Answers
And the perpendicular angle be line₂
If a line is perpendicular to another, then the product of their gradients is -1, which means that the gradient of line₂ would be the negative reciprocal of line₁
Based on that, if the gradient of line₁ is [tex] \frac{1}{2} [/tex]
then, the gradient of line₂ is - 2.
Now by using the point-slope form y - y₁ = m ( x - x₁)
If line₂ passes through the line (1,8) and have gradient -2,
then by exploiting the point-slope form y - 8 = -2 (x - 1)
∴ equation of the ine perpendicular to y = [tex] \frac{x}{2} [/tex] + 3 would be y = -2x + 10
Related Questions
find (f•g) when f(x)=x^2-7x+12 and g(x)=3/x^2-16
Answers
1) g(x) = 3 / (x^2 - 16),
2) f(x) = x^2 - 7x + 12, and
3) (f•g)(x) = the product of the two functions f(x) * g(x)
The solution is found by factoring the two polynomilas f(x) and g(x):
f(x) = x^2 - 7x + 12 = (x - 4) (x -3)
g(x) = x^2 - 16 = (x - 4) (x + 4)
=> (f•g) (x) = (x - 4) (x - 3) / [ (x - 4)(x + 4) ] = (x - 3) / (x + 4)
Answer: (x - 3) / (x + 4)
Triangle ABC is located at A (−2, 2), B (−2, 4), and C (0, 0). The triangle is then transformed using the rule (x+3, y− 2) to form the image A'B'C'. What are the new coordinates of A', B', and C'?
Answers
You deposit $5000 in an account earning 7.5% simple interest. How long will it take for the balance of the account to be $6500?
Answers
Final answer:
It will take 4 years for the balance of an account to grow from $5000 to $6500 at a 7.5% simple interest rate. The formula for simple interest I = P × r × t is used, and after rearranging to solve for t, we find t = 4 years.
Explanation:
To calculate how long it will take for the balance of an account to reach a certain amount with simple interest, we can use the formula for simple interest: I = P × r × t, where I is the interest earned, P is the principal amount (initial deposit), r is the annual interest rate, and t is the time in years. In this case, we want to find out when the account balance will be $6500 after depositing $5000. The total interest earned to reach $6500 will be $6500 - $5000 = $1500.
The given annual interest rate is 7.5% (or 0.075 when converted to decimal form). We will rearrange the simple interest formula to solve for t:
t = I / (P × r)
Now, substituting the given values:
t = $1500 / ($5000 × 0.075)
t = $1500 / $375
t = 4 years
Therefore, it will take 4 years for the balance of the account to be $6500 at a 7.5% simple interest rate.
State whether the triangles are similar.
Answers
A plane traveled from California and back. It took one hour longer on the way out than it did on the way back. The plane's average speed out was 300 mph. The average speed on the way back was 350 mph. How many hours did the trip out take? A. 7 hours B. 6 hours C. 13 hours D. 8 hours
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300t = 350(t-1)
300t = 350t-350
-50t=-350
t = -350 /-50
t = 7 hours
How do I solve this literal equation
Answers
au=k
2. Now divide both sides by u
a=k/u
(Please help) Which answer describes the polynomial?
[tex]3x^3+4x^2-7[/tex]
A) quatric trinomial
B) cubix trinomial
C) quadratic trinomial
D) cubic binomial
Answers
notice, there are three terms, therefore is a trinomial.
the term that has the highest degree, has a degree of 3, therefore the degree of the polynomial as a whole is 3, or a cubic degree.
so, is a cubic trinomial.
Kim's class voted on a location for a field trip. • 5/12 of the class voted for the museum. • 5/24 of the class voted for the zoo. The rest of the class voted for the nature park. What fraction of the class voted for the nature park? The nature park received of the class votes.
Answers
Final answer:
By adding the fractions of votes for the museum (5/12) and zoo (5/24), converting them to a common denominator, and subtracting from the whole, we find that 3/8 of the class voted for the nature park.
Explanation:
To determine what fraction of the class voted for the nature park, we first need to add up the fractions of the class that voted for the museum and the zoo, and then subtract that sum from the whole class, which is represented as 1 (or 12/12). Since 5/12 of the class voted for the museum and 5/24 of the class voted for the zoo, we need to find a common denominator to add these fractions together. The lowest common denominator for 12 and 24 is 24.
First, we convert 5/12 to a fraction with a denominator of 24, which would be 10/24 (since 5 × 2 = 10 and 12 × 2 = 24). Now we can add the two fractions:
10/24 (votes for the museum)
5/24 (votes for the zoo)
Therefore, 10/24 + 5/24 = 15/24. After that, we subtract the sum from the whole to find out what fraction voted for the nature park:
12/12 - 15/24 = 24/24 - 15/24 = 9/24.
Hence, 9/24 of the class voted for the nature park. However, we can simplify 9/24 by dividing the numerator and the denominator by their greatest common divisor, which is 3, giving us 3/8.
Therefore, 3/8 of the class voted for the nature park.
A ferris wheel is drawn on a coordinate plane so that the first car is located at the point (0,40). What are the coordinates of the first car after a rotation of 270 degrees° counterclockwise about the origin?
Answers
After a 270-degree counterclockwise rotation, the first car on the ferris wheel originally located at (0, 40) will be at (40, 0).
Explanation:If the first car of a ferris wheel is located at the point (0, 40) on a coordinate plane and undergoes a rotation of 270 degrees counterclockwise about the origin, the new coordinates of the first car can be determined by applying a rotation transformation. To perform a 270-degree counterclockwise rotation, we rotate the point 90 degrees clockwise. This equivalent action simplifies the calculation, as rotating (0, 40) 90 degrees clockwise results in the point moving to (40, 0). Therefore, after a 270-degree counterclockwise rotation (which is equivalent to a 90-degree clockwise rotation), the new coordinates of the first car on the ferris wheel are (40, 0).
A rancher needs to enclose two adjacent rectangularâ corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 180 yd of fencing isâ available, find the largest total area that can be enclosed.
Answers
Let L = Length parallel to the river,
Here, L + 3B = 180 yd
So, L = 180 - 3B
We know that the area of the rectangle,
A = L × B
= (180 - 3B) × B
= 180 B - 3[tex] B^{2} [/tex]
We know that quadratic equation has symmetry,
So, For maximum area Breadth B = [tex] \frac{-2a}{b} [/tex]
Here, a = -3 & b 180
So, B = [tex] \frac{-180}{2(-3)} [/tex]
= 30 yd
So, L = 180 - 3B
= 180 - 3(30)
= 180 - 90
= 90
So, Maximum Area = L × B
= 90 × 30
= 2700 square yards
Therefore, the correct answer is 2700 square yards.
x = the width of each rectangular area.
y = the length of each rectangular area.
The amount of fencing available is 180 yards, therefore
4x + 2y = 180
or
2x + y = 90
y = 90 - 2x (1)
The total enclosed area is
A = 2xy
= 2x(90 - 2x)
A = 180x - 4x² (2)
In order to maximize A,
A'(x) = 180 - 8x = 0
x = 180/8 = 22.5 yd
y = 90 - 2x = 45.0 yd
To verify that A will be maximum, A''(x) should be negative.
A'' = -8 (verified).
The maximum area is
Amax = 2*22.5*45.0 = 2025.0 yd²
Answer: 2025 yd²
The diameter of a circular clock is 12 inches. what is the approximate length of the outer edge of the clock between the numbers 3 and 6?
Answers
So to find the length of the outer edge between 3 and 6 = 2 x Pi x 6 = 37.7. And then divide 37.7 by 4 which equals to 9.425 inches
A golfer has 4 different hats, 3 gloves, and 2 pairs of shoes to pick from for his round of golf. In how many ways can he make his choices?
Answers
The number of ways the golfer can make his choices is 4 hats times 3 gloves times 2 shoes, resulting in 24 different combinations.
Explanation:The student is asking about the number of different ways a golfer can choose from 4 hats, 3 gloves, and 2 pairs of shoes. To find the total number of combinations, we multiply the number of choices for each category. Thus, the number of ways the golfer can make his choices is:
4 (hats) × 3 (gloves) × 2 (shoes) = 24 combinations.
This is not an instance where factorial calculation (4!) is necessary, since the golfer does not need to select one of each item in a specific order but simply needs to choose one from each category.
To calculate the number of ways the golfer can make his choices, we can use the concept of permutations.
For the hats, there are 4 choices. For the gloves, there are 3 choices. And for the shoes, there are 2 choices.
To find the total number of combinations, we multiply the number of choices for each category together: 4 hats * 3 gloves * 2 pairs of shoes = 24 different ways the golfer can make his choices.
Final answer:
The golfer can choose his accessories in 24 different ways by selecting 1 out of 4 hats, 1 out of 3 gloves, and 1 out of 2 pairs of shoes, and multiplying the choices together (4 × 3 × 2).
Explanation:
The question asks us to calculate the total number of ways the golfer can choose his outfit accessories assuming he chooses one of each type. To do this, we need to consider each type of accessory independently and multiply the number of choices for each type.
The golfer has 4 different hats, 3 pairs of gloves, and 2 pairs of shoes to choose from. Since these choices are independent of each other, we simply multiply the number of options for each type of accessory:
4 options for hats,3 options for gloves,2 options for shoes.Thus, the total number of combinations is 4 hats × 3 gloves × 2 shoes = 24 different ways the golfer can choose his accessories for the round of golf.
This is an example of a fundamental counting principle problem, where we multiply the number of choices in each step to get the total number of combinations.
Determine the equation of the graph, and select the correct answer below.
Courtesy of Texas Instruments
y = (x + 4)^2 + 1
y = (x + 4)^2 − 1
y = (x − 4)^2 + 1
y = (x − 4)^2 − 1
Answers
Equation is ..
Y = (x -h)^2 + k
Put in vertex (-4,-1) gives the equation
Y = (x+4)^2 - 1
The equations provided represent parabolas that have been translated or reflected from the standard form y = x^2. Without a given graph or additional details, we can't definitively determine which equation is correct.
Explanation:Without a graph or specific details regarding the shape, position, and characteristics of the graph, we can't definitively choose one of the given equations. However, each equation represents a parabolic function that is translated and/or reflected from the standard form, y = x².
The equation y = (x + 4)² + 1 represents a parabola that is shifted 4 units to the left and 1 unit up from the origin.
The equation y = (x + 4)² − 1 is a parabola that is shifted 4 units to the left and 1 unit down.
For the equation y = (x − 4)² + 1, the parabola is shifted 4 units to the right and 1 unit up.
And lastly, the equation y = (x − 4)² − 1 describes a parabola that is shifted 4 units to the right and 1 unit down.
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A message center receives calls from 6 p.m. until 6 a.m. Typically, 50% of the calls come in between 6 p.m. and 9 p.m.; 25% of the calls come in between 9 p.m. and midnight; 20% of the calls come in between midnight and 3 a.m.; and 5% of the calls come in between 3 a.m. and 6 a.m.
What is the probability that a call will come in between 6 p.m. and midnight?
Question 5 options:
25%
50%
55%
75%
Answers
3 a.m. to 6 a.m. 5%
Midnight to 6 a.m. = 20% + 5% = 25%
A car travels 308 miles in 5 hours and 30 minutes. how many miles does it travel per hour?
Answers
Factor the expression below x^2 -6x+9
Answers
Answer:
Factor: [tex](x-3)(x-3)[/tex]
Step-by-step explanation:
Given: [tex]x^2-6x+9[/tex]
Factor the given polynomial. It is quadratic equation.
[tex]\Rightarrow x^2-6x+9[/tex]
Using formula: [tex]a^2-2ab+b^2=(a-b)^2[/tex]
So, first we make given polynomial to perfect square.
[tex]\Rightarrow x^2-2\cdot x\cdot 3+3^2[/tex]
[tex]a\rightarrow x[/tex]
[tex]b\rightarrow 3[/tex]
[tex]\Rightarrow (x-3)^2[/tex]
[tex]\Rightarrow (x-3)(x-3)[/tex]
Hence, The factor of given polynomial is [tex]\Rightarrow (x-3)(x-3)[/tex]
Factorizing the polynomial expression x² - 6x + 9 = (x - 3)²
What is factorization?Factorization is the simplification of an expression into a smaller expression using its factors.
To factor the polynomial expression. x² - 6x + 9, we proceed as follows
Since we have the polynomial expression x² - 6x + 9, we multiply x² by 9 to get x² × 9 = 9x².
Now, we desire to find the factors of 9x² so that the sum of those factors equal - 6x
Thus, we have 9x² = -3x × (-3x)
So, -6x = -3x - 3x
Thus, we replace this with -6x, so
x² - 6x + 9 = x² - 3x - 3x + 9
So, factorizing, we have that
x² - 3x - 3x + 9 = x(x - 3) - 3(x - 3)
= (x - 3)(x - 3)
= (x - 3)²
So, factorizing x² - 18x + 81 = (x - 9)²
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Solve x2 + 8x − 3 = 0 using the completing-the-square method
Answers
Darius and Matthew have 3 fruit bars. They are both hungry after playing football and decide to split the fruit bars evenly.How much fruit bars will reach boy get.
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If you divide three by two you get 1.5, which translates to 1 1/2 fruit bars per boy if they split it evenly. Hope this helps!
What is the value of m?
0.61m−1.51m=9
Answers
9/-.9
m=-10
The value of m from the given expression would be; -10.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We have been given the expression as
0.61m - 1.51m = 9
Combine Like Terms;
-0.9m = 9
Divide -0.9 To Both Sides;
-0.9m/-0.9 = 9/-0.9
Simplify;
m = -10
Hence, m equals to -10.
The value of m from the given expression would be; -10.
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We’ve seen that natural numbers are closed under addition. Determine the closure of natural numbers under the other three operations, and give examples to support your answers.
Answers
Natural numbers are closed under multiplication but not under subtraction and division: subtracting or dividing two natural numbers can lead to results that aren't natural numbers (negative numbers or fractions, respectively).
Explanation:The student's question pertains to the closure of natural numbers under the operations of subtraction, multiplication, and division. Natural numbers are numbers used for counting and ordering that include all positive integers from 1 onwards. Let's evaluate each of these operations with respect to closure:
Subtraction: Natural numbers are not closed under subtraction because subtracting a larger number from a smaller one results in negative numbers, which are not part of the natural numbers. For example, 3 - 5 = -2 is not a natural number.
Multiplication: Natural numbers are closed under multiplication because the product of any two natural numbers is always a natural number. For example, 2 x 3 = 6, and both the numbers and result are natural numbers.
Division: Natural numbers are not closed under division because the division of two natural numbers can result in a fraction or a decimal that is not a natural number. For example, 1 / 2 = 0.5, which is not a natural number.
When a natural number is subtracted or divided by another, the result might not always be a natural number, indicating that natural numbers are not closed under these operations.
The closure property holds for addition and multiplication of natural numbers, but not for subtraction and division.
Explanation:Addition:The closure property states that when you add two natural numbers, the result is always a natural number. For example, 2 + 3 = 5.
Subtraction:Subtraction is not closed under natural numbers. For example, if you subtract 3 from 2, you get -1, which is not a natural number.
Multiplication:The closure property holds for multiplication as well. When you multiply two natural numbers, the result is always a natural number. For example, 2 x 3 = 6.
Division:Division is not closed under natural numbers. For example, 2 ÷ 3 = 0.67, which is not a natural number.
Is △RWS ~ △QWT?
yes
no
Answers
Answer: Yes ΔRWS≈ΔQWT.
Step-by-step explanation:
We know that when two chords intersect each other inside a circle, the products of their segments are equal.
Therefore, [tex]QW\times WS=TW\times RW\\\Rightarrow\frac{QW}{RW}=\frac{TW}{WS}[/tex]
Now in triangle QWT and triangle RWS
∠QWT=∠RWS [Vertically opposite angles]
[tex]\frac{QW}{RW}=\frac{TW}{WS}[/tex]
Therefore, By SAS similarity rule
ΔRWS≈ΔQWT
Therefore, yes ΔRWS≈ΔQWT.
which expression is equal to the expression below?
(2x6)^4
A 4 x (2x6)
B 8^4
C 2 x (6)^4
D 2^4 x 6^4
Answers
Hey there!
[tex]\bold{(2\times6)^4}[/tex][tex]\bold{2\times6=12}[/tex][tex]\bold{12\times12\times12\times12}[/tex][tex]\bold{12\times12=144}[/tex][tex]\bold{144\times144=20,736}[/tex][tex]\bold{A.\downarrow}[/tex]
[tex]\bold{4\times(2\times6)}[/tex][tex]\bold{2\times6=12}[/tex][tex]\bold{4\times12=48}[/tex][tex]\bold{48\neq20,736}[/tex][tex]\boxed{\bold{incorrect}}[/tex][tex]\bold{B.\downarrow}[/tex]
[tex]\bold{8^4}[/tex][tex]\bold{8\times8\times8\times8}[/tex][tex]\bold{8\times8=64}[/tex][tex]\bold{64\times64=4,096}[/tex][tex]\bold{4,096\neq20,736}[/tex][tex]\boxed{\bold{incorrect}}[/tex]
[tex]\bold{C.\downarrow}[/tex]
[tex]\bold{2\times(6)^4}[/tex][tex]\bold{6^4=1,296}[/tex][tex]\bold{2\times1,296=2,592}[/tex][tex]\bold{2,592\neq20,736}[/tex][tex]\boxed{\bold{incorrect}}[/tex][tex]\bold{D\downarrow}[/tex]
[tex]\bold{2^4\times6^4}[/tex][tex]\bold{2^4=16}[/tex][tex]\bold{6^4=1,296}[/tex][tex]\bold{16\times1,296=20,736}[/tex][tex]\bold{20,736=20,736}[/tex][tex]\boxed{\boxed{\bold{correct}}}[/tex][tex]\boxed{\boxed{\bold{Answer:D.2^4\times6^4}\checkmark}}[/tex]
Good luck on your assignment and enjoy your day!
~[tex]\bold{LoveYourselfFirst:)}[/tex]
How do you solve a quadratic formula
Answers
Which statement is true about the difference 2 square root of 7 − square root of 28? It is rational and equal to −2. It is rational and equal to 0. It is irrational and equal to −2square root of 7. It is irrational and equal tosquare root of 7.
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how many times can 32 go into 64
Answers
hope this helps
What is the eccentricity of a completely flat ellipse
Answers
The eccentricity of a completely flat ellipse ranges from one (1) to zero (0).
What is eccentricity of flat ellipse?Eccentricity of an ellipse is the measure of how 'out of round' an ellipse is.
The eccentricity of an ellipse ranges from 0 to 1.
If the eccentricity is 0, it is not squashed at all and it will remain a circle.
However, if the eccentricity is 1, it is completely squashed and looks like a straight line.
Thus, the eccentricity of a completely flat ellipse ranges from one (1) to zero (0).
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Line segment ab has a length of 4 units. it is translated 1 unit to the right on a coordinate plane to obtain line segment a prime b prime. what is the length of a prime b prime? 1 unit 4 units 5 units 6 units
Answers
Answer:
The length of A'B' is 4 unit.
Step-by-step explanation:
Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size,
That is, if the measurement of segment AB is 4 unit then after translation by any factor its measurement will not change,
So, the measurement of segment A'B' would be 4 unit.
Verification :
Let the coordinates of A and B are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively,
Also, the rule of translation 1 unit right is,
[tex](x,y)\rightarrow (x+1, y)[/tex]
By the distance formula,
The measure of segment AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Thus, if A'B' is the transformed segment of segment AB,
Then, coordinates of A' and B' are [tex](x_1+1, y_1)[/tex] and [tex](x_2+1, y_2)[/tex]
So, the measure of segment A'B' = [tex]\sqrt{(x_2+1-x_1-1)^2+(y_2-y_1)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence, the measure of AB = measure of A'B'
Ms. johnson's class is having a pizza party. if there are 14 students and 7 pizzas cut into 8 slices, what answer choice represents the fraction of one pizza that each student receives?
Answers
We are asked about the fraction of pizza each student gets, so the relevant numbers here is only 14 students and 7 pizzas. SO the fraction of pizza each student get is the ratio of the two:
fraction = 7 pizzas / 14 students
fraction = 1 / 2
So each student gets 1/2
Each student receives 4 slices out of 8, or half a pizza, which is represented by the fraction 1/2. There are 56 slices available in total (7 pizzas times 8 slices each), and when that is divided by 14 students, it equals 4 slices per student.
The question asks for the fraction of one pizza that each student receives at a pizza party. Given that there are 14 students and 7 pizzas, each pizza is cut into 8 slices. This information can be used to calculate the total number of slices available and then divide that by the number of students to determine the fraction of a pizza each student gets.
First, we find the total number of slices by multiplying the number of pizzas by the number of slices per pizza:
7 pizzas x 8 slices per pizza = 56 slices
Next, we divide the total number of slices by the number of students to find how many slices each student will receive:
56 slices ÷ 14 students = 4 slices per student
Since each pizza has 8 slices, 4 slices represent half a pizza. Therefore, the fraction of one pizza that each student receives is 1/2.
The subtraction property of equality let's you say that if 5x+6=21, then ____ = 15
Answers
What is the area of rhombus ABCD ?
Enter your answer in the box. Do not round at any steps.
Answers
Answer:
16 units
Step-by-step explanation:
The area of a rhombus is given by the formula A = bh. The base would be CB and the height would be DP. We will use the distance formula to find the length of each:
[tex]d=\sqrt{y_2-y_1)^2+(x_2-x_1)^2}[/tex]
For CB, we have
[tex]d=\sqrt{(2-0)^2+(3--1)^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}[/tex]
For DP we have
[tex]d=\sqrt{(2--1.2)^2+(-5--3.4)^2}=\sqrt{3.2^2+1.6^2}=\sqrt{10.24+2.56}=\sqrt{12.8}[/tex]
This makes the area of the rhombus
[tex]A=bh=\sqrt{20}\times \sqrt{12.8}=\sqrt{20\times 12.8}=\sqrt{256}=16[/tex]
The area of a rhombus can be found using the formula (diagonal1 * diagonal2) / 2. In this case, the area is 24 cm^2.
Explanation:The area of a rhombus can be found using the formula:
Area = (diagonal1 * diagonal2) / 2
where diagonal1 and diagonal2 are the lengths of the two diagonals of the rhombus.
For example, if diagonal1 = 6 cm and diagonal2 = 8 cm, the area of the rhombus is:
Area = (6 * 8) / 2 = 24 cm2
Therefore, the area of rhombus ABCD is 24 cm2.
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