Given:
The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is [tex]4 x-6 y=15[/tex]
We need to determine the equation of the line.
Slope:
Let us convert the equation to slope - intercept form.
[tex]-6 y=15-4x[/tex]
[tex]y=\frac{2}{3}x-\frac{5}{2}[/tex]
From the above equation, the slope is [tex]m_1=\frac{2}{3}[/tex]
Since, the lines are perpendicular, the slope of the line can be determined using the formula,
[tex]m_1 \cdot m_2=-1[/tex]
[tex]\frac{2}{3} \cdot m_2=-1[/tex]
[tex]m_2=-\frac{3}{2}[/tex]
Therefore, the slope of the equation is [tex]m=-\frac{3}{2}[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the point (6,9) and the slope [tex]m=-\frac{3}{2}[/tex] in the above formula, we get;
[tex]y-9=-\frac{3}{2}(x-6)[/tex]
Simplifying the terms, we get;
[tex]2(y-9)=-3(x-6)[/tex]
[tex]2y-18=-3x+18[/tex]
[tex]3x+2y=36[/tex]
Thus, the equation of the line is [tex]3x+2y=36[/tex]
The equation of a line that is perpendicular to the line 4x - 6y = 15 and passes through the point (6,9) is 3x + 2y = 36. This is because the slope of the new line is the negative reciprocal of the slope of the given line, and the line passes through the given point (6,9).
Explanation:The subject of this question is mathematics, specifically in the topic of linear equations. To find the equation of a line that is perpendicular to a given line and passes through a certain point, we first need to find the slope of the given line. The standard form of the equation of a line is Ax + By = C. The given line is 4x - 6y = 15. We can find its slope by taking the negative reciprocal of the coefficient of x (A) over the coefficient of y (B), so the slope of the given line is -4/-6 = 2/3. Since we want a line that is perpendicular to the given line, the slope of the line we are looking for would be the negative reciprocal of the slope of the given line, which would be -3/2, because perpendicular lines have slopes that are negative reciprocals of each other. Using the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, the equation of the line we are looking for is y - 9 = -3/2(x - 6), which simplifies to 2y - 18 = -3x + 18 and further simplifies to 3x + 2y = 36. So the answer is none of the given options.
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Which of the following are aspects of the building and construction trades?
Carpentry
Plumbing
Lawn care
Masonry
Electrical work
Explanation:
All of the mentioned points are the aspects of building and construction trades.Carpenter performs carpentry and deals mainly with wood such as making of wooden cabinets, furniture etc.Electrician deals with electric work such as electrical wiring of the buildings and related equipment.Plumber deals with installing and maintaining drainage system or water availability.Mason are skilled in brick and blocklaying, concrete finishing etc.Answer:
Everything except lawn care.
I am 97 cm tall and my elder brother is 2m tall. How much taller is my elder brother than I?
Answer: 1.3 meters taller. so 103 cm.
Step-by-step explanation:
Answer:
103cm
Step-by-step explanation:
From the question given, we obtained the following data:
Height of the boy = 97cm
Height of the elder brother = 2m
First let us convert the height of the elder brother to cm. This is illustrated below:
1m = 100cm
2m = 2 x 100 = 200cm
So, the elder brother is 200cm tall. To know how much taller the elder brother is than the boy, subtract the height of the boy from that of the elder bother' as shown below:
200 — 97 = 103cm
Therefore, the elder brother is 103cm taller than the boy
Plot 12, -2, and 4 on the number line.
Answer:
that's easy just with your number line put then to least to greatest
What are zeros of the quadratic expression. A) x = 1 or x = 5 B) x = 1 or x = −5 C) x = −1 or x = 5 D) x = −1 or x = −5
Answer:whats the expression
Step-by-step explanation:
Can you help me on this math problem pleaseee?
Answer:
a. - 1 3/4
b. 6
Step-by-step explanation:
For each, plug in the given number to the corresponding variable:
a. When x = -2. Plug in -2 for x in the given expression:
2^(-2) - 2
Simplify. Note that when a negative sign is located in the power sign, you would do the normal power, and then put the number over 1.
2^(-2) = 1/(2 x 2) = 1/4
Simplify:
1/4 - 2 = - 1 3/4
- 1 3/4, or -7/4 is your answer.
b. When x = 3. Plug in 3 for x in the given expression:
2^(3) - 2
Simplify. First solve the power, then subtract:
2^3 = 2 * 2 * 2 = 4 * 2 = 8
8 - 2 = 6
6 is your answer.
~
Answer:
a. - 1 3/4
b. 6
EWE
YUIU Problems DV
A florist has 9 tulips and 18 carnations. If the florist wants to create identical bouquets
without any leftover flowers, what is the greatest number of bouquets the florist can make?
Answer:
9
Step-by-step explanation:
GCF of 9 and 18 is 9. I hope it helps. Srry of the last mishap and i hope you accept my apology.
In 4 hours, you hike 10 miles.
Which unit rate describes your speed on the hike?
CLEAR CHECK
5 miles per hour
410 mile per hour
2.5 miles per hour
10 miles per hour
The equation y = mx+b is used to express the equation of a line which solution is a quick way to solve this equation for x in terms of y?
