Answer:
[tex]D = \frac{25\sqrt{13}}{13}[/tex]
Step-by-step explanation:
Given
[tex]y = 4 - \frac{2}{3}x[/tex]
[tex](x_1,y_1) = (-2,-3)[/tex]
Required
Determine the distance
[tex]y = 4 - \frac{2}{3}x[/tex]
Write the above equation in standard form:
[tex]Ax + By + C = 0[/tex]
So, we have:
[tex]\frac{2}{3}x+y - 4 = 0[/tex]
By comparison:
[tex]A = \frac{2}{3}[/tex] [tex]B = 1[/tex] and [tex]C = -4[/tex]
The distance is calculated using:
[tex]D = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}[/tex]
Where:
[tex](x_1,y_1) = (-2,-3)[/tex]
[tex]A = \frac{2}{3}[/tex] [tex]B = 1[/tex] and [tex]C = -4[/tex]
This gives:
[tex]D = \frac{|\frac{2}{3} * (-2) + 1 * (-3) - 4|}{\sqrt{(\frac{2}{3})^2 + 1^2}}[/tex]
[tex]D = \frac{|-\frac{4}{3} -3 - 4|}{\sqrt{\frac{4}{9} + 1}}[/tex]
Take LCM
[tex]D = \frac{|\frac{-4-9-12}{3}|}{\sqrt{\frac{4+9}{9}}}[/tex]
[tex]D = \frac{|\frac{-25}{3}|}{\sqrt{\frac{13}{9}}}[/tex]
[tex]D = |\frac{-25}{3}|/\sqrt{\frac{13}{9}}[/tex]
[tex]D = \frac{25}{3}/\sqrt{\frac{13}{9}}[/tex]
Split the square root
[tex]D = \frac{25}{3}/\frac{\sqrt{13}}{\sqrt{9}}[/tex]
Change / to *
[tex]D = \frac{25}{3}*\frac{\sqrt{9}}{\sqrt{13}}[/tex]
[tex]D = \frac{25}{3}*\frac{3}{\sqrt{13}}[/tex]
[tex]D = \frac{25}{\sqrt{13}}[/tex]
Rationalize
[tex]D = \frac{25}{\sqrt{13}} * \frac{\sqrt{13}}{\sqrt{13}}[/tex]
[tex]D = \frac{25\sqrt{13}}{13}[/tex]
Hence, the distance is:
[tex]D = \frac{25\sqrt{13}}{13}[/tex]
Answer:
A
Step-by-step explanation:
The perimeter of a flag is 474 inches. The flag is 100 inches tall. How long is it?
I need help with multiplying fractions
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Key skills needed --> Division of fractions, Multiplication of fractions
1) 2/4 over 5/8 is the same thing as division ---> [tex]\frac{2}{4}[/tex] ÷ [tex]\frac{5}{8}[/tex] = [tex]\frac{2}{4}[/tex] × [tex]\frac{8}{5}[/tex] = [tex]\frac{16}{20}[/tex] = [tex]\frac{4}{5}[/tex]
2) Dividing by a fraction is the same thing as multiplying by its reciprocal.
Basically if you are dividing by [tex]\frac{3}{4}[/tex], you are multiplying by [tex]\frac{4}{3}[/tex]. A reciprocal is when the fraction's numerator becomes the denominator, and the fraction's denominator becomes the numerator. [tex]\frac{1}{2}[/tex] --> reciprocal is [tex]\frac{2}{1}[/tex] (or 2)
Hope you understood and have a nice day!! :D
Mary wants to buy 8 pounds of
grapes. Each pound costs $1.89.
Mary has $15. Does she have enough
money to buy the grapes? Explain.
Answer:
No, he does not have enough money to buy the grapes because he only has 15$ when in total the the grapes are $28.35.
Step-by-step explanation:
Tell one the lines for the given points are parallel, perpendicular, or neither. Just your answer.
Line 1: (2, -3), (-4, -6)
Line 2: (-3, 2), (2, -8)
Answer:
Perpendicular
Step-by-step explanation:
Given
[tex]Line\ 1: (2, -3), (-4, -6)[/tex]
[tex]Line\ 2: (-3, 2), (2, -8)[/tex]
Required
Tell the relationship between both lines
We start by calculating the slopes (m) of both lines.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For Line 1:
[tex]m_1 = \frac{-6 - (-3)}{-4 - 2}[/tex]
[tex]m_1 = \frac{-6 +3}{-4 - 2}[/tex]
[tex]m_1 = \frac{-3}{-6}[/tex]
[tex]m_1 = \frac{1}{2}[/tex]
For Line 2:
[tex]m_2 = \frac{-8 - 2}{2 - (-3)}[/tex]
[tex]m_2 = \frac{-8 - 2}{2 +3}[/tex]
[tex]m_2 = \frac{-10}{5}[/tex]
[tex]m_2 = -2[/tex]
The lines are not parallel because [tex]m_1 \ne m_2[/tex]
However, they are perpendicular, because:
[tex]m_1 = -\frac{1}{m_2}[/tex]
To prove this, substitute values for m1 and m2
[tex]\frac{1}{2} = -\frac{1}{-2}[/tex]
[tex]\frac{1}{2} = \frac{1}{2}[/tex] --- Proved
a student claims that a neutral atom has 6 protons and 7 electrons what mistake is the student making
Answer:
A proton needs two electrons to operate. Just like if an electron needed nutrons.
