Final answer:
The normal form of x + 5y - 2 = 0 is (1/√26)x + (5/√26)y - (2/√26) = 0. The length of the normal is 1, and the angle it makes with the positive x-axis can be calculated using tan θ = 5, which gives the angle as tan-1(5).
Explanation:
To rewrite the equation x + 5y - 2 = 0 in normal form, we need to express it in the form Ax + By + C = 0, where A2 + B2 = 1. The equation is already in this form, but we must divide each term by the square root of (12 + 52) to satisfy the condition for A2 + B2. After the division, the normal form becomes (1/√26)x + (5/√26)y - (2/√26) = 0.
The length of the normal is the magnitude of the vector (A, B), which in this case, is 1 due to the normalization. To find the angle θ that the normal makes with the positive x-axis, we use the relationship tan θ = B/A. For our equation, tan θ = 5/1, so θ = tan-1(5).
The analytical method of vector addition involves identifying the x- and y-components of vectors and merging them to calculate the resultant vector's magnitude and direction.
The function y=3.75 + 1.5(x-1) can be used to determine cost in dollars for a taxi ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles?
Answer:
1.5 dollars/miles
Step-by-step explanation:
Given function [tex]y=3.75 + 1.5(x-1)[/tex] can be used to determine cost in dollars for a taxi ride of x miles.
Now we need to find about what is the rate of change of the cost in dollars with respect to the number of miles.
First we need to rewrite [tex]y=3.75 + 1.5(x-1)[/tex] in y=mx+b form
[tex]y=3.75 + 1.5(x-1)[/tex]
[tex]y=3.75 + 1.5x-1.5[/tex]
[tex]y=2.25 + 1.5x[/tex]
[tex]y=1.5x + 2.25[/tex]
comparing with y=mx+b, we get m=1.5
Hence rate of change of the cost in dollars with respect to the number of miles is 1.5.
Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared minus two.
Answer:
[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]
Step-by-step explanation:
We have the following limit
[tex]\lim_{x \to 0}\ x^2 -2[/tex]
To solve this limit using direct substitution to substitute the value that tends x into f(x) and simplify.
In this case x tends to zero, then we substitute x = 0 in the function and simplify
[tex]\lim_{x \to 0}\ x^2 -2= (0)^2 -2= -2[/tex]
Therefore
[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]
When x approaches 0 then f(x) it tends to -2
Find the surface area of the regular hexagonal prism. Round your answer to the nearest hundredth.
Answer:
860.55 mm²
Step-by-step explanation:
The surface area of an hexagonal prism, also known as an octahedron, is given by the following formula (since we have the apothem):
S= 6*b*(a+h)
where b = is the side of the base, a is the apothem length, and h = the height
S = 6 * 8 * (4√3 + 11) = 48 * 17.92812 = 860.55 sq mm
Could have also have used another formula without the apothem:
S =3 * √3 * b² + 6 * b * h
S = 3 * √3 * 8² + 6 * 8 * 11 = 3√3 * 64 + 528 = 332.55 + 528 = 860.55 sq mm
I NEED HELP ASAP PLZZZZ LOOK AT THE PIC
Answer:
The red line is g(x)
Step-by-step explanation:
* To solve this problem you must to know some fact about
transformation
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
- A vertical stretching is the stretching of the graph away from
the x-axis
• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically
stretched by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed
by multiplying each of its y-coordinates by k.
• if k should be negative, the vertical stretch or compress is
followed by a reflection across the x-axis.
* Now lets solve the problem
- g(x) = -1/2f(x + 2)
# x + 2 ⇒ means the graph moved 2 units to the left
# -1/2 ⇒ means the graph has vertical compressed followed
by a reflection across the x-axis, then multiply
each y-coordinate by -1/2
- The graph of f(x) intersects x-axis at point (3 , 0)
∴ The point will be (1 , 0) on g(x)
- The graph of f(x) intersects y-axis at point (0 , -6)
∴ The point will be (-2 , 3) on g(x)
* Look to the graph
# The red line is g(x)
# The blue line is f(x)
- To check your answer
# The equation of f(x) is f(x) = 2x - 6
∵ g(x) = -1/2f(x + 2)
∴ g(x) = -1/2[2(x + 2) - 6] = -1/2[2x + 4 - 6] = -1/2[2x - 2] = -x + 1
* g(x) intersect x-axis at point (1 , 0) and y-axis at point (0 , 1)
A jacket is on sale for 70% of the original price. If the discount saves $45, what was the original price of the jacket? What is the sale price?
100 - 70% = 30
0.30 × p (p=45)
0.30 × 45 = 13.5
the sale price is $13.50
Answer #6 and tell the steps of how u did it
Answer:
3131x+1
Step-by-step explanation:
Make equation simple
5x times 5x times 5x times 5x times 5x +x+1
Solve
5 times 5 times 5 times 5 times 5 = 3125
x times x times x times x times x times x = 5x
3125+5x=3130x
Now you might be thinking you cant add x but here your can because it is just broken apart
now add x+1
3131x+1
A car travels in the direction of 135°. What is its compass heading?
SE ( South East) is the answer I believe
A car travels in the direction of 135° its compass heading is South and East.
We have given the direction of 135°.
North 315 West East ASE South Car travels in a direction of 315.
315 = 270'+ 45".
What is the measure of angle?
The degree measure of an angle is determined by the amount of rotation in degrees from the initial side to the terminal side.
The angle 315" lies between south and east. Making an angle of 45 towards south and east.
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Identify the following as exponential or linear and growth or decay
This would be linear growth because the y values are increasing, but not at an exponential rate.
you find a triangle that has an area of 10 sq ft. the height of the triangle is 10 feet. what is the length of the base of the triangle?
Solution:
Given :
Area of triangle = 10 ft² Height of triangle = 10 ftSo, We have to find the Base of Triangle .
Area of triangle = 1/2*b×h, Where represents
B represent Base H represent HeightStep : Substitute those value in Formula;
Area of triangle = 1/2 × b × h
10 = 1/2 × b × 11
20 = 11 × b
b = 20/11
b = 1.81 ft
Therefore, Base of Triangle is 1.81 ft
Final answer:
To find the base of a triangle with an area of 10 sq ft and a height of 10 ft, use the formula 1/2 × base × height. By rearranging the formula and substituting the known values, the base is calculated to be 2 feet.
Explanation:
The question is asking to find the length of the base of a triangle when the area is 10 square feet and the height is 10 feet. The formula for the area of a triangle is 1/2 × base × height. In this case, we know the area (10 sq ft) and the height (10 ft), and we need to solve for the base.
Inserting the known values into the formula gives us:
Area = 1/2 × base × height
10 = 1/2 × base × 10
To solve for the base, we rearrange the formula:
base = 2 × Area / height
base = 2 × 10 / 10
base = 2 feet
Therefore, the length of the base of the triangle is 2 feet.
___ cosb =1/2 sin(a+b)+sin(a-b)?
Answer:
That would be sina.
Step-by-step explanation:
sin(a+b) = sinacosb + cosasinb
sin(a-b) = sinacosb - cosasinb
Adding we get sin(a+b) + sin(a-b) = 2sinaccosb
so sinacosb = 1/2sin(a+b) + sin(a-b)
Answer:
sina
Step-by-step explanation:
We have
sin(a+b) = sina cosb + cosa sinb ---------------------eqn 1
sin(a-b) = sina cosb - cosa sinb ---------------------eqn 2
eqn 1 + eqn 2
sin(a+b) + sin(a-b) = sina cosb + cosa sinb + sina cosb - cosa sinb
sin(a+b) + sin(a-b) = 2sina cosb
[tex]sina\times cosb =\frac{1}{2}(sin(a+b) + sin(a-b))[/tex]
So answer is sina
This table shows the length, in inches, of several nails.
Length (in.)
1
2
1
8
3
8
5
16
5
16
5
16
1
2
5
16
3
16
1
8
Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
A construction of the line plot for the length, in inches, of several nails is shown in the image attached below.
In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would make use of an online graphing calculator (tool) to graphically represent the given length (in yards) of several nails on a line plot as shown in the image attached below;
Length Frequency
1/2 2
5/16 4
1/8 2
3/8 1
3/16 1
In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 5/16 because it has the highest frequency of 4.
Complete Question;
This table shows the length, in inches, of several nails.
Length (in) 1/2, 5/16, 1/8, 1/2, 3/8, 5/16, 5/16, 3/16, 5/16, 1/8.
Create a line plot to display this data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
simplify the expression for the length? A) x + 6 B)x – 6 C)x + 2 D)x – 2
Answer:
A on edge
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
kate has 2/3 yards of fabric to make small flags each flag requires 1/6 yards of fabric how many flags cane kate make
Answer:
THE ANSWER IS 7
Step-by-step explanation:
CAUSE UR MOM IS A TRASHIE i'm sorry i meant YO MAMA
Final answer:
Kate can make 4 small flags from 2/3 yards of fabric since each flag requires 1/6 yards of fabric.
Explanation:
Kate has 2/3 yards of fabric and each small flag requires 1/6 yards of fabric. To find out how many flags Kate can make, you divide the total amount of fabric by the amount needed for one flag:
2/3 yards \/ 1/6 yards = 4 flags.
Here's the step-by-step calculation:
First, recall that dividing by a fraction is the same as multiplying by its reciprocal. In this case, the reciprocal of 1/6 is 6/1.
So, multiply 2/3 by the reciprocal of 1/6:
2/3 × 6/1 = 12/3 = 4.
Thus, Kate can make 4 small flags from the fabric she has.
Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product?
Simplifying the expression requires expanding the brackets, combining like terms, and applying algebraic rules including distribution. The resulting simplified form is – 35x2 + 8x – 8 after properly eliminating unnecessary terms and ensuring the solution is valid.
Explanation:To simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2, we need to apply standard algebraic techniques such as distribution, combining like terms, and simplifying polynomial expressions.
Firstly, distribute the 3x across the parentheses: 3x×(x – 12x) becomes 3x2 – 36x2.
Then, expand the square: – 2(x – 2)2 becomes – 2(x2 – 4x + 4).
Next, we can simplify the expression by combining like terms and further distributing where necessary:
3x2 – 36x2 + 3x2 – 2x2 + 8x – 8Combine like terms:
– 35x2 + 8x – 8Eliminate terms wherever possible and check to see if the simplified expression is reasonable. We are using multiplication, distribution, and combination of like terms to simplify the algebraic expression.
Write the phrase "twelve more than the product of seventeen and a number" as a mathematical expression.
A. 12 – 17x
B. 12 + 17x
C. 12 > 17x
D. 17 + 12x
Answer:
The answer is B. 12+17x
Step-by-step explanation:
Twelve more stands for +12 and the product of seventeen and a number is equal to 17*x or 17x.
Answer: OPTION B.
Step-by-step explanation:
You need to remember that a product is the result of a multiplication.
Let be the number mentioned in the problem "x", "the product of seventeen and a number" means that:
[tex](17)(x)=17x[/tex]
Now "twelve more than the product of seventeen and a number" indicates that you need to add 12 to [tex]17x[/tex].
Therefore, you can write the phrase in the following mathematical expression:
[tex]17x+12[/tex] or [tex]12+17x[/tex]
This matches with the option B.
(17 points)
Determine if line AB is tangent to the circle
1. If AB is tangent to the circle, then
[tex]18^2=(2\cdot7.2)^2+10.8^2[/tex]
We have
[tex]18^2=324[/tex]
[tex](2\cdot7.2)^2+10.8^2=324[/tex]
so AB is indeed tangent to the circle.
2. The unlabeled leg is another radius of the circle so it has length 8. Then if AB is tangent to the circle,
[tex](10+8)^2=8^2+15^2[/tex]
but we have
[tex](10+8)^2=324[/tex]
[tex]8^2+15^2=289[/tex]
so that cannot be a right triangle and AB is not tangent to the circle.
Which statistical question could the data below answer ? Cost of toys
The statistical question that could be answered by the data is "maximum cost of toys".
The graph shown is a line graph which is a type of chart that displays data points connected by a line. It's a common way to visualize how a particular quantity changes over time or across different categories.
Line graphs makes it easy to determine statistical measures including minimum and maximum values of a category or data.
Here, the maximum cost of toys is 10 and the minimum is 5.
Which of the following is an outlier in the set of data below? I think it’s 12 but I’m not so sure.
I think the answer might be 2
because
in the data given above all the numbers are between 12-19 they are all bigger than 10
and then there's 2 which is very far from 12 or any other numbers there and it is also less than 10
which makes more sense for it to be an outlier.
Hope this helps
suppose that F(x)=x^3 and G(x)=-2x^3
Answer:
A
Step-by-step explanation:
Given a function f(x) = x^2, we can say:
g(x) = -(x^2) is the reflection of f(x) in the x-axish(x) = ax^2 is a vertical stretch if a > 1 and a vertical compression if 0 < a < 1The negative sign in front says that G(x) is flipped over the x-axis with respect to F(x). Also, the 2 in front tells us that it is a vertical stretch of the function F(x), since a > 1.
Hence, answer choice A is right.
Answer:
it is answer A
Step-by-step explanation:
Ap*x
Find the perimeter of each figure in questions. use 3.14 pi
Answer: 10.5
Step-by-step explanation:Find the perimeter of the figure. Use 3.14 for the pie and round your answer to one decimal.
This looks like a square with a line going from the right corner slanted down to the bottom left, but there is a half circle there so it doesnt actually touch the bottom left. on the right half of the line is 13 in.
x^2+y^2-16x-161=0 factor it
(x-8)^2+y^2=225 I'm not able to factor it
what is the value of the expression below 3 1/4 - 1 78
Answer:1 3/8
Step-by-step explanation:
3 1/4 = 3 2/8
1 7/8 =1 7/8
3 2/8 = 2 10/8
1 7/8 = 1 7/8
2 10/8-1 7/8 =1 3/8
Answer: =1 [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
First, Rewriting our equation with parts separated:
=3 + 1/4 − 1 − 7/8
Then, Solving the whole number parts:
3 − 1= 2
After, Solving the fraction parts
1/4−7/8=?
Find the LCD of 1/4 and 7/8 and rewrite to solve with the equivalent fractions.
LCD = 8
2/8−7/8=−5/8
Then, Combining the whole and fraction parts
2 − 5/8=1 3/8
Next, converting mixed numbers to fractions, our initial equation becomes,
134−158
Finally, doing all the work you answer is going to be :
=1/38* Hopefully this helps:)Mark me the brainliest:)!!
∞ 234483279c20∞
Type the correct answer in the box. Round your answer to the nearest hundredth.
Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º.
Scarlett's height is 1.65 meters, so the height of the dam is meters.
Answer:
top question is not correct
Step-by-step explanation:
Answer:
what
Step-by-step explanation:
The volume of a cube is 85.184 cubic inches. What is the length of each side of the cube?
Answer:
4.4 inches
Step-by-step explanation:
To work out the length of each side of the cube you would need to cube root of the volume as seen below:
[tex] \sqrt[3]{85.184} [/tex]
And this gives the answer 4.4 inches.
Answer:
Volume = Length * Width * Height
A cube has equal length, width, and height values.
[tex]\sqrt[3]{85.184}[/tex] is 4.4
So the length of each side is 4.4 units
Jasmine wants to make a path from one corner of her yard to the other as shown. The path will be 3 feet wide. What is the area of the path?
Answer:
The answer is 90.
Step-by-step explanation:
Area of the path will be 90 square feet.
How to find the area of the path?The yard is rectangular in shape.In the figure, there are two right angles triangles on two sides of the pathArea of the path = (Area of the rectangular yard) - (Area of two right angled triangles)The width of the path is 3 feet. So, the base of the right angled triangle = (12-3) feet = 9 feet Area of the right angled triangle = base x height/2
= (9 x 30/2) square feet = 135 square feet
Area of the yard = ( length x breadth)= ( 30 x 12) square feet = 360 square feet
Area of the part = {360 - 2(135)} square feet= 90 square feet
Area of the path will be 90 square feet.
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answer this fast
will mark brainlist for sure
answer the question whichever u know
:)
Answer:
[tex]\large\boxed{1.\ 38\ and\ 22}\\\boxed{1'.\ 42\ and\ 30}[/tex]
Step-by-step explanation:
[tex]1.\\x,\ y-the\ numbers\ (x>y)\\\\\text{We have the system of equations:}\\\\\underline{\left\{\begin{array}{ccc}x-y=16\\x+y=60\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=76\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=38}\\\\\text{Put the value of x to the second equation.}\\\\38+y=60\qquad\text{subtract 38 from both sides}\\\boxed{y=22}[/tex]
[tex]1'.\\x-larger\ part\\x-12-smaller\ page\\\\x+(x-12)=72\\x+x-12=72\qquad\text{add 12 to both sides}\\2x=84\qquad\text{divide both sides by 2}\\\boxed{x=42}\\\boxed{x-12=30}[/tex]
Which statement about these rectangles is true ?
the answer for this question is the dilation is reduction
The statement which is true about these rectangles is:
The dilation is an enlargement.
Step-by-step explanation:Dilation Transformation--
It is the translation which changes the size of the original figure.The shape of the figure is conserved.Also, in dilation either the size increases (i.e. the figure enlarges) or it decreases( i.e. the figure reduces).Also, in a polygon if there is a dilation then there is a scalar multiplication in each of the sides of the polygon.If the scalar multiple is greater than 1 then there is a enlargement.and if the scalar multiple is less than 1 but greater than 0 then there is a reduction.Here we see that each of the sides of the original figure is multiplied by "1.5" to obtain a larger rectangle.
This means that the dilation is a enlargement.
( since the scalar is strictly greater than one )
Please expla your answer as well. THX!!!
Answer:
[-7,5]
Step-by-step explanation:
The range is all the permitted values of y in the function. The lowest to the highest.
Looking at the function, the lowest y value is -7
and
the highest y value is 5
So we can say the range is [-7,5], the last choice
An electronics company can spend no more than $4,000 on raw materials for circuit boards. The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
To summarize the situation, a worker writes the inequality:
10c + 20s ≤ 4,000, where c is the number of ounces of copper material and s is the number of ounces of silver material.
Which graph's shaded region shows the possible combinations of raw materials the company can buy?
Answer:
Option B is the correct answer.
Step-by-step explanation:
In a symphony orchestra, there are 2 vacancies for cellists only, 4 vacancies for violinists only and 4 vacancies for any of these musicians. In how many ways can these vacancies be filled from 15 applicants, of whom 7 are violinists and 8 are cellists?
Answer:
123480
Step-by-step explanation:
We have to choose:
2 cellists from 8 cellists;4 violonists from 7 violonists;4 cellists or violonists from 9 remaining musicians (8-2=6 - cellists left, 7-4=3 - violonists left, 6+3=9 - left musicians in total)1. 2 cellists from 8 can be chosen in
[tex]C_8^2=\dfrac{8!}{2!(8-2)!}=\dfrac{8!}{2!6!}=\dfrac{6!\cdot 7\cdot 8}{2\cdot 6!}=28[/tex]
different ways.
2. 4 violonists from 7 can be chosen in
[tex]C_7^4=\dfrac{7!}{4!(7-4)!}=\dfrac{7!}{4!3!}=\dfrac{4!\cdot 5\cdot 6\cdot 7}{4!\cdot 2\cdot 3}=35[/tex]
different ways.
3. 4 musicians from 9 can be chosen in
[tex]C_9^4=\dfrac{9!}{4!(9-4)!}=\dfrac{9!}{4!5!}=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9}{5!\cdot 2\cdot 3\cdot 4}=126[/tex]
different ways.
In total, there are [tex]28\cdot 35\cdot 126=123480[/tex] differnt ways to fill all vacancies.