What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)?
y + 5 = x + 2
y − 2 = x − 5
y − 5 = −(x − 2)
y + 2 = −(x + 5)
We are given point (2,5).
We need to find the equation of line perpendicular to the given line and passes through the point (2, 5).
We know point-slope form :
y-y1 = m(x-x1).
Plugging values of (x1,y1) = (2,5) in above slope-intercept form, we get
y - 5 = m(x-2).
Which matches 3rd option y − 5 = −(x − 2).
So, the correct option is y − 5 = −(x − 2).Answer:
The answer is C.
Step-by-step explanation:
Given: ABCD is a parallelogram m∠A = 60º ; BK ⊥ AD AK = KD; Perimeter of ABCD = 24 Find: BD.
Final answer:
To find BD, we can use the fact that the opposite sides of a parallelogram are equal in length. The length of BD is 4.8 units.
Explanation:
In the given problem, we have a parallelogram ABCD with m∠A = 60º. BK is perpendicular to AD and AK = KD. The perimeter of ABCD is 24. To find BD, we can use the fact that the opposite sides of a parallelogram are equal in length. Since AK = KD, the length of AD is twice the length of AK.
Let AK = x. Then AD = 2x. The perimeter of ABCD is given by P = AB + BC + CD + AD. Substituting the given values, we have 24 = AB + BC + CD + 2x. We know that AB = CD, so the equation becomes 24 = 2AB + 2BC + 2x. Rearranging the terms, we get AB + BC + x = 12.
Using the fact that opposite sides of a parallelogram are equal in length, we can deduce that BC = AB. Substituting this into the equation, we have 2AB + AB + x = 12. Simplifying, we get 3AB + x = 12. Since AK = KD, we have x = KD. Substituting this into the equation, we have 3AB + KD = 12. Since AK = KD, we have 3AB + AK = 12. Since AK = KD, we have 3AB + 2AK = 12. Simplifying, we get 3AB + 2AB = 12. Combining like terms, we get 5AB = 12. Dividing both sides by 5, we get AB = 12/5. Since AB = CD, we have CD = 12/5. Since opposite sides of a parallelogram are equal in length, we have BD = AD = 2x = 2(12/5) = 24/5 = 4.8.
What is 51.875 rounded to the nearest tenth
In the Venn diagram, consider U = {students in 10th grade at Lee High School}.
The diagram shows the electives chosen by the students in the 10th grade.
How many students chose to participate in the painting class?
We have been given a Venn diagram in which U = {students in 10th grade at Lee High School}. We are asked to find how many students have chosen to participate in the painting class.
We can see from our Venn diagram that 3 students are participating in chorus and painting. 2 students are participating in chorus, theater and painting. 4 students are participating in painting and theater.
To find total students who have chosen to participate in the painting class we will add all the students who are participating in other activities with painting.
[tex]\text{Students participating in painting class}=8+3+2+4[/tex]
[tex]\text{Students participating in painting class}=17[/tex]
Therefore, 17 students have chosen to participate in painting class.
Answer:
17
Step-by-step explanation:
You are making lemonade for your lemonade stand. Each liter of lemonade you make uses 3.5 tablespoons of lemonade powder, and you have 14 tablespoons of lemonade powder. Can you make 5 liters of lemonade?
Evaluate the Expression - show your work :)
Thanks!
Let P be the point (1,1,-2). Suppose that the point P0(2, -5, 2) is 1/5 of the way from P to Q. Find the point Q.
The population of city A is 26% less than the population of city B, so city A's population is _____% of city B's.
Answer:
The population of city A is [tex]74\%[/tex] of the population of city B
Step-by-step explanation:
Let
y------> population of the city A
x-----> population of city B
we know that
[tex](100\%-26\%)=74\%=\frac{74}{100}=0.74[/tex]
so
[tex]y=0.74x[/tex]
therefore
The population of city A is [tex]74\%[/tex] of the population of city B
A bedroom is 15 ft long and 12 ft wide. How much will it cost to carpet the room if carpeting coats $22 per square foot. (1 yd=3 ft)
PLEASE HELP WILL MARK BRAINLIEST
Let p: x = 4 Let q: y = −2 Which represents "If x = 4, then y = −2”? p ∨ q p ∧ q p → q p ↔ q
Answer:
C. p → q
Step-by-step explanation:
We are given that,
'p' is represented by 'x = 4' and 'q' is represented by 'y = -2'.
That is, we have,
p: x = 4
q: y = -2
The given statement is, 'If x = 4, then y = -2'.
This means that whenever x = 4, then y = -2.
That is, 'x = 4 implies y = -2'.
Thus, it will be represented by p → q.
You can use a calculator for this question.
Greg builds a new pond which has a volume of 7.35 m3.
It is 4.2 m long and 50 cm deep.
What is the width of the pond? m
There will be a circular patio with a diameter of 7 metres.
Greg is going to put a tiled edge around the patio.
What is the circumference of the patio? m
Circumference of a circle = 2πr
Use π = 3.14
Average speed of Car 1 = 55 mph.
Average speed of Car 2 = 70 mph.
Time elapsed between start of Car 1 and start of Car 2 = 4 minutes.
How long before Car 2 overtakes Car 1? __hour(s).
An open area at a local high school is in the shape of a quadrilateral. two sidewalks crisscross this open area as diagonal of the quadrilateral. If the walkways cross at their midpoints and the walkways are equal in length, what is the shape of the open area?
a rectangle
a rhombus
a parallelogram
a trapezoid
Identify the quadratic term in the function, f(x)=2x^2-3x+5
The sum of two numbers is 52. If twice the smaller number is subtracted from the larger number, the result is 13. Find the two numbers.
You estimate the distance from your house to your school to be 1.6 miles. The actual distance is 1.9 miles. Find the percent error. Round your answer to the nearest tenth of a percent.
Final answer:
The percent error of the estimated distance from your house to school is 15.8% when rounded to the nearest tenth.
Explanation:
To find the percent error of your estimate, you use the formula:
Error = (|Estimated value - Actual value| / Actual value) × 100
Plugging the values from your question:
Error = (|1.6 miles - 1.9 miles| / 1.9 miles) × 100
Error = (|-0.3 miles| / 1.9 miles) × 100
Error = (0.3 miles / 1.9 miles) × 100
Error = 0.15789473684 × 100
Error = 15.789473684%
When rounded to the nearest tenth of a percent, the percent error is 15.8%.
2/5 of the Jazz is by musicians from New Orleans. How much of New Orleans music does Ivan have
Ivan has 24 minutes of New Orleans jazz on his MP3 player.
To find out how much of an hour of New Orleans jazz Ivan has, we use the following steps:
1. We know that Ivan has an hour of jazz music on his MP3 player.
2. We are given that 2/5 of this jazz music is by musicians from New Orleans.
3. To find out how much of New Orleans jazz music that is, we calculate 2/5 of 1 hour.
Here's the calculation:
[tex]\( \frac{2}{5} \times 1 \text{ hour} = \frac{2}{5} \times 60 \text{ minutes} \)[/tex]
[tex]\( \frac{2}{5} \times 60 = \frac{120}{5} \text{ minutes} \)[/tex]
[tex]\( \frac{120}{5} = 24 \text{ minutes} \)[/tex]
Therefore, Ivan has 24 minutes of New Orleans jazz on his MP3 player.
complete question given below:
what function is vertically stretched by a factor of 3 and translated 4 units right from the parent function
A. log_(5) (3x+4)
B. 3log_(5) (x-4)
C. 3(5^x+4)
D. 5^3x-4
Final answer:
The correct function is B, 3log_5(x-4), which represents a logarithmic function that is vertically stretched by a factor of 3 and translated 4 units to the right.
Explanation:
The student is asking about transformations of a parent function, specifically a vertical stretch and a horizontal translation. When a function is vertically stretched by a factor of 3, this involves multiplying the function by 3. A translation of 4 units to the right would mean adjusting the input variable x by subtracting 4. Considering the options given, option B, 3log5(x-4), is the correct answer because it represents a function that has been vertically stretched by a factor of 3 and horizontally translated 4 units to the right from its parent function log5x.
A wall map has a scale of 128 miles = 6 inches. The distance between Springfield and Lakeview is 2 feet on the map. What is the actual distance between Springfield and Lakeview? Question 4 options: 42.7 miles 1.13 miles 512 miles 384 miles
what is the LCM of 6 and 8
Cpm/pert graphically displays the scheduling of tasks required to complete a project.
a. True
b. False
On a coordinate grid, point M is at (−8, 2) and point S is at (10, 2). The distance (in units) between points M and S is ______. (Input only whole numbers, such as 2.)
Mae's cat weighs 5 3/8 pounds. What is the weight written as a decimal
?
A snail crawls at a pace of 3 cm a minute. What is the snail Pace in feet per hours?
The world's smallest gecko is 3/4 inch long. An adult male Western Banded Gecko is 7 1/3 times as long. How long is an adult male Western Banded Gecko
a rectangular swimming pool is 3 meter wide. The surface area is 30 sq meters...what is the length of the pool?
Solve this equation: 3x-1/5-2/9x=124/5
Step 1: Simplify by combining like terms. Which terms can be combined?
A) 3x and -1/5
B) -1/5 and -2/9x
C) 3x and -2/9x
Answer:
The correct option is C.
Step-by-step explanation:
The given equation is
[tex]3x-\frac{1}{5}-\frac{2}{9}x=\frac{124}{5}[/tex]
If two terms have the same variables having same powers, then they are known as like terms.
In the given equation [tex]3x[/tex] and [tex]-\frac{2}{9}x[/tex] are like terms.
So, when we simplify the given equation by combining like terms. we need to combined [tex]3x[/tex] and [tex]-\frac{2}{9}x[/tex] .
Therefore the correct option is C.
The solution to the equation is approximately x = 45.48.
To solve the equation 3x - 1/5 - 2/9x = 124/5, to combine like terms. Like terms are terms that have the same variable and exponent.
The terms in the equation are:
3x (coefficient is 3, and the variable is x)
-1/5 (coefficient is -1/5)
-2/9x (coefficient is -2/9, and the variable is x)
Now, let's identify the like terms that combined:
C) 3x and -2/9x
The terms 3x and -2/9x both have the variable x, so they are like terms and can be combined.
Step 1: Combine the like terms:
3x - 2/9x = (3 - 2/9)x = (27/9 - 2/9)x = (25/9)x
Now, after combining the like terms, the equation becomes:
(25/9)x - 1/5 = 124/5
Step 2: Isolate x on one side of the equation. To do this, we can first get rid of the fraction by multiplying the entire equation by the least common multiple (LCM) of the denominators, which is 45 (LCM of 9 and 5):
45 × [(25/9)x - 1/5] = 45 × (124/5)
This simplifies to:
25x - 9 = 1128
Step 3: Now, isolate x by moving the constant term (-9) to the other side of the equation:
25x = 1128 + 9
25x = 1137
Step 4: Finally, divide by 25 to solve for x:
x = 1137 / 25
x ≈ 45.48
To know more about equation here
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Trigonometric Identities and Applications? help
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