Step-by-step explanation:
A trough is an open container that is used to hold food or water for animals. The figure below shows a water trough.
1 4. How much ground is covered by the trough?
15. How much metal is needed to make the trough?
16. How much water can the trough hold?
Answer:
8 ft², 21.8ft², and 11.2ft²
Step-by-step explanation:
20
Question
Mrs Holland wants to paint her garage wall.
The wall measures
6 ſm by 31m
Each can of paint covers 5m2
Each can costs £7.50
How much will it cost Mrs Holland to paint her garage wall?
Answer:
Try the answer as £37.50
Step-by-step explanation:
Answer: £37.50
Step-by-step explanation:
Solve the inequality. Graph the solution. b- 2 ≥ -1
Answer:
Hopefully this can help
Step-by-step explanation:
someone help with this question please
Answer:
m=1/6
Step-by-step explanation:
which expression will have the same value as 3(4x + 9) - 6x for all values of ?
is 4 a solution of 3x+8=4 ? complete the statement
andy runs 441.6 meters in 16 seconds. if andy runs at a constant speed, how far does her run in one second? give your answer to the nearest tenth of a second.
Please help me on this question please?
Answer:
Rosie is incorrect.
Step-by-step explanation:
3600/200
The zeros get cancelled
36/2
The answer is 18.
what is the slope? (IXL)
Answer:
The slope is 2/3.
Step-by-step explanation:
Rise over run.
The speed of one car is 20% less than the speed of a second car. What per cent more time does the first car need to travel the same route as the second car?
Answer:
25% or more
Step-by-step explanation:
t1 = d1/v1 , t2 = d2/v2.
d1 = d2 , and v1 = 0.8 v2
t1 / t2 = d1/d2 x v2/v1 = v2/v1 ( as d1 = d2 )
t1/t2 = v2 / v1 = v2/0.8 v2 = 1/0.8 = 1.25
Select the correct answer from the drop-down menu.
8
3
For a certain base, blogi
and
slog, 0.5 = -1
The value of log, 46
Re
Answer:
the correct answer is 3
Step-by-step explanation:
just took it on edmentum
The value of the expression [tex]log_b(4b) = 3.[/tex]
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We can use logarithmic rules to solve this problem.
First, we know that log_b(8) = 3.
Using the definition of logarithms, this means that b³ = 8.
Solving for b, we find that b = 2.
Next, we know that log_b(0.5) = -1.
Using the definition of logarithms, this means that b^(-1) = 0.5.
Solving for b, we find that b = 2.
Since both expressions have the same base, we can use the logarithmic rule that states log_b(xy) = log_b(x) + log_b(y) to simplify log_b(4b) as follows:
[tex]log_b(4b) = log_b(4) + log_b(b)[/tex]
We can use the logarithmic rule that states:
log_b(b) = 1 to simplify log_b(b):
[tex]log_b(4b) = log_b(4) + 1[/tex]
Now, we can use the logarithmic rule that states:
[tex]log_b(x) = log_c(x)/log_c(b)[/tex]
To convert log_b(4) to a base 2 logarithm:
[tex]log_b(4) = log_2(4)/log_2(b) = 2/1 = 2[/tex]
Substituting this into the expression we found earlier, we get:
[tex]log_b(4b) = log_b(4) + 1 = 2 + 1 = 3[/tex]
Therefore,
[tex]log_b(4b) = 3.[/tex]
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ7
list the first multiples of 6
Answer:
1,2,3, and 6.
Step-by-step explanation:
Answer:the first multiples of six are 1,2,3,6
Step-by-step explanation:
look it up hope this helps
A 22 km walk is completed in 5 hours and 30 min.
What is the average speed?
Answer:
121 km\hr
Step-by-step explanation:
displacement=speed÷time
then. speed = displacement×time
= 22 × 5.5
= 121 km\hr
write an equation that describes the function
Answer:
Answer D
Step-by-step explanation:
For each one simple put one of the x values in the x in the given equation. You will find that 9/3 give you 3, 12/3 give you 4. In other questions follow that rule for each and if the answer is the Y value then you know you are right.
