Write an equation of the line that pass through the given point and is (a) parallel and (b) perpendicular to the given line.
Answer:
Step-by-step explanation:
Here we need to write the equations that passes through the point (4 , 3) and is parallel to the given line and perpendicular to it. So lets get started,
a)
First we calculate the slope of the given line by using any two points on the given line by the help of the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
we take the points (1 , 6) and (2 , 2) i chose these two you can choose any other two doesn't matter so now we calculate the slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{2-6}{2-1}\\\\m=\frac{-4}{1}\\\\m=-4[/tex]
now since our slope is -4 and the line is parallel to the given line so the line that we need in part a would also have the same slope by the law parallel lines have same slope/gradient.
[tex]m_1=m_2[/tex]
so the slope/gradient of our new line that we need which passes through the point (4,3) is -4
Now using the point slope form formula:
[tex]y-y_1=m(x-x_1)[/tex]
we have our point (4,3) which corresponds to [tex](x_1,y_1)[/tex] and m which corresponds to -4 , so now
[tex]y-y_1=m(x-x_1)\\y-3=-4(x-4)\\y-3=-4x+16\\y=-4x+19[/tex]
sow our new line in part a is
[tex]y=-4x+19[/tex]
b)
In this part we need a line that is perpendicular to the given line which means we use the formula to calculate the slope of the perpendicular line which is:
[tex]m_1m_2=-1[/tex]
where [tex]m_1=-4[/tex] the slope of our given line so the slope of the perpendicular line is,
[tex]m_1m_2=-1\\-4m_2=-1\\\\m_2=\frac{1}{4}[/tex]
so using the point (4,3) and the new slope 1/4 we find the equation of the perpendicular line again by using the point-slope form formula:
[tex]y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x-4)\\\\4y-12=x-4 \\4y=x+8\\\\y=\frac{x+8}{4}\\\\y=\frac{x}{4}+2[/tex]
I have attached of the graphs as well you can check it out for better understanding.
Tamara wants to calculate the height of a tree outside her home. Using her clinometer (angle measuring device) she measures the angle from 35 feet away from the base of the tree and gets an angle of 62 degrees Tamara's eye level is 5.5 feet above the ground.
1. What trigonometric relationship (sine, cosine or tangent) would be used to determine how tall the tree is?
2. Write an equation to determine how tall the tree is, in feet.
3. How tall is the tree, in feet? Round your answer to the nearest tenth.
4. Marcus lives across the street from Tamara Marcus's eye-height is 4.25 feet, and he estimates that he views the top of the tree with an angle of elevation of 50 degrees and is standing 65 feet away from the tree. Are Marcus's estimates reasonable? Explain why or why not.
Answer:
61.922 feet
Step-by-step explanation:
For this problem, we simply want to set up a trigonometric function that computes the height of the tree, and we want to add the height of Tamara.
We are given a distance from the tree of 30 feet with an angle from her eye-level to the top at 62 degrees. So we can say the following:
y = tan(Θ) * x
Where Θ = 62 degrees, x = 30 feet, and y is the height of the tree from Tamara's eye level.
y = tan(Θ) * x
y = tan(62) * 30
y = 56.422
So we also need to include the height of Tamara to get the total height of the tree from the ground to the top.
56.422 ft + 5.5 ft = 61.922 ft
Hence, the total height of the tree is 61.922 feet.
The height of the tree is 71.32 feet.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We set up a trigonometric function to get height of tree.
Distance ,
x = 35 feet away from tree base
Angle = 62⁰ at eye level
Then we get;
Y = tan(angle) x
Y = tan(62⁰) x 35
Y = 1.881 x 35
Y = 65.82 feet
We add Tamara's height to the total height of the tree that forms an equation as;
= 65.82feet + 5.5 feet
= 71.32 feet is the height of the tree
The height of the tree is 71.32 feet.
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Hallo! I have a question for you to answer! Please answer if you can C: its worth 10 points and brainliest!
Which quotient in simplest form?
3/4 ÷ 5/16
o 15/64
o 15/16
o 2 2/5
o 2 8/20
thank you!
Answer:
2 2/5
Step-by-step explanation:
3/4 divided by 5/16 = 3/4 times 16/5, which equals 48/20.
4 goes into each.
thus, giving you 12/5.
we write this as a mixed number, which gives us 2 2/5
Pleaseeeee helpppplsksxmkdks
Answer:
b
Step-by-step explanation:
Answer:
reflection!!
Step-by-step explanation:
Which equation describes the function shown on the graph?
A.
y = -3x + 4
B.
y = 3x – 4
C.
y = 1
3 x – 4
D.
y = - 1
3 x – 4
LaToya is 7 years old. Her brother, Brian, is 3 more than twice LaToya's age. Which expression correctly represents Brian's age? Group of answer choices (7 x 7) + 3 (7 x 2) + 3 (3 + 2) x 7 (7 + 2) + 3
PLEASE ANSWER DESPERATE
Answer:
Than answer is (7 x 2) + 3
Answer: free robux
Step-by-step explanatiofre
5/6 divided by 1 and 1/2?
Answer:
5/9
Step-by-step explanation:
(5/6)/1 1/2
5/9
Merry Christmas
in which quadrant is (4,1) located.
Answer:
Quadrant 1
Step-by-step explanation:
Find the type and number of solution for g(x) = x2 -14x = -50
Answer:
Step-by-step explanation:
x² -14x+50= 0
this equation has 2 solutions because is a quadratic
the solurions are imaginary roots because the discriminant is less then 0
b²-4ac = (-14)²-4*1*50 = 194-200= -6
to find the actual roots use the quadratic formula
Jerome solves the inequality y–2 ⩽ 9 in one step, writing y ⩽ 11 as the solution. What property best justifies the step he used to solve the inequality?
A. multiplication or division property of inequality
B. addition or subtraction property of inequality
C. distributive property
dimensions of a cuboid are consecutive terms of a geometric sequence. the volume of the cuboid is 216 cm^3 and the surface of the cuboid is 312 cm^3 . determine the dimensions of the cuboid
Answer:
Dimensions 2, 6, 18
Step-by-step explanation:
Given:
Volume of the cuboid = 216 cm³
Surface of the cuboid = 312 cm³
Find:
Dimensions of the cuboid
Computation:
Assume sides ; a/d , a , ad
So,
Volume of the cuboid = 216 cm³ = side1 x side2 x side3
216 = a/d x a x ad
a = 6
Surface of the cuboid = 312 cm³
312 = 2[lb+bh+hl]
312 = 2[a²/d + a²d + a]
312 = 2[36/d + 36d + 36]
d = 3
So,
Dimensions 2, 6, 18
Do you think all rectangles are similar to each other? What about squares?
Answer: they are all similar
Step-by-step explanation: they all are the same shape no matter how long or tall they are
You and your family enjoy baking Christmas cookies together. Last year, you baked 120 cookies to pass out to friends and family. However, since you are unable to share cookies this year, you made 60% less cookies. How many total cookies did you make this year? First person to anwser correctly, gets brainleist!
Answer:
We can make 48 cookies.
Step-by-step explanation:
60 percent of 120 = 72
120 - 72 = 48
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
The length s of this circular segment is 1.0 m and its radius r is 2.0 m. The area of the shaded triangle is most nearly:
Answer:
[tex]A=0.95m^2[/tex]
Step-by-step explanation:
From the question we are told that
Length of circular segment[tex]l =1.0m[/tex]
Radius [tex]r =2.0m[/tex]
Generally considering points A's angle
[tex]\angle A = \frac{1}{2} radian[/tex]
Mathematically converting [tex]\angle[/tex] to degree
[tex]\angle A= 1/2*100/\pi[/tex]
[tex]\angle A=20.6 \%[/tex]
Mathematically solving for the triangles Area
[tex]A=\frac{1}{2} * AB* AC*sinA[/tex]
[tex]A=\frac{1}{2} * 2* 2*sin(28.64)[/tex]
[tex]A=0.95m^2[/tex]
A jar contains 770 beans. Of them, 350 are mung beans and the rest are kidney beans. What is the ratio of mung beans to all the beans?
Answer:
5 MB : 16 B
Step-by-step explanation:
First, find the GCF of 770 and 350. ( 70 )
Next, divide both numbers by 70
770 / 70 = 11 Kidney beans
350 / 70 = 5 Mung beans
It says ratio of mung beans to all beans.
11 KB + 5 MB = 16 B
5 Mung beans to 16 Beans
:)
Select all that apply.
Which of the following ratios are equlvalent to 6:8?
24:36
9:12
12 to 16
16 to 24 36/40 15/20
Answer:
multiply 6:8 by 2
12:16
Evaluate x – 3y if x = –4 and y = –6.
22
14
–14
–22
Answer:
-22
Step-by-step explanation:
x-3y
(-4)-3(-6)
(-4)-(-18)
(-22)
Estimate the quotient. Round your answer to the nearest whole number.
39.8 ÷ 4 ≈ ??
Answer:
10
Step-by-step explanation:
39.8/4=9.95, rounds to 10
10 pts Question 4 A horizontal line passing though the origin that includes both positive and negative numbers is called Y-Axis O X-Axis Point Ordered Pair 4 Previous Next >
then A If it’s a horizontal line passing through
A worker uses 750 inches of steel wire to make 300 springs of the same size. At this rate how many inches of steel wire are needed to make 1 spring?
2.5 inches steel wire
We can use an equation to find the answer. 750/300 = 2.5
Answer:
2.5 inches of steel wire are needed to make one spring.
Step-by-step explanation:
In order to answer this, we can set up a proportion (setting two fractions equal to each other) to solve for how many inches of steel wire are needed to make one spring.
We are given a ratio: 750 inches of steel wire are required to make 300 springs. Therefore, this is represented as:
[tex]\bullet \ \ \ \text{750 inches of steel wire : 300 springs}[/tex]
This can be rewritten in fraction form:
[tex]\displaystyle \bullet \ \ \ \frac{\text{750 inches of steel wire}}{\text{300 springs}}[/tex]
Therefore, we have our first proportion.
We want to make one spring, so we need to find how much steel is required to make one spring. Therefore, for our second fraction, the inches of steel wire is unknown. We can define this as x.
[tex]\bullet \ \ \ \text{x inches of steel wire}[/tex]
Finally, our ratio can be written in the same manner as the previous ratio:
[tex]\bullet \ \ \ \text{x inches of steel wire : 1 spring}[/tex]
This can be rewritten in fraction form:
[tex]\displaystyle \bullet \ \ \ \frac{\text{x inches of steel wire}}{\text{1 spring}}[/tex]
Now, we need to set up our proportion. We do this by setting our two ratios equal to each other.
[tex]\displaystyle \bullet \ \ \ \frac{\text{750 inches of steel wire}}{\text{300 springs}} = \frac{\text{x inches of steel wire}}{\text{1 spring}}[/tex]
To solve a proportion, we need to cross multiply. We can flip our fractions and solve for the reciprocal since there is not really a way to represent cross-multiplication.
[tex]\displaystyle \bullet \ \ \ \frac{\text{750 inches of steel wire}}{\text{300 springs}} = \frac{\text{1 spring}}{\text{x inches of steel}}[/tex]
First, we can drop our labels/units.
[tex]\displaystyle \bullet \ \ \ \frac{750}{300} = \frac{1}{\text{x}}[/tex]
Then, we can multiply across.
[tex]\displaystyle \bullet \ \ \ 750 = 300x[/tex]
Finally, we can solve for x.
[tex]\displaystyle 750 = 300x\\\\\frac{750}{300}=\frac{300x}{300}\\\\2.5 = x\\\\x = 2.5[/tex]
Therefore, to make one spring, exactly 2.5 inches of steel wire are needed.
What is the value of (2/3) -(5/6) ÷ ¾ =
Answer:
-4/9 or -0.4
Step-by-step explanation:
Elizabeth runs a farm stand that sells apples and raspberries. Each pound of apples sells for $2.25 and each pound of raspberries sells for $1.50. Elizabeth sold 32 more pounds of raspberries than pounds of apples and made $108 altogether. Graphically solve a system of equations in order to determine the number of pounds of apples sold, x, and the number of pounds of raspberries sold,y.
Answer:
Im confused?
Step-by-step explanation:
The number of pounds of apples is 16 and the number of pounds of raspberries is 48.
Given that, the cost of a pound of apples = $2.25 and the cost of a pound of raspberries = $1.50.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of pounds of apples be x, then the number of pounds of raspberries(y) be y=x+32.
Now, the total cost of apples = The number of pounds of apples × The cost of a pound of apples
=x × 2.25
= 2.25x
The total cost of raspberries = The number of pounds of raspberries × The cost of a pound of raspberries
=(x+32) × 1.50
=1.50x+48
So, the total cost = The total cost of apples + The total cost of raspberries
⇒108 = 2.25x+1.50x+48
⇒3.75x=60
⇒x=16
So, y=x+32=48
The graph is plotted below for y=x+32=48
Therefore, the number of pounds of apples is 16 and the number of pounds of raspberries is 48.
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6 times the difference of n and 9 is 54
Answer:
18
Step-by-step explanation:
the angles of a triangle are in the ratio 2:3:4 find the size of each angle
Answer:
40:60:80
Step-by-step explanation:
2x+3x+4x=180 (sum of ang. In tri. Is 180)
X=20
2x is 40
3x is 60
4x is 80
40 plus 60 plus 80 is 180.
Someone wanna help me, Maths my weakest subject. I need it done by 11
Answer:
6 is -10
Step-by-step explanation:
Please help me with this question
-7+(63/9) Evaluate the Following Expression
Answer:
0
Step-by-step explanation:
[tex]-7+(\frac{63}{9})=-7+7=0[/tex]
A gear makes 50 revolutions each minute. It can be represented by the equation r-50t, where r is the total revolutions and t is the number of minutes. Which is the correct answer and explain.
Bennett says that it will take more than 7 minutes to make 300 revolutions
or
Betty says that 50 represents the constant of proportionality, k.
Answer: I believe Betty
Step-by-step explanation:
Betty because bennet says 300 divided by seven is 50 but is 42
Answer:
betty
Step-by-step explanation:
#2: List the numbers shown below in order from least to greatest. USE A COMMA
TO SEPARATE. *
-12, 23, 18, 12, -19, -25,8
HELP ASAP
Answer:
-25 < -19 < -12 < 8 < 12 < 18 < 23
Step-by-step explanation:
Sorry if im wrong
What is the image point of (3, 7) after a translation right 5 units and up 1 unit?
I don't actually know, im not smart, I'm just answering for the points
Answer:
(8, 8)
Step-by-step explanation:
Since the 3 replaces the x in (x, y), that means you would add the 5 to the three, making 8. Same thing for the 7 and the y. 7 plus 1 is 8.
