Write the equation of the line that is perpendicular to y = -2/3 x +2 and goes through the point (-1, 4). Make sure your final answer is in slope-intercept form
Given:
The equation of a line is
[tex]y=-\dfrac{2}{3}x+2[/tex] ...(i)
The perpendicular line passes through the point (-1,4).
To find:
The equation of the perpendicular line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(ii)
Where, m is the slope and b is the y-intercept.
On comparing (i) and (ii), we get
[tex]m=-\dfrac{2}{3}[/tex]
Product of slopes of two perpendicular lines is -1.
Let the slope of perpendicular line is [tex]m_1[/tex].
[tex]m\times m_1=-1[/tex]
[tex]-\dfrac{2}{3}\times m_1=-1[/tex]
[tex]m_1=\dfrac{3}{2}[/tex]
The slope of the perpendicular line is [tex]m_1=\dfrac{3}{2}[/tex] and it passes through the point (-1,4). So, the equation of the line is:
[tex]y-y_1=m_1(x-x_1)[/tex]
[tex]y-4=\dfrac{3}{2}(x-(-1))[/tex]
[tex]y-4=\dfrac{3}{2}(x+1)[/tex]
[tex]y-4=\dfrac{3}{2}x+\dfrac{3}{2}[/tex]
Add 4 on both sides.
[tex]y-4+4=\dfrac{3}{2}x+\dfrac{3}{2}+4[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{3+8}{2}[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex]
Therefore, the equation of required line is [tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex].
Find the median for each set of data. Round to the nearest tenth if necessary.
15, 42, 28, 32, 30, 34
A) 35
B) 37
C) 30
D) 31
Answer: The answer I got was D) 31
Step-by-step explanation:
Hope this helps!!!!!
Eric bought two jars of peppers and six jars of pickles for $49. Andrew bought three jars of peppers and 5 jars of pickles for $47.50. Find the cost of a jar of pickles.
Answer:
one jar of pickles is $1.50, 49-47.50 =1.50
Step-by-step explanation:
plsss help i’ll give brainliest if you give a correct answer
Answer:
It is x=7.
Step-by-step explanation:
(7)+8=15 You can subtract and you can get 7!!!
Answer:
X = 7
Step-by-step explanation:
If we take the equation
x + 8 = 15
and then subtract 8 on both sides we get
x = 7
so therefore x is 7 to make the value true.
Lauryn wants to analyze the weights of
the dogs for people that own that animal
in her class. She records the following
weights in a class survey:
28, 61, 17, 42, 37, 37, 22, 40, 13, 14, 33,
41, 25
What is the median of the data?
Answer: 33
If you put all the numbers In order from least to greatest and find the middle number you'll get the answer
An airplane climbs at an angle of 11 decrease with the ground. Find the ground distance it has traveled when it has attained an altitude of 400 ft.
A. 2057.82
B. 407.49
C. 76.32
D. 2096.34
Step-by-step explanation:
yall lazy figure this out yourself
What does a perimeter of this figure consist of? Please help asap please
Answer:
i think its the third section choice
The perimeter of the rectangular top of a bookcase is 54 in. Find the length of the width is 7 in.
Step-by-step explanation:
P = L × B
54 = L × 7
54 = 7L
Therefore, L = 54 ÷ 7
L = 7.71
Pleasssssssse help me with this
Answer:
B. 15x-35
Step-by-step explanation:
multiply 5 by both 3x and -7
5(3x-7)
5(3x) 5(-7)
15x-35
Answer:
your answer will be option B
Step-by-step explanation:
hope it helps
Slope:3,y-intercept:10
To write slope intercept form from 2 numbers, you take the 3 and covert it to 3/1, or rise/run form. Then you find the y-intercept. Now listen, this is very complicated. Ready? It's the y-coordinate. 10. Veery complicated.
So y=3/1+10
---
hope it helps
Solve for x.
A. 4°
b. 4.5 °
C. 6 °
d. 11.50 °
Answer: 5(2x+13)
Step-by-step explanation: Hope this was helpful....
Given that the measure of ∠x is 20°, and the measure of ∠y is 30°, find the measure of ∠z.
Answer:
130°
Step-by-step explanation:
20° + 30° =50°
a triangles full angle is 180°
180° - 50° = 130°
Regina writes the expression y + 9. 3/4 Which expression is equivalent to the one Regina writes? answer choices in picture
Answer:
the second one
Step-by-step explanation:
the y cannot be inside of the parenthesis
Answer: A
Step-by-step explanation: In all of the other equations your including y in the multiplication, BUT it is supposed be added
Use the equation below to answer the division question. A/b+(1/4x1/b)=1/2 What is 1/2 divided by a/b?