Need help don’t know what to do I’m confused
Answer:
last option; h = 2t - d
Step-by-step explanation:
t = 1/2(d + h)
t = [tex]\frac{d}{2}[/tex] + [tex]\frac{h}{2}[/tex]
now multiply each side by 2 to eliminate denominator
2t = 2 ([tex]\frac{d}{2}[/tex] + [tex]\frac{h}{2}[/tex])
2t = d + h
h = 2t - d
The price paid for a $4.50 pen after a 60% discount is applied
Answer:
1.80
Step-by-step explanation:
The Art Club at Northwest Middle School is selling candy bars as a fundraiser. The box plots below show the number of candy bars the members of the Art Club sold in the first two weeks of the fundraiser.
Select all of the following statements that are true about the Art Club’s candy bar sales.
The median number of sales in weeks one and two are equal.
The median number of sales in week one is greater than the median number of sales in week two.
The median number of sales in week two is greater than the median number of sales in week one.
The range of sales in weeks one and two are equal.
The range of sales for week one is greater than the range of sales for week two.
The range of sales for week two is greater than the range of sales for week one.
Answer:The median number of sales in weeks one and two are equal and The range of sales to in weeks one and two are equal
Step-by-step explanation:
3/4 divided by 1/2 brainleist if answer
Answer:
1 2/4 (1 1/2)
Step-by-step explanation:
keep, change, flip is how you solve these kinds of problems
the 3/4 stays the same
you turn the ÷ into x
and flip the 1/2 (2/1)
so it becomes
3/4x2/1= 1 2/4 (simplified is 1 1/2)
I need help if you help I’ll give you extra points!!!!!!!
Answer:
a=66m b=4.58cm
Step-by-step explanation:
a=5610 divided by 85=66 so 66m ×85 m =5610 meters squared
b=330cm ÷ 72 cm is 4.58. So 72×4.58=329.76 so rounded =330
Suppose six students from the class are chosen at random what is the probability none are mechanical engineering majors
Complete question :
In a class of 125 students, 27 are computer science majors, 51 are mechanical engineering majors, 12 are civil engineers and the rest are general engineering majors. Assume students only have one major.
Suppose six students from the class are chosen at random what is the probability none are mechanical engineering majors?
Answer:
0.039
Step-by-step explanation:
Total = T = 125
Computer Science = S = 27
Mechanical Engineering = M = 51
Civil Engineering = C = 12
General engineering, G = 125 - (27 + 51 + 12) = 35
Probability that none out of six chosen at random are Mechanical Engineering major :
Probability = required outcome / Total possible outcomes
Non mechanical engineering majors = 125 - 51 = 74
Probability none of 6 selected are mechanical engineering majors :
74C6 / 125C6
Recall :
nCr = n! / (n-r)! r!
, using calculator :
74C6 / 125C6 = 185250786 / 4690625500
= 0.0394938
= 0.039
y=−12x+. HELP PLEASE
Answer:
(-2,4), (0,3), (2,2)
Step-by-step explanation:
You can use the 3 points above to plot out the line on the graph and to find other points.
Use the equation 2m + 4s = 16 to complete the table, then graph the line using s as the
dependent variable.
Answer:
S. 4
M. 2
S. 5
M. 8
And the graphing you just do those as m/s -->(M,S)
You can put the value of m or s in the given equation of m and s to obtained the missing value.
The completed table would look like:
[tex]\begin{array}{ccccc}m & 0 & 2 & -2 & 8\\s & 4 & 3 & 5 & 0\end{array}[/tex]
Simplifying the relation between m and s:[tex]2m + 4s = 16\\\\ \text{Dividing by 2 on both sides}\\\\ \dfrac{2m + 4s}{2} = \dfrac{16}{2}\\\\ m + 2s = 8[/tex]
How to evaluate the missing values?Use one of the given value and the equation to find the missing value:
For m = 0:[tex]m + 2s = 8\\ 0 + 2s = 8\\ 2s = 8\\\\ s = \dfrac{8}{2}\\\\ s = 4[/tex]
For s = 3:[tex]m + 2s = 8\\ m + 2 \times 3 = 8\\ m = 8 - 6\\ m = 2[/tex]
For m = -2:[tex]m + 2s = 8\\ -2 + 2s = 8\\ 2s = 10\\ \\ s = \dfrac{10}{2} \\\\ s= 5[/tex]
For s= 0:[tex]m + 2s = 8\\ m + 2 \times 0 = 8\\ m = 8[/tex]
Thus, the completed table would be:
[tex]\begin{array}{ccccc}m & 0 & 2 & -2 & 8\\s & 4 & 3 & 5 & 0\end{array}[/tex]
Learn more about linear equations here:
https://brainly.com/question/25826868
FACTOR and list your 4 steps: 5x^2y - 30xy^2
Answer:
5x • (x + 3y) • (x - 2y)
Step-by-step explanation:
for the Indicated variable.
15) z=-, for a
m
A) a = zm
m
B) a=
C) a=-z- m
D) a= 2
Answer:
D.
Step-by-step explanation:
which is the best deal
12oz. for $.99
64oz for $2.99
128 oz. $4.99
Answer:
best deal is 64oz for $2.99
Answer:
I would say 64oz for $2.99
Step-by-step explanation: