The standard form equation of the line connecting the two points is [tex]2x + y = -2[/tex]
Linear equation in a standard form is given as [tex]Ax + By = C[/tex]
where,
A, B, and C are constants or numbers
x and y are the variables.
To solve this problem, the following steps would be taken:
Step 1: Find the slope of the line connecting points (-3,4) and (2,-6)
[tex]slope (m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where,
[tex](x_1, y_1) = (-3,4)\\(x_2, y_2) = (2,-6)[/tex]
Substitute
[tex]slope (m) = \frac{-6 - 4}{2 -(-3)} \\m = \frac{-10}{5}\\m = -2[/tex]
Step 2: Find the y-intercept (b) of the line by substituting [tex](x, y) = (-3,4)[/tex] and [tex]m = -2[/tex] into [tex]y = mx + b[/tex] (slope-intercept form)
[tex]4 = -2(-3) + b\\4 = 6 + b\\4 - 6 = 6 + b - 6\\-2 = b\\b = -2[/tex]
Step 3: Write the equation of the line in slope-intercept form by substituting [tex]m = -2[/tex] and [tex]b = -2[/tex] into [tex]y = mx + b[/tex]
[tex]y = -2x + (-2)\\y = -2x - 2[/tex]
Step 4: Rewrite the equation in standard form [tex](Ax + By = C)[/tex]
[tex]y = -2x - 2\\[/tex]
Add [tex]2x[/tex] to both sides
[tex]2x + y = -2x - 2 + 2x\\2x + y = -2[/tex]
The standard form equation of the points (-3,4) and (2,-6) is [tex]2x + y = -2[/tex]
Learn more about standard form of two points of a linear equation here:
https://brainly.com/question/18446164
What is the solution to the equation 1 over the square root of 8 = 4^(m + 2)? A) m = − 15 over 4 B) m = − 11 over 4 C) m = 5 over 4 D) m = 9 over 4
Answer:
B) m = -11/4
Step-by-step explanation:
What is the solution to the equation 1/sqrt(8) = 4^(m+2)
1 over the square root of 8 = 4^(m + 2)?
A) m = − 15 / 4
B) m = − 11 / 4
C) m = 5 / 4
D) m = 9 / 4
1/sqrt(8) = 4^(m+2) apply law of exponents
1/2^(3/2) = (2^2)^(2m+4)
2^(-3/2) = (2)^(2m+4)
-3/2 = 2m+4
2m = -11/2
m = -11/4
How to do this question plz.
plz work out for me in your notebook or sheet if you can plz the question so I can understand more plzz
Answer:
[tex]3\pi[/tex]
Step-by-step explanation:
The circumference of a circle is [tex]2\pi r[/tex].
If we want to find the circumference of this semi-circle, we can find the circumference if it was a whole circle then divide by 2.
[tex]2 \cdot \pi \cdot r\\2 \cdot \pi \cdot 3\\6 \cdot \pi\\ 6\pi[/tex]
Now we know the circumference of the whole circle.
To find the circumference of half the circle we divide by 2.
[tex]6\pi \div 2 = 3\pi[/tex]
Hope this helped!
PLEASE HELP WILL MARK BRAINLIEST
Answer:
18 m
Step-by-step explanation:
Answer:
18m
Step-by-step explanation:
Becky's ship is 43 miles west all the harbor.
Clyde's yacht is a5 miles north from Beery. How
far is Clyde from the Harbor? Show your work.
С
x= Harbor
25
B.
43
Answer:
Clyde is 49.74 away from the harbor
Step-by-step explanation:
Here in this question, we are interested in knowing the distance of Clyde from the harbor.
The key to answering this question is having a correct diagrammatic representation. Please check attachment for this.
We can see we have the formation of a right angled triangle with the distance between Clyde’s ship and the harbor the hypotenuse.
To calculate the distance between the two, we shall employ the use of Pythagoras’ theorem which states that the square of the hypotenuse is equal the sum of the squares of the two other sides.
Let’s call the distance we want to calculate h.
Mathematically;
h^2 = 25^2 + 43^2
h^2 = 625 + 1849
h^2 = 2474
h = √2474
h = 49.74 miles
If there are:
6 red marbles
10 yellow marbles
5 green marbles
and 1 blue marble
What is the probability of picking 1 red marble and 1 green marble?
(Once a marble is chosen it IS put back into the box).
(Write your answer in the form of a decimal, round to 2 places).
Answer:
[tex]probability = \frac{1}{2}[/tex]
Step-by-step explanation:
Probability is the chance of an event happening. It can simply be defined by the following formula,
[tex]probability = \frac{desired\ outcomes}{total\ outcomes}[/tex]
The total outcome is all of the possible outcomes or the sum of all of the types of marbles. The desired outcomes are the outcomes that one wants or the sum of the number of wanted marbles,
[tex]total\ outcomes = red+yellow+green+blue\\=6+10+5+1\\=22[/tex]
[tex]desried\ outcomes= red+green\\= 6 + 5\\=11[/tex]
Substitute into the formula to find the probability of an event:
[tex]probability = \frac{desired\ outcomes}{total\ outcomes}[/tex]
[tex]probability = \frac{11}{22}[/tex]
Simplify,
[tex]probability = \frac{11}{22}[/tex]
[tex]probability = \frac{1}{2}[/tex]
Steel chain costs $0.75 per foot from Company
X, which provides free shipping. The same
steel chain costs $1.20 per yard at Company Y,
which charges a $120.00 shipping fee for all
orders. How much more does Company
Y charge, in dollars, than company X for 300
feet of steel chains?
Answer:
Company Y charges 255 dollars more then Company X :)
Step-by-step explanation:
Company X: 0.75 * 300 = 225 + 0 shipping
Company Y: 1.20 * 300 = 360 + 120 shipping = 480
480 - 225 = 255
BRAINIEST!!! only answer if you know and can give an explanation, will report for non-sense answers
Answer:
Below
Step-by-step explanation:
For a given shape to be a rhombus, it should satisfy these conditions:
● The diagonals should intercept each others in the midpoint.
● The diagonals should be perpendicular.
● The sides should have the same length.
We will prove the conditions one by one.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's prove that the diagonals are perpendicular:
To do that we will write express them as vectors
The two vectors are EG and DF.
The coordinates of the four points are:
● E(0,2c)
● G (0,0)
● F (a+b, c)
● D (-a-b, c)
Now the coordinates of the vectors:
● EG (0-0,0-2c) => EG(0,-2c)
● DF ( a+b-(-a-b),c-c) => DF (2a+2b,0)
For the diagonals to be perpendicular the scalar product of EG and DF should be null.
● EG.DF = 0*(2a+2b)+(-2c)*0 = 0
So the diagonals are perpendicular.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's prove that the diagonals intercept each others at the midpoints.
The diagonals EG and DF should have the same midpoint.
● The midpoint of EG:
We can figure it out without calculations. Since G is located at (0,0) and E at (0,2c) then the distance between E and G is 2c.
Then the midpoint is located at (0,c)
● The midpoint of DF:
We will use the midpoint formula.
The coordinates of the two points are:
● F (a+b,c)
● D(-a-b,c)
Let M be the midpoint of DF
●M( (a+b-a-b,c+c)
● M (0,2c)
So EG and DF have the same midpoint.
■■■■■■■■■■■■■■■■■■■■■■■■■■
There is no need to prove the last condition, since the two above guarante it.
But we can prove it using the pythagorian theorem.
Please help me with these questions please.
Answer:
see image
Step-by-step explanation:
Simplify square roots
Simplify.
Remove all perfect squares from inside the square root.
12
Answer:
[tex]2\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{12}[/tex]
[tex]\sqrt{(4)(3)}[/tex]
square root of 4 is 2
[tex]2\sqrt{3}[/tex]
the 3 stays inside
32.
What is the value of x for ∆DEF?
HELP! Answer if you can!!
Step-by-step explanation:
[tex]c^{2} = {a}^{2} + { b}^{2} [/tex]
Pythagoras theorem
x²=12² + 5²
x²=144+25
x²=169
[tex]x = \sqrt{169} [/tex]
x=13
Answer:
x = 13
Step-by-step explanation:
Using the Pythagorean Theorem to find the missing hypotenuse side:
[tex]a^2+b^2=c^2[/tex]
12 and 5 are a and b. 'x' would be c.
[tex]12^2+5^2=c^2\\\\12^2=144\\5^2=25\\\\144+25=c^2\\\\169=c^2\\\\\sqrt{169}=\sqrt{c^2}\\\\\boxed{13=c}[/tex]
'x' should be equal to 13.
a bottle is completely filled with olive oil the mass of the bottle is 500 grams if the density of the oil os 0.92 grams per milliliter what is the volume of the bottle to the nearest milliliter?
Answer:
543.48 millimetre
Step-by-step explanation:
mass/density = volume
500 grams / 0.92 grams per millimetre = 543.48
Answer:
volume = 543.478 cm³
Step-by-step explanation:
Density = mass / volume
0.92g/ml = 500g / volume
volume (0.92g/ml) = 500g
volume = 500g / (0.92g/ml)
volume = 543.478 ml (aprox. to the nearest mililiter)
1 ml = 1cm³
543.478ml = 543.478 cm³
Find the length of side x in simplest radical form with a rational denominator.
Answer:
x = 3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp side / adj side
tan 30 = sqrt(3) / x
x tan 30 = sqrt(3)
x = sqrt(3) / tan 30
x =sqrt(3) / (1 / sqrt(3))
x = sqrt(3) * sqrt(3)
x = 3
I'LL GIVE BRAINLIEST !! FASTER
please provide explaination
Answer:
532
A
Step-by-step explanation:
A=86
B=180
C=94
D=266
now,
a+b+c+d_94
=86+180+94+266_94
=532
Two lines cross to make the letter x. The letter is 5 inches wide. What is the angle where the lines cross
Answer:
24
Step-by-step explanation:
trudt
PLEASE HELP!!!
Write the correct geometric sequence formula for each of the sequences listed below
1st sequence:
1,3,9,27,…
2nd sequence:
400,200,100,50,…
3rd sequence:
4,8,16,32,…
4th sequence:
400,100,25,6.25,…
5th sequence:
1,5,25,125,…
6th sequence:
1000,500,250,125,…
7th sequence:
2,10,50,250,…
What are the geometric formulas???
Here are the options:
A.) y=1600(0.25)^x
B.) y=800(1/2)^x
C.) y=2/5(5)^x
D.) y=1/5(5)^x
E.) y=2000(1/2)^x
F.) y=1/3(3)^x
G.) y=2(2)^x
Please match the formulas with the correct sequence.
It’s a lot I know but I just absolutely suck at this stuff.
Answer:
1st sequence is F
2nd sequence is B
3rd sequence is G
4th sequence is A
5th sequence is D
6th sequence is E
7th sequence is C
Step-by-step explanation:
A) 1600*0.25= 400- the first term of the sequence
1600*0.25^2= 100- the second term
so it is 4th sequence
B) y=800* (1/2)^x
The first term is 800*1/2=400
The second term is 800*(1/2)^2= 800*1/4=200
the 2nd sequence
C) y= 2/5*5^x
The first term is y=0.4*5=2
The second term is y= 0.4*5^2=10
7th sequence
D) y=1/5* 5^x
The first term is y=1/5*5=1
The second term is y= 1/5 *5*5=5
The 5th sequence
E) y=2000*(1/2)^x
The first term of 2000*1/2=1000
The only sequence with such the first term is 6th sequence
F) y=1/3*3^x
y= 1/3*3=1 - the first term
y= 1/3*3*3=3
1st sequence
G) y= 2*2^x
y=2*2= 4 - the first term
it is the third sequence
If Eric can paint $3$ cars in $4$ hours and $2$ trucks in $5$ hours, then how long, in hours, would it take him to paint $4$ cars and a truck? Express your answer as a common fraction.
Answer:
47/6
Step-by-step explanation:
Given that :
Time taken to paint 3 cars = 4 hours
Time taken to paint 2 trucks = 5 hours
How long will it take him to paint 4 cars and a truck
If 3 cars = 4 hours ;
Then ;
1 car = (4/3)hours
If 2 trucks = 5 hours
Then;
1 truck = (5/2) hours = 2 1/2 hours
Time required To paint 4 cars :
4 × (4/3) = 16/3 hours
Time required to paint 1 truck :5/2 hours
Total time required :
(16/3 + 5/2) = (32 + 15) / 6 = 47/6
A rectangular bathroom mirror has a perimeter of 22 feet. Its area is 18 square feet. What are the dimensions of the mirror?
Answer:
The dimensions of the mirror is 9 feet and 2 feet
Step-by-step explanation:
Keep in mind that the area and perimeter of a rectangle is:
Area - length x width
Perimeter - 2 (l + w)
List the factors of 18 (the area of the mirror):
1, 2, 3, 6, 9, 18
POSSIBLE DIMENSIONS OF MIRROR:
1 ft and 18 ft
Area = 18 ft^2
Perimeter = 38 feet
2 ft and 9 ft
Area = 18 ft^2
Perimeter = 22 feet
3 ft and 6 ft
Perimeter = 18 feet
The rectangle with dimensions 2 feet and 9 feet corresponds with the area and perimeter of the mirror mentioned. So those are the correct dimensions.
Hope these helps!
I need help ASAP!! Please explain how to solve the problem
Answer:
B=.5*8*6=.5*48=24
h = 8
P=10+6+8=24
Surface area =2*24+24*8=48+192=240
Step-by-step explanation:
The base is a triangle, and the area of a triangle is 1/2 base (or width) times height (or length). In this case, base is 8 and height is 6, so the area can be found either by multiplying .5*8*6 or by dividing 8*6 by 2, either of which will give you the same answer of B=24.
Height is given, h=8.
Perimeter is simply the sum of the sides, which are given, so the perimeter is 8+6+10=24.
The formula for surface area is given, so all you need to do is plug in your previous answers and you've got it!
A piece of aluminum occupies a volume of 12.7 milliliters and weighs 87.3 grams. What is its density of the aluminum rounded to the nearest hundredth? Only enter numerical values, which can include a decimal point.
Answer:
6.87 g/mL
Step-by-step explanation:
The density of an object can be found by dividing the mass by the volume.
[tex]density=\frac{mass}{volume}\\\\ d=\frac{m}{ v}[/tex]
We know that the aluminum occupies a volume of 12.7 milliliters and weighs 87.3 grams. Therefore, the mass is 87.3 g and the volume is 12.7 mL.
[tex]m= 87.3 g\\\\v=12.7 mL[/tex]
Substitute the values into the formula.
[tex]d= \frac{87.3 g}{12.7 mL}[/tex]
Divide 87.3 g by 12.7 mL
[tex]d=6.87401575 g/mL[/tex]
Round to the nearest hundredth. The 4 in the thousandth place tells us to leave the 7 in the hundredth place.
[tex]d= 6.87 g/mL[/tex]
The density of the aluminum is about 6.87 grams per milliliter.
GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
Three stores have the same tablet computer on sale. The regular price of the tablet is $150. Store A is offering the tablet on sale at 15% off the regular price. Store B is offering a $25 coupon to be deducted from the regular price. Store C is offering a rebate of $20.00 to purchasers. Store D has the tablet on sale for $120.00. Which store is offering the tablet at the lowest cost?
A. Store A
B. Store B
C. Store C
D. Store D
Show ALL work please! <3
Answer: Store D
Step-by-step explanation:
Store A - 15% off:
$150 times 15/100 = 22.5
$150 - $22.50 = $127.50 so the price at store A is $127.50
Store B - $25 coupon
$150 - $25 = $125 so the price at store B is $125
Store C - $20 rebate
$150 - $20 = $130 so the price at store B is $130
Store D - $120
$120 is the lowest so the answer is Store D
Answer:
[tex]\Large \boxed{\mathrm{Store \ D}}[/tex]
Step-by-step explanation:
Store A is offering the tablet on sale at 15% off the regular price.
150 × (1 - 15%) = 127.5
Store B is offering a $25 coupon to be deducted from the regular price.
150 - 25 = 125
Store C is offering a rebate of $20.00 to purchasers.
150 - 20 = 130
Store D has the tablet on sale for $120.00.
Store D is offering the tablet at the lowest cost.
Determine if the expression 464 +c+ cº is a polynomial or not. If it is a polynomial,
state the type and degree of the polynomial.
Answer:
I wish I could help but I'm not sure
Rearrange the equation below to identify the variables a, b and c.
0 = 4x – 5x2
Answer:
a = -5x
b = 4
c = 0
Step-by-step explanation:
binomial equation is written in form of
[tex]ax^2 + bx + c = 0[/tex]
given equation
[tex]0 = 4x - 5x^2[/tex]
rearranging it we have
[tex]0 = - 5x^2 + 4x + 0[/tex]
comparing this equation with [tex]ax^2 + bx + c = 0[/tex]
comparing coefficient of variables with same power.
a = -5x
b = 4
c = 0
Geometry, please answer question ASAP
Answer:
D. 101
Step-by-step explanation:
(25x+1)+(25x-2)+(20x-1)+82=360
70x=360-1+2+1-82
70x=280
x=4
A=25x+1=101
Can anyone help me with this please and maybe explain it?..
Q. A factory uses 800 watts of electricity in 40 minutes. How many watts does it uses in 3 hours?
Answer:
3600 i think
Step-by-step explanation:
You move down 5 units and up 5 units. You end at (1,3). Where did you start?
Answer:
(1, 3)
Step-by-step explanation:
Since up and down are opposites, the point didn't move at all.
I hope this helps!
pls ❤ and mark brainliest pls!
the number ten is raised to a power between 0 and 1. The answer has to be between which two numbers?
Value of [tex]10^x[/tex] will be between 1 and 10.
Given in the question,
A number [tex]10^x[/tex] where, 0 < x < 1If we have to find the range of the value of the number, substitute x = 0 and 1
[tex]10^0=1[/tex]
[tex]10^1=10[/tex]
Therefore, value of [tex]10^x[/tex] will vary between 1 and 10.
Learn more,
https://brainly.com/question/19465964
Simplify the expression
Answer:
B
Step-by-step explanation:
[tex] \frac{{3}^{5} }{ {3}^{3} } = {3}^{5 - 3} = {3}^{2} = 9 [/tex]
convert -1.2i - 1.6j to polar cordinates
Answer:
Step-by-step explanation:
z=xi+yj
x=-1.2=r cosθ (say)
y=-1.6=r sinθ(say)
square and add
r²cos²θ+r² sin ² θ=(-1.2)²+(-1.6)²=1.44+2.56=4
r²=4
r=2
divide
tanθ=y/x=-1.6/(-1.2)=16/12=4/3
θ=tan ^{-1}(4/3)≈53.13°
so polar coordinates are (2,53.13°)
The population of fruit flies tripled every day and the population today is 200 fruit flies.
a) Write an equation modeling the growth in the population of fruit flies.
b) What was the population of fruit flies 3 days ago?
Answer:
Equation = 600nNumber of fruit flies after 3 days = 1800 fruit fliesStep-by-step explanation:
Given:
Number of fruit flies = 200
Rate of growth = 3 times per day
Find:
A . Equation
B . Number of fruit flies after 3 days
Computation:
A . Equation = 3n(200)
Equation = 600n
B. Number of fruit flies after 3 days
Number of fruit flies after 3 days = 600(3).
Number of fruit flies after 3 days = 1800 fruit flies
Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.
Answer:
The coordinates of the point Q is (4, 1)
Step-by-step explanation:
The given parameters are;
The directed line segment extends from R(-2, 4), to S(18, -6)
The ratio in which the point Q partitions the directed line segment = 3:7
Therefore, the proportions of the R to Q = 3/(3 + 7) = 3/10 the length of RS
Which gives;
(-2 + (18-(-2))×3/10, 4 +(-6 -4)×3/10) which is (4, 1)
The coordinates of the point Q = (4, 1)
We check the length from R to S is given by the relation for length as follows
[tex]l =\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where;
R(-2, 4) = (x₁, y₁)
S(18, -6) = (x₂, y₂)
Length of segment RS = 22.36
length from R to Q = 6.7086
We check RQ/RS = 6.7082/22.36 = 0.3
Also QS/RS = (22.36 - 6.7082)/22.36 = 0.6999≈ 0.7
The coordinates of the point Q = (4, 1).