Answer:
An equation of the line that passes through the point (6,−4) and is perpendicular to the line will be:
[tex]y=-\frac{1}{2}x-1[/tex]Step-by-step explanation:
We know that the slope-intercept form of the line equation
y = mx+b
where m is the slope and b is the y-intercept
Given the line
[tex]2x-y=5[/tex]
converting the line into slope-intercept form
y = 2x-5
comparing with the slope-intercept form of the line equation
The slope of the line = m = 2
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 2
Thus, the equation of new line = – 1/m = -1/2 = -1/2
using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values of the slope = -1/2 and the point (6,−4)
[tex]y-\left(-4\right)=-\frac{1}{2}\left(x-6\right)[/tex]
[tex]y+4=-\frac{1}{2}\left(x-6\right)[/tex]
Subtract 4 from both sides
[tex]y+4-4=-\frac{1}{2}\left(x-6\right)-4[/tex]
[tex]y=-\frac{1}{2}x-1[/tex]
Therefore, an equation of the line that passes through the point (6,−4) and is perpendicular to the line will be:
[tex]y=-\frac{1}{2}x-1[/tex]An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5 is [tex]y=-\frac{1}{2}x-1[/tex]
Given:
An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5
First we find the slope of given equation 2x-y=5
y=mx+b is the equation of the line . where 'm' is the slope
[tex]2x-y=5\\2x-5=y\\y=2x-5[/tex]
Slope m=2.
Slope of perpendicular lines are negative reciprocal of one another
Slope of perpendicular line is [tex]-\frac{1}{2}[/tex]
The line passes through the point (6,-4)
Use the point and slope to get the equation of the perpendicular line
slope m = [tex]-\frac{1}{2}[/tex]
Point slope form of line is
[tex]y-y_1=m(x-x_1)\\y+4=-\frac{1}{2}(x-6)\\y+4=-\frac{1}{2}x+3\\y=-\frac{1}{2}x-1[/tex]
An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5 is [tex]y=-\frac{1}{2}x-1[/tex]
Learn more : brainly.com/question/19864665
plss help me find this hcf
3a-6,a²-4
Step-by-step explanation:
1st expression = 3a - 6 = 3 ( a - 2 )
2nd expression = a² - 4 = a² - 2² = ( a + 2) (a - 2)
The HCF is (a -2).
Hope it helps :)❤
Solve the system: (MAFS.912-A-REI.3.6)
4+7=41
4
x
+
7
y
=
41
4+7=41
4
x
+
7
y
=
41
−7=−16
Step-by-step explanation:
[tex]4x + 7y = 41 \\ 4 \times ( - 7) + 7 \times ( - 16) = 41[/tex]
HELP ME PLEASE I NEED THESE
Answer:
13.5
Step-by-step explanation:
equilateral triangle (all sides are equal) thus, if one side is 4.5 u will need to take 4.5x3=13.5
Well let me help.
For the first Question, the question is asking for the perimeter of the plot so assuming the plot is a rectangle, the perimeter will be (2*3)+(2*4.3)
=6+8.6
=14.6km.
Question 2
The problem involves finding the perimeter of the triangular garden. since the garden is an equilateral triangle, the perimeter will be thrice the side given ("equilateral" means "equal sided triangle"). So the answer will be 3*4.5
= 13.5 km.
Question 3
Same type of question as Q2 but this type is isosceles triangle (only two equal sides with one being different)
So the perimeter will be (2*15)+20
=30+20
=50km.
I hope this'll help
Is RS perpendicular to DF? Select Yes or No for each statement ...
Answer:
depends
Step-by-step explanation:
I need help help......
Answer:
5 DVD's
Step-by-step explanation:
So Basically It means the 25$ a month Plan is the same if you pay
5 DVD's
Ok each DVD costs 3$ and if you buy 5 of them you just bought 15 bucks worth of DVD's plus the membership which is 10$ in which the equation is
3(x)+10=25
X=5 by the way
So Basically it means if you Buy 5 DVD's plus the member ship thats the same money as the 25$ a month deal for unlimated DVD's
Simplified version: 5 DVD's
The diagram shows a square based cuboid. Work out the volume of the cuboid. State the units of your answer.
Answer:
160cm³
Step-by-step explanation:
square based means equal sides
therefore 4cm×4cm=16cm²
16cm²×10cm=160cm³
I really need help. And its setted up-
Answer:
4: 300
5: 95
have a good day :]
Lenny has a model train layout on a large, rectangular board. The length, l, of the board is 3 times the width, w. Which equation can be used to find P, the perimeter of the board?