Answer:
[tex]\mathbf{\dfrac{2b- 1}{2b}}[/tex]
Step-by-step explanation:
[tex]\text{The given equation is:}[/tex]
[tex]\dfrac{a}{b}+ (\dfrac{1}{4} \times \dfrac{1}{b}) = \dfrac{1}{2}[/tex]
[tex]\text{To find:}[/tex]
[tex]\dfrac{1}{2} } \div {\dfrac{a}{b} }[/tex]
[tex]\text{From the given equation:}[/tex]
[tex]\dfrac{a}{b}+ (\dfrac{1}{4b}) = \dfrac{1}{2}[/tex]
[tex]\dfrac{a}{b} = \dfrac{1}{2} - (\dfrac{1}{4b})[/tex]
[tex]\dfrac{a}{b} = \dfrac{4b- 2}{(2) (4b)}[/tex]
[tex]\dfrac{a}{b} = \dfrac{4b- 2}{8b}[/tex]
[tex]\text{Now; the value of}[/tex] [tex]\dfrac{a}{b} \div \dfrac{1}{2}[/tex]
∴
[tex]\implies \dfrac{4b- 2}{8b} \div \dfrac{1}{2}[/tex]
[tex]\implies \dfrac{4b- 2}{8b} \times \dfrac{2}{1}[/tex]
[tex]\implies \dfrac{4b- 2}{4b}[/tex]
[tex]\implies \dfrac{2b- 1}{2b}[/tex]
Penn State extension is interested in comparing the body length southern grass cicadas and citrus cicadas. The extension collected a random sample of 20 southern grass cicadas and found that they have a mean body length of 16.22 millimeters and a standard deviation of 1.34 millimeters. A separate random sample of 20 citrus cicadas resulted in a mean body length of 13.41 millimeters and a standard deviation of .73 millimeters. What is the standard error of the difference parentheses southern grass minus citrus) between the sample means
Answer:
The standard error between the sample mean is approximately 0.3412
Step-by-step explanation:
The equation for the standard error of a difference in sample mean of equal sample sizes is given as follows;
[tex]SE(\overline x_1 - \overline x_2)={\sqrt{\dfrac{s_{1}^{2} }{n_{1}}+\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
The given parameters are;
The number of sample of southern grass cicadas, n₁ = 20
The mean body length of the southern grass cicadas, [tex]\overline x _1[/tex] = 16.22 mm
The standard deviation, s₁ = 1.34 mm
The number of sample of citrus cicadas, n₂ = 20
The mean body length of the citrus cicadas, [tex]\overline x _2[/tex] = 13.41 mm
The standard deviation, s₂ = 0.73 mm
[tex]SE(16.22 - 13.41)={\sqrt{\dfrac{1.34^{2} }{20}+\dfrac{0.73^{2}}{20}}} \approx 0.3412[/tex]
The standard error between the sample mean, SE ≈ 0.3412
Somebody please help
Answer:
Yes, No, No, No
Step-by-step explanation:
To decide whether the point lies on the circle, what you need to do it simply substituting the x and y values into the equation and check if it add up to be 25
(-5)² + 0² = 25, = RHS [Yes]
1² + (√7)² = 8, ≠ RHS [No]
(√21)² + (-3)² = 30, ≠RHS [No]
0² + 7² = 49, ≠RHS [No]
Calculate the area of the shapes below.
Answer:
the answer should be 24ft
Step-by-step explanation:
Answer:
24 ft
Step-by-step explanation:
1/2hb
4=h
12=b
plug in
1/2(4)(12)= 24
Find the sale price to the nearest cent.
5. The sale price of a video game that has been
discounted 40% is $15.48. What was the original
price of the video game?
Answer:
38.70
Step-by-step explanation:
if you divide it it u can get the answers.
40÷15.48
3x2 equals..WHAT DOES IT EQUAL
Answer:
6
Step-by-step explanation:
OOO OOO = 6
Please answer the question above.
Answer:113
Step-by-step explanation:
How many rays can you see in the picture?
Answer:
41
Step-by-step explanation:
please mark me as brainliest
I have no idea how to do this....and I need help...
Which is the graph of 4x + 2y < 3?
Erin uses 2/8 yard of string to make 1 bracelet. Erin will make 6 bracelets. (A) How many yards of string will Erin use to make 6 bracelets? Show or explain how you got your answer. Erin uses 3/8 yard of string to make 1 necklace. Erin will make 5 necklaces. (B) How many yards of string will Erin use to make 5 necklaces? Show or explain how you got your answer.
Answer:
use math papa
Step-by-step explanation:
Answer:
the answer is A because thats the answer
6) Ty is saving for college. His goal is to save 750 dollars each year and he wants to set
aside the same amount each month.
How much should Ty save per month?
• To meet his goal. Ty needs to save 3
per month
Answer:
ty should save $62.50 a month to meet his goal
What type of function can be used to model the scenario?
Burton Guster invests $15,000 into an account that earns 6.5% compounded annually.
Linear
Exponential
Quadratic
2. What type of function can be used to model the scenario?
Jack adds 2 quarters to his piggy bank each week.
Linear
Exponential
Quadratic
Answer:
1. Exponential
2. Linear
Step-by-step explanation:
1. Exponential
Principal = 15000
Rate, r = 6.5% compounded annually
A = P(1 + r)^t
A = 15000(1 + 0.065)^t
A = 15000(1.065)^t
2. Linear
Let initial amount in bank = x
Amount added per week = 2
Number of weeks or period = t
A = x + 2t
please help!!! i have been doing bad in math right now .
V=pi r ^2 h solve for pi
Pls help me I can’t figure this one out...
Answer:
pi = V - r^2
Step-by-step explanation:
subtract r^2 from both sides !!!
is 120.4 hundredths or ones or tens or hundreds
Answer:
Not sure what you're asking but 120.4 is
one hundred
two tens
and four tenths
a number , x, decreased by the sum of 4x and 6
Answer:
-3x - 6
Step-by-step explanation:
x - (4x + 6) becomes x - 4x - 6 after we've distributed the multiplication.
We can simplify this result as follows: -3x - 6
Given: cos θ > 0, csc θ < 0
Which quadrant does θ lie?
A.) I
B.) II
C.) III
D). IV