We need to find the equation which is equidistant to the given points.
[tex]A(-2,6,3)[/tex] and [tex]B(5,3,-3)[/tex]
This can be done using the distance formula.
Let us take a point [tex]P(x,y,z)[/tex] which is equidistant from both points so
[tex]\sqrt{(x+2)^2+(y-6)^2+(z-3)^2}=\sqrt{(x-5)^2+(y-3)^2+(z+3)^2}\\\Rightarrow y^2-12y+x^2+4x+z^2+49-6z=y^2-6y+x^2+z^2+6z+43-10x\\\Rightarrow 7x-3y-2z+1=0[/tex]
The required equation is [tex]7x-3y-2z+1=0[/tex]
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Gavin and Jim win some money and share it in the ratio 5:2. Gavin gets £39 more than Jim. How much did they get altogether?
Answer:
They got $91 in total
Step-by-step explanation:
I did some trial and error and when I reached 65 dollars for Gavin I realized that Jim would be $29. So 65 - 29 = $39. Btw substitute $ for £
Answer: £91
Step-by-step explanation:
Let x be the amount of money Jim gets
Let x + 39 be the amount of money Gavin gets
Given information
Ratio = 5 : 2 (Gavin to Jim)
Jim = x
Gavin = x + 39
Set up proportion
5 / 2 = (x + 39) / x
Cross multiply to reduce fraction form
5x = 2 (x + 39)
Expand parentheses and apply the distributive property
5x = 2 · x + 2 · 39
5x = 2x + 78
Subtract 2x on both sides
5x - 2x = 2x + 78 - 2x
3x = 78
Divide 3 on both sides
3x / 3 = 78 / 3
x = 26
Find the amount of money they get altogether
Gavin + Jim
=x + 39 + x
=(26) + 39 + (26)
=65 + 26
=[tex]\boxed{91}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A pole vault stick is leaning against a wall, touching the wall 16 ft above the ground. The bottom end of the stick is 12 ft from the wall. How many feet long is the stick?
Answer:
20ft
Step-by-step explanation:
Height from the ground=16ft
distance from wall= 12ft
length of the stick=?
According to the Pythagoras theorem the square of the hypotenuse is equal to the sum of the squares of the opposite sides.
Here the stick is the hypotenuse.
[tex]12^{2} +16^{2} = x^{2}[/tex]
144+ 256= [tex]x^{2}[/tex]
[tex]x^{2}[/tex]= 400
[tex]x=\sqrt{400} \\x= 20[/tex]
Hence the length of the stick is 20ft.
Hope this helps.
Which tree is growing faster
Answer:
tree 1 is growing faster
Using the slope of a linear function, it is found that Tree 1 is growing faster.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1. It can be given by the change in the input divided by the change in the output.b is the y-intercept, which is the value of y when x = 0.In this problem:
Tree 1 is growing 1.5 inches every week.For tree 2, when the week increasing by 1, the height also increases by 1, hence the slope is 1, which means that it is increasing 1 inch per week.Thus, tree 1 is growing faster.You can learn more about the slope of a linear function at https://brainly.com/question/24674549
-8b+x evaluate the expression 1B equals five and X equals -7
please help
Answer:
-47
Step-by-step explanation:
Find an equation of the plane that passes through the point P0 = (6, 3, 2) and is parallel to the xy-plane. g
The xy-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.
Then the equation of the plane through (6, 3, 2) that is parallel to the xy-plane has equation
〈x - 6, y - 3, z - 2〉 • 〈0, 0, 1〉 = 0
==> z - 2 = 0
==> z = 2
Which ratio expresses the scale used to create this drawing? The post office has dimensions of 24 meters by 60 meters
Answer: 2:5
Step-by-step explanation:
To find the ratio, we need to find the greatest common factor and divide both of the dimensions by the greatest common factor. In this case 12 is the greatest common factor.
24/12=2
60/12=5
Therefore, the ration that expresses the scale used to create this dimension is 2:5.
Hayden has 6 rolls of dimes there are 50 dimes in each row how many dimes does he have all together
Answer:
300 dimes in total
Step-by-step explanation:
He has 6 rows with 50 in each. 6 times 50 = 300 dimes
Answer:
300
Step-by-step explanation:
1 roll = 50 dimes
6 roll = x Cross multiply
1*x = 50 * 6
x = 300 dimes
He has 300 dimes altogether.
Which expression is equivalent to 10° ?
o 10 - 10 - 10 - 10 - 10 - 10
O 6.6.6.6.6.6.6.6.6.6
0 10. 10. 10. 10.10
o I don't know.
Hi
Answer:
The first one: 10*10*10*10*10*10
Step-by-step explanation:
This is because the power of a number is how many times you multiply it by itself (example: [tex]2^{4}[/tex] = 2*2*2*2 because the power is 4 which means you multiply the base by itself 4 times, in this case the base is 2)
Answer:
A. 10 · 10 · 10 · 10 · 10 · 10
Step-by-step explanation:
[tex]10^6[/tex] is just 10 times itself, 6 times.
suppose the functions u and w are defined as follows u(x)=x+9 w(x)=the square root of x+8 find the following (wou)(8)= (uow)(8)=
Answer:
5 and 13
Step-by-step explanation:
To evaluate (w ￮ u)(8) , evaluate u(8) then substitute the value obtained into w(x) , that is
u(8) = = 8 + 9 = 17 , then
w(17) = [tex]\sqrt{17+8}[/tex] = [tex]\sqrt{25}[/tex] = 5
---------------------------------------
To evaluate (u ￮ w )(8) , evaluate w(8) then substitute the value obtained into u(x) , that is
w(8) = [tex]\sqrt{8+8}[/tex] = [tex]\sqrt{16}[/tex] = 4 , then
u(4) = 4 + 9 = 13
Answer:
Step-by-step explanation:
[tex]u(x)=x+9\\\\w(x)=\sqrt{x+8} \\\\(wou)(x)=u(w(x))=u(\sqrt{x+8} )=\sqrt{x+8}+9\\(wou)(8)= \sqrt{8+8}+9=4+9=13\\\\\\(uow)(x)=w(u(x))=w(x+9)=\sqrt{x+9+8}=\sqrt{x+17}\\(wou)(8)= \sqrt{8+17}=\sqrt{25}=5\\\\[/tex]
is 1.0227 a rational number? explain
Answer:
Yes.
Step-by-step explanation:
1.0227 is a rational number. Although it is a decimal, it is terminating meaning that it ends. This is what makes it rational.
Step-by-step explanation:
Yes as it can be written in p/q form means 10227/10000 which is rational
Simplify the following 1)0.002 x 3421. 2)584.23 x 4.3214. 3)1000 x 4.3214. 4)31.234 x 300. 5)333.333 x 0.0003 Plsssss show working
Answer:
Step-by-step explanation:
Basically you just multiply everything together
1) 6.842
2) 2524.691522
3) 4321.4
4) 9370.2
5) 0.0999999
Best way to solve these questions is either a calculator or write the questions down and figure it out yourself. It isn't that hard.
Explanation on how to place the decimal places I found on a good website:
Decimals are multiplied as if they were whole numbers, and then the decimal point is placed in the product.
To find out where the decimal point should be placed, count the number of decimal places after the decimal point in each factor.
Multiply 0.7 by 0.352
0.7 1 decimal place
0.352 3 decimal places
A total of 4 decimal places
Once you have found the sum of the decimal places in each factor, you know how many decimal places the product will need after its decimal point. Starting at the far right of the number, move the decimal point toward the left that number of decimal places.
0.2464 (4 decimal places after the decimal point)
Dividing decimals
1. Move the decimal point in the divisor to the right to make the divisor a whole number.
2. Move the decimal point in the dividend the same number of places to the right.
3. Place the decimal point in the quotient directly over the decimal point in the dividend for the final quotient.
4. Divide as if working with whole numbers
Calculate the ratios in the table using the side lengths that you recorded in Part C.
Step-by-step explanation:
The ratios are;
\dfrac{BC}{AB} = \dfrac{3}{5}
AB
BC
=
5
3
\dfrac{AC}{AB} = \dfrac{4}{5}
AB
AC
=
5
4
\dfrac{BC}{AC} = \dfrac{3}{4}
AC
BC
=
4
3
\dfrac{DE}{AD} = \dfrac{3}{5}
AD
DE
=
5
3
\dfrac{AE}{AD} = \dfrac{4}{5}
AD
AE
=
5
4
\dfrac{DE}{AE} =\dfrac{3}{4}
AE
DE
=
4
3
koGiven that the lengths of the sides are;
\overline {AB}
AB
= 20
\overline {BC}
BC
= 12
\overline {AC}
AC
= 16
\overline {AD}
AD
= 10
\overline {DE}
DE
= 6
\overline {AE}
AE
= 8
The ratios are;
\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{BC}{AB} = \dfrac{12}{20} = \dfrac{3}{5}
Hypothenus
Length opposite ∠A
=
AB
BC
=
20
12
=
5
3
\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AC}{AB} = \dfrac{16}{20} = \dfrac{4}{5}
Hypothenus
Length adjacent ∠A
=
AB
AC
=
20
16
=
5
4
\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{BC}{AC} = \dfrac{12}{16} = \dfrac{3}{4}
Length adjacent ∠A
Length opposite ∠A
=
AC
BC
=
16
12
=
4
3
\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{DE}{AD} = \dfrac{6}{10} = \dfrac{3}{5}
Hypothenus
Length opposite ∠A
=
AD
DE
=
10
6
=
5
3
\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AE}{AD} = \dfrac{8}{10} = \dfrac{4}{5}
Hypothenus
Length adjacent ∠A
=
AD
AE
=
10
8
=
5
4
\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{DE}{AE} = \dfrac{6}{8} = \dfrac{3}{4}
Length adjacent ∠A
Length opposite ∠A
=
AE
DE
=
8
6
=
4
3
A salesman's salary is $18,500 per year. In addition, the salesman earns 5% commission on the year's sales. Last year the salesman earned $25,400. How much was sold that year?
Answer:
138000
Step-by-step explanation:
25,400 - 18,500
6900
5% = 6900
100% = ?
cross multiplication
5x6900 / 100
yearly sale = 138000
plzzzzzzzz HELP ASPPPP
Select the correct answer.
This graph represents the function f(x) =cos(4x).
Answer:
π/2
Step-by-step explanation:
steps are in the picture above.
Note:if you need to know any question please let me know.
Is square root of 49/5 a rational number?
Which one of the following is an example of algebraic expression?
a. 22+7÷4
b. 12=7−1
c. x,y,z
d. x2+y−2
Answer:
Option D. x²+y-2
Step-by-step explanation:
Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.
Answer:
The correct option is choice D. x^2+y−2
Algebraic expression means that equation needs to have one variable, meaning any alphabet and one kind of operation. Operations are + - / and*
If you look at your answer choices, option d is the only that has an expression as well as the operation, so both things in one equation.
What property is show in this problem? 11 x (4+5) = 11 x 4 + 11 x 5
PLEASE HELP
3/5x+22=28
Show your work in details if you can, I have a hard time understanding this.
Step-by-step explanation:
3/5x+22=28
3/5x=28-22
3/5x=6
3x=6*5
3x=30
X=30/3
X=10
The following image is a piece of tile from a kitchen floor. What does the bolded line represent?
A. a line
B. a line segment
C. a ray
D. a plane
Answer:
a line segment in the correct answer
Solve the system of equations.
y=3x + 24
y=9x
Answer:
x = 4
y = 36
Step-by-step explanation:
use substitution
y=3x+24
y=9x
therefore . 9x=3x+24
x = 4
sub 4 in for x and solve for y
y = 9(4) = 36
Group discounted lift tickets were $14 for those paying with cash and $15 for those
paying with a credit card. The total paid by the group was $177.00. Three times as many
people paid with a credit card as those who paid with cash. How many people paid with
cash?
PLEASE ANSWER WITH AN EXPLANATION
Answer:
3 people
Step-by-step explanation:
Let "x" represent the number of people who payed with cash
Let "y" represent the number of people who payed with credit card
14x +15y = 177 ---------1
3x =y--------- 2
solving simultaneously,
put eqn 2 into eqn 1
14x + 15 (3x) = 177
14x + 45x = 177
59x = 177
x=3
From eqn 2 , y = 3 x
y = 3 (3)
y=9
therefore the number of people who paid with cash were 3.
full form of ALU please tell
Answer:
ALU stands for arithmetic logic unit. which is part of the central processing unit of a computer which performs arithmetic and logical operations.
I hope this helps
Answer:
In computer science: Architecture and organization. …of a control unit, an arithmetic logic unit (ALU), a memory unit, and input/output (I/O) controllers. The ALU performs simple addition, subtraction, multiplication, division, and logic operations, such as OR and AND.
Step-by-step explanation:
Complete the slope-intercept form of this line.
y=-4x +
Answer:
It is y = -4x + 9
Step-by-step explanation:
General equation of a line:
[tex]y = mx + c[/tex]
For a y-intercept, c :
consider point (2, 1):
y is 1, x is 2 and m is -4
[tex]y = mx + c \\ 1 = (2 \times - 4) + c \\ 1 = - 8 + c \\ c = 1 + 8 \\ c = 9[/tex]
therefore, equation is:
[tex]y = - 4x + 9[/tex]
The complete form of the equation is y = - 4x + 9
The slope intercept form of the line is given as:
y = - 4x + c
Where c = intercept , we need to calculate, c
Take any given value of y and x and substitute into the equation, the solve for c
Take x = 1, y = 5
5 = - 4(1) + c
5 = - 4 + c
Add 4 to both sides
5 + 4 = - 4 + c + 4
9 = c
Hence, the complete form of the equation is y = - 4x + 9
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i need help please and thank you
Answer:
the length of each shape will alternate between even numbers and is numbers.
Step-by-step explanation:
just think !
there are 3 cubes in the basic shape.
now, with every step he adds 1 more cube to the length, and one more cube to the height. that means 2 more cubes.
so, it goes 3, 5, 7, 9, ... cubes
therefore, the first answer is wrong. the shape in every step will always have an uneven (odd) number of boxes. remember, adding an even number to an uneven number will always result in an uneven number. only uneven and uneven or even and even can have even results.
but the length itself - he only adds there one box at a time, will go
2, 3, 4, 5, 6, ...
so, it will alternate between even and uneven numbers.
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
slope=2/2 or 1
Step-by-step explanation:
From (-2,0) rise up by 2 and then run to the right and land on 2. So the slope will be 2/2. To simplify it's 1.
Remember this Rise goes⬆/Run to the right➡ or the other way around depends on how the graph is but you get my drift, right? ☺
A=1/2pie r squared solve for pie
Answer:
[tex]A = \frac{1}{2} \pi r [/tex]
multiply all sides by 2:
[tex]2 \times A = ( \frac{1}{2} \pi r) \times 2 \\ \\ 2A = \pi r[/tex]
divide all sides by r:
[tex] \frac{2A}{r} = \frac{\pi r}{r} \\ \\ \frac{2A}{r} = \pi[/tex]
therefore:
[tex]{ \boxed{ \sf{\pi = \frac{2A}{r} }}}[/tex]
5,926 in scientific notation
B
How many degrees must
Figure A be rotated
counterclockwise around
the origin in order to line
up with Figure B?
A
A 90
B. 180
C. 270
D. 360
Answer:
90 degree is my guess please
Answer:
90
Step-by-step explanation:
it's 90 because if it needs to be in line with a it has to be rotated a bit and since the lowest is 90 the answer is 90
Find the value of a.
Answer:
86°
Step-by-step explanation:
try suggested solution (see the attached picture), note, the suggested way is not the shourtest one.
a company spent 36% of its annual budget developing a new bicycle. What fraction of the company's budget was spent on developing the new bicycle?
Answer:
9/25
Step-by-step explanation:
36% = 36/100
Simplify the fraction and you'll have:
9/25
Answer:
9/25
Step-by-step explanation:
36% = 0.36 = 36/100 = 18/50 = 9/25
If my answer is incorrect, pls correct me!
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-Chetan K