Answer:
See Step-by-step explanation
Step-by-step explanation:
[tex]y=mx+b\\y-b=mx\\x=\frac{y-b}{m}[/tex]
What is the volume of a cylinder With base radius 4 and height 5
Answer:
it's a base of 18 hope it works
Answer:80 pie
Step-by-step explanation:
Which answer choice states the range of the following
relation?
A) {-2, -5}
B) (-9,-8, -7, -6, -5}
C) {-2, -1, 0, 1, 2, -9,-8, -7, -6, -5}
D) {-2, -1, 0, 1, 2
Hello! Remember you have to write complete questions in order to get good and exact answers. Here you forgot to write the relation so I could help you providing my own relation.
Remember that for any relation, we have a set [tex]A[/tex] that matches the the domain (also called the set of inputs) of the function and the set [tex]B[/tex] that contains the range (also called the set of outputs).
Suppose our relation is:
[tex]y=-10+x \\ \\ For \ x=1,2,3,4,5[/tex]
So the x-values represents the set A and the y-values the set B. Therefore, by evaluating the x-values into our relation we get:
[tex]\text{If x=1} \\ \\ y=-10+1=-9 \\ \\ \\ \text{If x=2} \\ \\ y=-10+2=-8 \\ \\ \\ \text{If x=3} \\ \\ y=-10+3=-7 \\ \\ \\ \text{If x=4} \\ \\ y=-10+4=-6 \\ \\ \\ \text{If x=5} \\ \\ y=-10+5=-5[/tex]
So in this context, the correct option is:
B) (-9,-8, -7, -6, -5}
Answer:
the answer is b
Step-by-step explanation:
i took the test
If a car travels 150km for 1hour and 30 minutes how long in hours will it take the car to travel 260km
Time taken by the car to cover 260 km is 2.6 hrs
Step-by-step explanation:
Step 1: Find the speed of the car given distance covered = 150 km and time = 1.5 hrs.Speed = Distance/Time = 150/1.5 = 100 km/hr
Step 2: Find the time taken by the car to cover 260 km.Time = Distance/Speed = 260/100 = 2.6 hrs
3 is what percent of 5
Answer:
we can write
3 as a percent of 5 as
as is = to sign
percent is 100
and of is multiplication sign that gives us
3=x/100×5
x=(3×100)/5
x=300/5
x=60
so 3 is 60% of 5
Answer:
The answers would be 60%
Step-by-step explanation:
In a fraction, this is the number under the fraction bar.
Which distance measures 5 units?
Answer:
the only thing i can think of is a 5K so kilometers
Step-by-step explanation:
more context in the question? all distance measures 5 units
Answer:
can you give options please
Step-by-step explanation:
Yoryi bought an Apple Watch for $470. He paid $200 at the time of purchase and will make monthly payments of $30 to finish paying for the Apple Watch. He used the equation 200 + 30m = 470 to determine the number of months (m) he needs to make payments. For how many months will he make payments?
Answer:
9 months
Step-by-step explanation:200+30m=470
30m=270
m=9
He will pay for 9 months
Yoryi will make payments for 9 months.
Explanation:To determine the number of months (m) Yoryi needs to make payments, we can solve the equation 200 + 30m = 470. Here's how:
Subtract 200 from both sides of the equation: 30m = 270.Divide both sides of the equation by 30: m = 9.Therefore, Yoryi will make payments for 9 months.
Could someone explain linear functions to me? I dont get them at all. Thanks!
Answer:
Step-by-step explanation:
Linear functions are whose graph is a straight line. They contain a slope and a constant also known as the y intercept.
Example: y = 3x + 2
The slope is 3 and the y intercept is 2.
fill in the blanks
a ---÷48=-1
Ans is -48.
Hope this will help u..
Is 7/8 proportional or non proportional
Answer:
non-proportional
Step-by-step explanation:
7/8 is a fraction
A proportion is a relation that says two ratios are equal. A fraction is one ratio, so is not a proportion.
___
Something may be proportional to something else with a scale factor of 7/8. It seems some context may be missing from the question.
With similar triangle, the ratios of all three paris of corresponding sides are equal
Answer:
TRUE
Step-by-step explanation:
If this is a True/False question, the answer is True.
__
One of the ways to define triangle similarity is by the ratios of the sides. If the ratios of corresponding sides are the same, the triangles are similar.
Another way to define triangle similarity is by the angle measures. If corresponding angles are congruent, the triangles are similar.
Both conditions will be met by similar triangles.
Factor this polynomial
2x²+19x+24
Josie and her brother, Sean both have a job after school. For every $5.50 José earns, her brother earns $6.50. On Tuesday, they earned a total of $30.00. How much did Josie earn? How much did her brother earn?
What is the following quotient 6-3(^3+6)/^379
Answer:
Quotient given:
\frac{6-3 \sqrt[3]{6} }{ \sqrt[3]{9} }
Answer:
2 \sqrt[3]{3} - \sqrt[3]{18}
Explanation:
1) Rationalize by multiplying numerator and denominator by \sqrt[3]{9}
2)
\frac{6-3 \sqrt[3]{6} }{ \sqrt[3]{9} } \frac{\sqrt[3]{9}}{\sqrt[3]{9}}
3) Due the operations
\frac{6 \sqrt[3]{3}-3 \sqrt[3]{6.3}}{ \sqrt[3]{27} }
\frac{6 \sqrt[3]{3}-3 \sqrt[3]{6.3}}{ 3 }=2 \sqrt[3]{3} - \sqrt[3]{18}
Step-by-step explanation:
What is the area of this figure?
Enter your answer in the box.
in²,
Answer:
400 in²
Step-by-step explanation:
(20×16) + (½×8×20)
320 + 80 = 400 in²
The height of an object off the ground, h (in feet) t seconds after it is launched into the air is given by
h(t) = −16t2 + 128t, 0 ≤ t ≤ 8.
Find the average rate of change of h over the interval
[4, 8].
The height of an object off the ground h after t seconds is [tex]h(t)=-16t^2+128t[/tex] and the rate of change of h is 192.
Given data:
The average rate of change of a function over an interval [a,b] is given by the formula:
[tex]R=\frac{f(b)-f(a)}{b-a}[/tex]
Now, the function [tex]h(t)=-16t^2+128t[/tex] represents the height of an object off the ground at time t seconds. We are asked to find the average rate of change of h over the interval [4,8].
So, the value of a = 4 and b = 8.
[tex]h(8)=-16(8)^2+128(8)[/tex]
[tex]h(4)=-16(4)^2+128(4)[/tex]
On simplifying the equation:
[tex]R=\frac{h(8)-h(4)}{8-4}[/tex]
[tex]R=\frac{768}{4}[/tex]
[tex]R=192[/tex]
Hence, the average rate of change of h over the interval is 192 feet per second.
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The average rate of change of h over the interval [4,8] is -64 feet per second. This is found by substituting the values of a = 4 and b = 8 into the equation h(t) = -16t² + 128t and into the formula for average rate of change.
Explanation:To find the average rate of change of h over the interval [4, 8], we use the formula for the average rate of change: (h(b) - h(a)) / (b - a). Here, a = 4 and b = 8.
First, calculate h(a) and h(b) using the given equation h(t) = -16t² + 128t:
h(4) = -16*(4)² + 128*(4) = -256 + 512 = 256.h(8) = -16*(8)² + 128*(8) = -1024 + 1024 = 0.Substitute h(a) and h(b) into the formula to get:
(0 - 256) / (8 - 4) =-256/4 = -64.
So, the average rate of change of h over the interval [4, 8] is -64 feet per second.
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How can you express 1/100 as a decimal
Answer:
0.01
Step-by-step explanation:
1/100=0.01
Answer: 0.01
Step-by-step explanation:
Me. Sanchez bought some books at a book sale, including 15 paperback books. 75% of all the books he bought were paperbacks
The total number of books based on the given percentage will be 20 including 15 paperback books.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
Suppose Mr. Sanchez bought a total of x number of books.
75% of x = (75/100)x
This is the paperback thus,
(75/100)x = 15
x = 1500/75 = 20
Thus, the number of total books = 20 including 15 paperback books.
Hence "The total number of books based on the given percentage will be 20 including 15 paperback books".
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Make the number sentence true 5/10=blank/100
Answer:
50 = blank
Step-by-step explanation:
Step 1: Cross multiply
5/10 = ?/100
5*100 = 10?
500 / 10 = 10? / 10
50 = ?
Answer: 50 = blank
How much money must be deposited now in an
account paying 7.25% annual interest, compounded
quarterly, to have a balance of $1000 after 10
years?
Answer:
[tex]\$487.48[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ A=\$1,000\\ r=7.25\%=7.25/100=0.0725\\n=4[/tex]
substitute in the formula above
[tex]1,000=P(1+\frac{0.0725}{4})^{4*10}[/tex]
[tex]1,000=P(\frac{4.0725}{4})^{40}[/tex]
[tex]P=1,000/(\frac{4.0725}{4})^{40}[/tex]
[tex]P=\$487.48[/tex]
An envelope is 5 inches tall and 11 inches wide. What is its perimeter?
Answer:
32 inches
Step-by-step explanation:
5 + 5 + 11 + 11 = 32 inches
90 in terms of pi please help
90 in terms of pi is [tex]\frac{\pi}{2}[/tex] .
Step-by-step explanation:
We know that ,
Degrees are a unit of angle measure. A full circle is divided into 360 degrees. For example, a right angle is 90 degrees. A degree has the symbol ° and so ninety degrees would written 90°. Another unit of angle measure is the radian.The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.We have to convert 90 in terms of pi i.e. degree to radians:
⇒ [tex](90)\frac{\pi }{180}[/tex]
⇒ [tex]\frac{90 }{180}(\pi)[/tex]
⇒ [tex]\frac{1 }{2}(\pi)[/tex]
⇒ [tex]\frac{\pi}{2}[/tex]
Therefore, 90 in terms of pi is [tex]\frac{\pi}{2}[/tex] .