Answer:
8w
Step-by-step explanation:
Given that:
Length = l
Width = w
l = 3w
Perimeter of rectangular board :
Perimeter of a rectangle = 2(l + w)
Perimeter = 2(3w + w)
Perimeter = 2(4w)
Perimeter of rectangular board = 8w
Using trigonometry Solve the triangle please help me
Answer:
The angle m ∠ W = 33°
The length of XZ = 9.8 units
The length of WX = 15.1 units
Step-by-step explanation:
Given
The right-angled triangle ΔWXZ
m ∠ X = 90°m ∠ Z = 57°Hypotenuse WZ = 18We know that the sum of the measure of angles in any triangle is 180°.
Therefore,
m ∠ W + m ∠ X + m ∠ Z = 180°
substiute m ∠ X = 90° and m ∠ Z = 57° in the formula
m ∠ W + 90° + 57° = 180°
m ∠ W + 147 = 180°
m ∠ W = 180° - 147
m ∠ W = 33°
Therefore, the angle m ∠ W = 33°
NOW,
Determining the lengths of WX and XZ
Length XZ
Using the trigonometric ratio
The adjacent to 57° is XZ.
so
cos 57° = adjacent / hypotenuse
substituting adjacent = XZ, and hypotenuse = 18
cos 57° = XZ / 18
XZ = 18 × cos 57°
XZ = 9.80 units
Therefore, the length of XZ = 9.8 units
Length WX
As
m ∠ W = 33°
The adjacent to m ∠ W = 33° is WX.
so
cos 33° = adjacent / hypotenuse
substituting adjacent = WX, and hypotenuse = 18
cos 33° = WX/ 18
WX = 18 × cos 33°
WX = 15.1 units
Therefore, the length of WX = 15.1 units
Summary:
The angle m ∠ W = 33°
The length of XZ = 9.8 units
The length of WX = 15.1 units
On a standardized test, Rasi answered the fast: 22 questions in 5 minutes. There are 7]
questions on the test. If he continues to answer questions at the same rate how long will
it take him to complete the test?
Answer:
they are directly proportional
so
5/22*7=1.59
he would finish in 1.59 min
Find the missing side. Round your
answer to the nearest tenth.
9514 1404 393
Answer:
missing side: 29.7 feetmissing angle: 53.5°Step-by-step explanation:
The missing side is found using the Pythagorean theorem:
X = √(37^2 -22^2) = √885 ≈ 29.7 . . . feet
The missing angle is found using the cosine relation:
Cos = Adjacent/Hypotenuse
cos(x) = 22/37
x = arccos(22/37) ≈ 53.5°
_____
The posted question asks for side length; the picture asks for angle.
pls help
Quadrilateral ABCD is an isosceles trapezoid. What is the m∠B?
Answer:
<B=105°
Step-by-step explanation:
as it's an isosceles trapezoid. AD parallel to BC
ACCORDING TO THE QUESTION
75°+<B=180°
<B=180°-75°
<B=105°
Help would be great thank you!
Answer:
I think 3x doesn't belong because it is the only positive number.
I think -5x doesn't belong because it is the only one without a 3.
I think -3 doesn't belong because it is the only one without an x.
I think -3x² doesn't belong because it is the only one with an exponent.
Step-by-step explanation:
Just use one of the ones above!
(hope this helps!)
A school is selling concert tickets. The cost is $4 per adult and $2.50 per student. If the school
sells 45 adult tickets and 32 student tickets, how much will they earn in total?
$115.50
$260
$500.50
$240.50
Answer:
4 x 45=180
32 x 2.5=80
180+80=260
so $260 is the correct answer
Step-by-step explanation:
choose the definition for the function y={x+1 x≤2 x+2 x>2 y={x+1 x>2 x+2 x≤2 y={x+1 x
Answer:
D
Step-by-step explanation:
easy question in photo
Answer:
14
Step-by-step explanation:
always subtract the highest number from the lowest and I believe that is your range
Answer:
14
Step-by-step explanation:
A 24-f0ot ladder rests against a house near a second story window 20 feet from the ground. Assume that the ladder
and the house both stt on level ground.
To the nearest whole nurmber, find the following values:
A The measure of the angle formed by the base of the ladder and level ground is
B. The measure of the angle formed by the top of the ladder and the second story window is
C. The distance, on level ground, between the base of the ladder and the house is
feet
degrees.
feet.
Answer:
c
Step-by-step explanation:
Pedro has a square practice net in his backyard. The diagonal of the net is 6 feet. Find the length of one side of the net.
Answer:
3sqrt2
Step-by-step explanation:
If a side length is a, then a^2 + a^2 = 36
2a^2 = 36
a^2 = 18
a = 3sqrt2
Or, you can remember that in a square, if you cut it in half diagonally, you get a 45-45-90 triangle, so the sidenglth is diagonal/sqrt2
You are opening a savings account with $500 that you have saved. The bank offers 3.2% interest, compounded yearly. How much money will you have in you account after 7 years?
Answer:
You will have $623.3441462 in your account after 7 years
Step-by-step explanation:
The formula of the compounded interest is A = P [tex](1+\frac{r}{n})^{nt}[/tex] , where
A is the new valueP is the initial valuer is the rate in decimaln is the number of periodst is the time in years∵ You are opening a savings account with $500
∴ P = 500
∵ The bank offers 3.2% interest, compounded yearly
∴ r = 3.2% ⇒ divide it by 100 to change it to decimal
∴ r = 3.2 ÷ 100 = 0.032
∵ The interest is compounded yearly
∴ n = 1
∵ The time is 7 years
∴ t = 7
→ Substitute these values in the rule above to find A
∵ A = 500 [tex](1+\frac{0.032}{1})^{1(7)}[/tex]
∴ A = 500 [tex](1.032)^{7}[/tex]
∴ A = 623.3441462
∴ You will have $623.3441462 in your account after 7 years
What is the degree of 9x^4 + 3x
Answer:
4
Step-by-step explanation:
1234567791234556677889
Step-by-step explanation:
The rate of pictures per minute.
8 pictures per minute
8 pictures/ minute
This is a new subject in my math class and I don’t understand anything pls helppp
Answer:
the width is 21 feet
Step-by-step explanation:
because if each inch is equal to 3 feet 7x3=21 so its 21 feet yw have a great day
Find the twelfth term in a sequence whose general term is given by an = 5n– 9.
Answer:
51
Step-by-step explanation:
N means that numbered term. If n is 1 then you are getting the first term, and so on.
So for the 12th term, n=12.
5(12)-9 = 60-9 = 51
Answer:
51
Step-by-step explanation:
please mark me as brainliest!!
A.pex VLS Algebra 1: 6.2.4 Practice - HELP NEEDED!!!
The file below is a picture of the problem I'm stuck on... it's hard to explain. I found Coin A and Coin C, but Coin B is confusing me.
Equations to find the value:
Coin A: V=25(1.07)^t
Coin B: V=40(1.05)^t
Coin C: V=60(1.04)^t
V represents the coin's value and t represents what year it is (kind of).
Please help! Even if you can't do the problem, if you explain how to do it to find Coin B, that would be so appreciated! If you are confused about anything, I'll be happy to explain! Thank you!
Answer:
Answer:1.) I chose coin A and B
2.) Coin: B Value: $40 Annual rate: %5
Coin: A Value: $25 Annual rate: %7
3.) Coin: A P: 25 R: 1.07 Function: v = 25(1.07)^t
Coin: B P: 40 R: 1.05 Function: v = 40(1.05)^t
4.) Base: 1+r Initial: P Exponent: t
If R increased, then P would also increase because you must distribute, and you would be distributing R into P there for if R changes then so would P.
5.) Coin A: Initial value: $25 10 years: $25.70 20 Years: $26.40 30 years: $27.10 60 years: $29.20
Coin B: Initial value: $40 10 years: $40.50 20 years: $41 30 years: $41.50 60 years: $43
Coin C: Initial value: $60 10 years: $60.40 20 years: $60.80 30 years: $61.50 60 years: $62.40
6.) Coin A because the value goes up the most and I probably wouldn't be able to keep the coin for more than 60 years because I would lose it.
the first 3 terms of the arithmetic sequence are given. find an expression t_ n in the terms of n and write the tenth term of each sequence
Answer:
We get tₙ: [tex]\mathbf{t_n=an}[/tex]
10th term is [tex]t_{10}=10a[/tex]
Step-by-step explanation:
The given arithmetic sequence is: a,2a,3a
We need to find tₙ and tenth term
Finding tₙ
The formula used is: [tex]t_n=t1+(n-1)d[/tex]
We need to find d, the common difference
a₁ = a
a₂ = 2a
We can find common difference using the formula:
[tex]t_n=t_1+(n-1)d\\Put\:n=2\\t_2=t_1+(2-1)d\\2a=a+d\\d=2a-a\\d=a[/tex]
So, we get common difference d = a
Now, finding tₙ
[tex]t_n=t_1+(n-1)d\\t_n=a+(n-1)a\\t_n=a+an-a\\t_n=an[/tex]
So, we get tₙ: [tex]\mathbf{t_n=an}[/tex]
Now, finding 10th term
By putting n=10 in the equation [tex]t_n=an[/tex]
[tex]t_n=an\\Put\:n=10\\t_{10}=a(10)\\t_{10}=10a[/tex]
So, 10th term is 10a
what is distributive of property
(6e - 3f - 4) * 2
Answer:
12e - 6f - 8
Step-by-step explanation:
(a+b)*c = a*c + b*c
6e * 2 -3f * 2 -4 * 2
Pls help due ASAP
Show workings please!!!
Answer:
AB=8
Step-by-step explanation:
First, you get figure out x. Since both sides are equal, use the equation x+3=2x-2, then subtract x from both sides, 3=x-2, and then add 2 to both sides, x=5. Then use one of the equations to get the length of the side, I used x+3=8, which is your answer.
(hope this helps :P)
Joe bought some CD's and DVD's at the store.
• He bought a total of 12 items.
• The CD's were $14.
• The DVD's were $22.
• He spent $200.
How many of each did he buy?
Answer: x=8 and y=4
Step-by-step explanation:
x+y=12 x=12-y x=12-4
14x+22y=200 x=8
14(12-y)+22y=200
168-14y+22y=200
-168 -168
-14y+22y=32
8y=32
8y/8=32/8
y=4
ASAP! Please do 1-5 and show work if possible!
Answer :
(1) The radius of a circle is 1.5 m.
(2) The diameter of a circle is 28 ft.
(3) The radius of a circle is 10 in.
(4) The circumference of circle is 47.14 m.
(5) The circumference of circle is 44 yd.
Step-by-step explanation :
Part 1:
Given: d = 3 m
Now we have to determine the radius of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Radius of a circle = [tex]\frac{3m}{2}=1.5m[/tex]
The radius of a circle is 1.5 m.
Part 2:
Given: r = 14 ft
Now we have to determine the diameter of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Diameter of a circle = [tex]Radius\times 2[/tex]
Diameter of a circle = [tex]14ft\times 2=28ft[/tex]
The diameter of a circle is 28 ft.
Part 3:
Given: d = 20 in
Now we have to determine the radius of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Radius of a circle = [tex]\frac{20in}{2}=10in[/tex]
The radius of a circle is 10 in.
Part 4:
Given: d = 15 m
Now we have to determine the circumference of circle.
Formula used:
[tex]C=\pi d[/tex]
where,
C = circumference
d = diameter
So,
[tex]C=\frac{22}{7}\times 15m[/tex]
[tex]C=47.14m[/tex]
The circumference of circle is 47.14 m.
Part 5:
Given: r = 7 yd
Now we have to determine the circumference of circle.
Formula used:
[tex]C=\pi d[/tex]
or we can write,
[tex]C=\pi (2\times r)[/tex]
where,
C = circumference
d = diameter
r = radius
So,
[tex]C=\frac{22}{7}\times (2\times 7yd)[/tex]
[tex]C=44yd[/tex]
The circumference of circle is 44 yd.
Herman is decorating his bedroom ceiling with lights. If the rectangular ceiling is 15 meters by 8 meters, how long will the string of lights need to be to reach from one corner of the ceiling to the opposite corner?
Answer:
x = 17 m
Step-by-step explanation:
The dimensions of the rectangular ceiling are 15 m by 8 m
We need to find the length of the string of lights need to be to reach from one corner of the ceiling to the opposite corner. Let it is x.
We need to find the diagonal of the rectangular ceiling. It can be calculated using Pythagoras theorem.
[tex]x^2=15^2+8^2\\\\x^2=225+64\\\\x^2=289\\\\x=\sqrt{289}\\\\x=17\ m[/tex]
So, the length of the string of lights is 17 m.