end of the term?
Interest be I
I=PRT/100I=500(5)(2)/100I=5²(2)I=25(2)I=$50Total:-
P+I500+50$550Find the mean
X. 10 20 30 40 50 60
F. 4 5 6 2 3 5
Answer:
Mean:To find the mean, you must add all the given numbers in your data then divide the sum of that by the many numbers you added together.X.
10, 20, 30, 40, 50, 60
Add them:
10 + 20 + 30 + 40 + 50 + 60
= 210
Then divide that sum by the many numbers there are, and there are 6 numbers in which we added.
210 ÷ 6
= 35, the mean for this is 35.
F.
4, 5, 6, 2, 3, 5
Add them:
4 + 5 + 6 + 2 + 3 + 5
= 25
Then divide that sum by the many numbers there are, and there are 6 numbers in which we added.
25 ÷ 6
= 4.1666..., the mean for this is 4.17.
PLEASE HELP I WILL GIVE BRAINLIEST IF CORRECT
I belive the correct answer would be A because if M and N are the signatures it would make sense to add them. Multiply the signatures by the days, and you have your self an equation. So because we added the first two... Nikkis's petition is still the same so we would have to add hers to M again leaving you with the equation of A.
Hope this helps :)
Find the volume of the cylinder.
Either enter an exact answer in terms of pi or use 3.14 for pi
Volume of cylinder,=πr²h
(22÷7)×5²×3
3.14×25×3
235.5
Answer :
235.5 units³
∣x−7∣<9 what is the answer
Answer:
x < 16
Step-by-step explanation:
∣x−7∣ < 9
x < 9 + 7
x < 16
Answer:
7x < 9
Step-by-step explanation:
because the absolute value of -7 is 7 and 7 + x = 7x.
How many sets of three consecutive integers are there whose sum is between 51 and 60?
Answer:
4 sets
Step-by-step explanation:
16 + 17 + 18 = 51
17 + 18 + 19 = 54
18 + 19 + 20 = 57
19 + 20 +21 = 60
PLEASE ANSWER FAST! NO LINKS!
Answer:
the first one
Step-by-step explanation:
absolute value is a number's distance from zero, so distance from zero can not possibly be negative. Therefore, |4x-2|=-6 has no solution.
Answer:
It would be the first one because there is no value of x that makes the equation be true since an absolute value can never be negative.
Step-by-step explanation:
Hope this helps:)....if don't help then sorry for wasting your time and may God bless you:)
Sadie is saving for a new car. Below is the total amount of money in her savings account on the last day of each month. Show all steps to find the mean amount of money Sadie saves each month. Round your answers to the nearest cent.
Bertha bought a cake that weighs 7 kilograms. Jessup's cake weighs 6,537 grams.
A. Jessup’s cake weighs more than Bertha’s cake.
B. The expression 7 x 1,000 can be used to find the weight of
Bertha’s cake in grams.
C. Bertha’s cake weighs 463 grams more than Jessup’s cake.
D. Jessup’s cake weighs more than 6 kilograms.
Which deal is better $1.95 for 5 kg or $0.96 for 2 kg
Answer:
$1.95 for 5kg
Step-by-step explanation:
0.96 x2 is 1.92 and not even 5kg so if you get 5kg worth of the 0.96$ per kg then it will be more expensive.
So $1.95 for 5kg is the better deal.
Which is f(5) for the function –2x2 2x – 3? –107 –63 –43 –37
Answer:
- 43
Step-by-step explanation:
f ( x ) = - 2x² + 2x - 3
To find : f ( 5 )
f ( 5 ) = f ( x )
Here,
x = 5
f ( 5 ) = - 2x² + 2x - 3
= - 2 ( 5 )² + 2 ( 5 ) - 3
= - 2 ( 25 ) + 10 - 3
= - 50 + 7
f ( 5 ) = - 43
Answer:
-43
Step-by-step explanation:
oon edge
mark me brain
A solid wooden post in the shape of a right rectangular prism measuring 10 cm by 12
cm by 30 cm is drilled with a cylindrical hole of radius 2 cm. Find the volume of the
post after the hole has been drilled. Round your answer to the nearest tenth if
necessary?
The volume of the post = volume of rectangular prism - volume of cylindrical hole = 3,223.0 cm³.
What is the Volume of a Rectangular Prism?Volume = (l)(w)(h)
What is the Volume of a Cylinder?Volume = πr²h
Volume of the post = volume of rectangular prism - volume of cylindrical hole
= (l)(w)(h) - πr²h
= (10)(12)(30) - π(2²)(30)
Volume of the post = 3,223.0 cm³
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What is the volume of a right rectangular prism with a length of 4.8 meters, a width of 23 meters, and a height of 0.9 meters?
A.4.968 m
B.9.936 m
C.11.94 m
D.34 86 m
Answer:
Volume of prism = Area of base× height
= l×b×h
=4.8×23×0.9
= 99.36 m³
All options are incorrect : )
Answer:
The answer is B
Step-by-step explanation:
Im 3 weeks late lol sorry. I took the quiz.
Simplify.
(7sqrt(2))(3sqrt(3))
A sqrt(14) * sqrt(9)
B. 10sqrt(5)
C. 21sqrt(6)
D. 10sqrt(6)
E. 63
Answer:
21sqrt(6)
Step-by-step explanation:
Hope it helps......
What is the lateral area of the prism? What is the surface area of the prism?
Answer:
Lateral surface area=perimeter×Height
Total surface area=Perimeter (p)×Height(h)+2×Area of cross section
The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table below. stopping distance of a car vs. speed stopping distance, d (in feet) speed, s (in miles per hour) 20 17.89 40 25.30 60 30.98 80 35.78 100 40.00 which equation best represents the data in the table? s = 4 startroot d endroot s = 0.37 d 20 s = 13.7log(d) s = startfraction 1 over 25 endfraction d squared
Answer:
The answer is (A.)
Step-by-step explanation:
Answer: A on edge 22
Step-by-step explanation: