Answer:
The equation of line perpendicular to given line passing through (-15,-4) is:
[tex]y = -\frac{4}{3}x-24[/tex]
Step-by-step explanation:
Given equation is:
[tex]3x-4y = 9[/tex]
The given equation is in standard form. We have to convert it into slope intercept form first.
The slope intercept form is:
[tex]y = mx+b[/tex]
So,
[tex]3x-4y=9\\3x-9 = 4y\\4y = 3x-9\\\frac{4y}{4} = \frac{3x-9}{4}\\y = \frac{3}{4}x - \frac{9}{4}[/tex]
The co-efficient of x is the slope of the line.
m = 3/4
The product of slopes of two perpendicular lines is: -1
Let m1 be the slope of line perpendicular to given line then
[tex]m.m_1 =-1\\\frac{3}{4} . m_1 = -1\\m_1 = -1 * \frac{4}{3} \\m_1 = -\frac{4}{3}[/tex]
Putting in slope-intercept form
[tex]y = m_1x+b\\y = -\frac{4}{3}x+b[/tex]
To find the value of b, putting (-15,-4) in equation
[tex]-4 = -\frac{4}{3}(-15) +b\\-4 = 20+b\\-4-20 = b\\b = -24[/tex]
The equation will be:
[tex]y = -\frac{4}{3}x-24[/tex]
Hence,
The equation of line perpendicular to given line passing through (-15,-4) is:
[tex]y = -\frac{4}{3}x-24[/tex]
Translate the phrase into algebraic expression seven more than twice Jose’s height using the variable J to represent Jose height what would be the algebraic expression
Answer:
2j+7
Step-by-step explanation:
Phrase Into Algebraic Expression
If a problem is correctly phrased, it should be easily translated into algebraic language by following simple and concrete rules.
We have the phrase:
7 more than twice Jose's height.
Usually, we first deal with products and divisions before sums and subtractions because of the natural order of mathematic operations.
In the given phrase, the '7 more' part is left to the end and we start with the 'twice' part because it's a product.
Since we are using the variable j for Jose's height, then twice Jose's height is 2j.
Now we finish the expression by adding 7: 2j+7
Thus, the translation to algebraic expression is: 2j+7
Find the derivative of cos^4(5x^2)
Answer:
[tex]\displaystyle \frac{dy}{dx} = -40x \sin (5x^2) \cos^3 (5x^2)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \cos^4 (5x^2)[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = 4 \cos^3 (5x^2)[\cos (5x^2)]'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = 4 \cos^3 (5x^2) \sin (5x^2) (5x^2)'[/tex]Basic Power Rule [Derivative Property - Multiplied Constant]: [tex]\displaystyle y' = -40x \sin (5x^2) \cos^3 (5x^2)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What is the slope of the line that contains these points?
Answer:
-5/4
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
Slope = (5-10)/(49-45)
Classify the triangle shown by its sides and angles. Check all that apply.
73°
349
730
Equilateral
Scalene
Isosceles
Obtuse
Right
Acute
Equiangular
What number can be replaced with K to make
this a function?
(-5,8) (4,9) (K, 9) (9,9)
A)-5
B)4
C)-9
D)9
were becca and celia both correct or both wrong?
where's the problem? lol
Find the area and perimeter pls
Answer:
Perimeter: 23.8 feetArea: 24 square feetStep-by-step explanation:
To find the perimeter, add the lengths of all of the sides.
9.9 + 7.5 + 6.4 = 23.8
To find the area of a triangle, multiply the height by the width, and then divide by two.
7.5 * 6.4 = 48
48 / 2 = 24
A photo 5 inches wide and 8 inches long is enlarged.
How long is the new photo if it is (1)10 inches; (2)15 inches; (3)8 inches wide?
The new photo is_long if it is 10 in wide.
The new photo is_long if it is 15 in wide.
The new photo is_long if it is 8 in wide.
Answer:
1.16 in
2.24 in
3.12.8 in
Step-by-step explanation:
We are given that
Width of photo=5 in
Length of photo=8 in
We have to find the length of new photo in each case.
1. Let x represent the width and y represents the length of photo.
When width increase then length of photo is also increases then it is direct proportion.
Substitute the values then we get
Hence, the length of photo=16 in
2.Width=x=15 in
Again using the formula
Hence, the length of new photo=24 in
3. Width =x=8 in
Substitute the values in the given formula
Hence, the length of new photo=12.8 in
Answer:
1.16 in
2.24 in
3.12.8 in
Step-by-step explanation:
We are given that
Width of photo=5 in
Length of photo=8 in
We have to find the length of new photo in each case.
1. Let x represent the width and y represents the length of photo.
When width increase then length of photo is also increases then it is direct proportion.
Substitute the values then we get
Hence, the length of photo=16 in
2. Width= x=15 in
Again using the formula
Hence, the length of new photo=24 in
3. Width = x=8 in
Substitute the values in the given formula
Hence, the length of new photo= 12.8 in
A model house is 12 cm wide. If it was built with a scale of 3 cm : 4 m then how wide is the real house?
draw it pls
Answer:144
Step-by-step explanation:12 x 3 x 4=
Answer:
144
Step-by-step explanation:
A kite is flying 99 ft off the ground, and it's string is pulled taut. The angle of elevation of the kite is 41°. Find the length of the string. Round your answer to the nearest tenth
Answer:
150.90 feet
Step-by-step explanation:
It is given that,
A kite is flying 99 ft off the ground
The angle of elevation is 41°.
We need to find the length of the string. Let it is H.
Here, 99 ft is the perpendicular of a right angled triangle. We need to find hypotenuse of the triangle. Using trigonometry we can find it as follows :
[tex]\sin\theta=\dfrac{P}{H}\\\\H=\dfrac{P}{\sin\theta}\\\\H=\dfrac{99}{\sin(41)}\\\\H=150.90\ \text{feet}[/tex]
So, the length of the string is 150.90 feet.
A physician assistant orders 500 mL of D5NS over 5 hours. How many milliliters per hour will the patient receive? (Round to the nearest whole number)
Answer:
100
Step-by-step explanation:
500ml÷5h=100ml/h
The assistant will receive 100 mL per hour.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units. . For example, if a car runs 44 km on 2 litres of petrol then we can use the unitary method to find out the kilometres it will cover on 1 litre of petrol.
Given here, A physician assistant orders 500 mL of D5NS over 5 hours.
Therefore, he will receive 500/5 = 100 mL of D5N5 per hour
Hence, the asistant wil recieve 100 mL per hour
Learn more about the unitary method here:
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Explain in words the equation 42÷6=
Answer:
The quotient of forty-two and six is seven.
Please help if u get these all right i will mark brainliest
Answer:
1st: 8x +2
2nd: 17x + 11
3rd: 8x + 19
4th: 9x + 125
5th: 17x + 21y + 18
Answer:
2(4x+1)/8x+211+17x19+12x²9x+12517x+18+12yStep-by-step explanation:
My number has ones, tenths and hundredths. Rounding to the nearest whole number, you get 4. Rounding it to the nearest tenth, you get 3.5. The number of the hundredths is greater than 3. What number am I?
Answer:
3.54
Step-by-step explanation:
Well, we know it has to be 3.5 as our ones, and tenths place, (Thats what I did), and we know it can't be less than 3 for our hundredths place
If we do 0.05, or more as our hundredths place, than we won't be rounding right for the tenths place, so it has to be 3.54
The number in question that shows the decimal digits is; 3.54
We are told that the number has;
- Ones
- tenths
- hundredths
Thus means that the number is in 2 decimal places.
If we approximate to the nearest tenth and get 3.5, it means that the last number on the right of the decimal which is the hundredths is less than 5. It also means that the first number to the right of the decimal will remain as 5.
We are now told that this hundredths number is greater than 3. Thus, the hundredths number is 4.
If the approximation to the nearest whole number gives 4, it means that the number before the decimal will be 3.
Thus,in conclusion, the number is 3.54.
Read more at; https://brainly.com/question/12458734
2. The reciprocal of 4 3/6 is
a. 6/27
b. 6/30
c. 4 6/3
d. 6 3/4
Answer:
6/27
Step-by-step explanation:
[tex]4 \frac{3}{6} \\ \\ = \frac{4 \times 6 + 3}{6} \\ \\ = \frac{24 + 3}{6} \\ \\ 4 \frac{3}{6} = \frac{27}{6} \\ \\ reciprocal \: of \: 4 \frac{3}{6} = \frac{6}{27} [/tex]
The selling price of a watch is rs 220. If 10% profit has been included in the marked price of the watch, what is the marked price??
Answer:
22 is 10 of 220
Step-by-step explanation:
hope it help
THIS IS IMPORTANT!!!! WHO EVER CAN DO EVERYTHING IN THE PICTURE RIGHT ILL GIVE ALL NY POINTS TO!
Answer:
Step-by-step explanation: welp
Answer:welp
Step-by-step explanation:
PLEASE HELP WHO KNOWS THIS?
Answer:
I don't know how you would submit this but I do know it's a transformation. So you would move it across the x-axis 4 or 5 times depending on the shape. So I would maybe just write out each individual number like 3,4,5
Step-by-step explanation:
The Point (0,0) is a solution to which of these inequalities?
Answer:
(0, 0) s the solution of y-4 < 3x-1 as it satisfies the inequality.
Hence, option C is true.
Step-by-step explanation:
Given the point (0, 0)
a)
Putting the point (0, 0) the inequality
y+4 < 3x-1
0+4 < 3(0)-1
4 < -1
This is false as -1 can not be greater than 4
b)
y-1 < 3x-4
Putting the point (0, 0) the inequality
0-1 < 3(0)-4
-1 < -4
This is false as -1 can not be lesser than -4
c)
y-4 < 3x-1
Putting the point (0, 0) the inequality
0-4 < 3(0)-1
-4 < -1
This is true as -4 is lesser than -1
d)
y+4 < 3x+1
Putting the point (0, 0) the inequality
0+4 < 3(0)+1
4 < 1
This is false as 4 can not be lesser than 1
Therefore, (0, 0) s the solution of y-4 < 3x-1 as it satisfies the inequality.
Hence, option C is true.
Given m = -6/5 and the point (6,5), which of the following is the point-slope form of the equation?
Use the distributive property to remove the parentheses (x+12)8
Answer:
Using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]
Step-by-step explanation:
We need to used distributive property to solve (x+12)8
The distributive property of multiplication or addition states that: [tex]a(b+c)=ab+ac[/tex]
Using the property:
[tex](x+12)8\\=8x+8*12\\=8x+96[/tex]
So, using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]
Is there an ordered pair to both of these linear equations?
Y= x+1
Y= -x+5
Answer:
Yes (2,3)
Step-by-step explanation:
x+1 = -x+5
x+x = 5-1
2x=4
x=2
y=x+1=2+1
y=3
Answer:
(2, 3)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define systems
y = x + 1
y = -x + 5
Step 2: Solve for x
Substitution.
Substitute in y: x + 1 = -x + 5Add x on both sides: 2x + 1 = 5Subtract 1 on both sides: 2x = 4Divide 2 on both sides: x = 2Step 3: Solve for y
Define original equation: y = x + 1Substitute in x: y = 2 + 1Add: y = 3Step 4: Graph
We can graph the systems and check if the point is the actual solution set.
someone please help ;-;
6.58+7.64-10.006 adding and subtracting decimals
Answer:
4.214
Step-by-step explanation:
Original Equation:
6.58 + 7.64 - 10.006
Add 6.58 to 7.64
14.22
Subtract 10.006 from 14.22
4.214
Hope this helps :)
Please consider Brainliest :)
WILL MARK BRAINLIST!
5.Monty made a scale drawing of his room on grid paper, as shown below.
If each square on the grid paper represents a side length of 2 feet, what is the length, in feet,
of the longest wall in the room
Answer: 16 feet
Step-by-step explanation:
Looking at the drawing, the longest wall in the room is the horizontal length of the scale drawing.
Looking at the longest wall, the number of squares with a side length on the line of the wall are 8 in number.
If each square represents a side length of 2 feet, the length of the wall will be;
= 2 * 8
= 16 feet
Solve the equation:
y^2=-11y
Answer:
-5.5
Step-by-step explanation:
divide both sides by y which deleted y on the right side. then the left side turns into y instead of y squared. then you have y equals -5.5
Atlantic boat rental charges a $35.50 deposit fee plus $12.25 per hour to rent the boat. Pacific boat rental charges $25.99 plus $14.99 per hour to rent the boat. How many hours would you have to rent the boat for the cost of both rentals be the same? Select the equation that represents this situation. 35.50 - 12.25x = 25.99 - 14.99x 35.50 - 12.25x = 25.99 - 14.99x 35.50 + 12.25x = 25.99 + 14.99x 35.50 + 12.25x = 25.99 + 14.99x 35.50x + 12.25 = 25.99x + 14.99 35.50x + 12.25 = 25.99x + 14.99 12.25x - 35.50 = 14.99x - 25.99
Answer:
35.50 + 12.25x = 25.99 + 14.99x
Step-by-step explanation:
Given
Atlantic Boat
Deposit = $35.50
Hourly Rate = $12.25
Pacific Boat
Deposit = $25.99
Hourly Rate = $14.99
Required
Determine the equation that represents when both charges would be equal
Represent the number of hours with x
For both rental agencies, the hourly rate would be calculated using:
Deposit + Hourly Rate * x
So, for Atlantic Boat, the expression is:
35.50 + 12.25 * x
35.50 + 12.25x
For Pacific Boat, the expression is:
25.99 + 14.99 * x
25.99 + 14.99x
Next, is to equate both expressions.
This, when solved would get the number of hours when there charges would be the same.
35.50 + 12.25x = 25.99 + 14.99x
Solving further:
Collect like terms
35.50 - 25.99 = 14.99x - 12.25x
9.51 = 2.74x
Divide through by x
x = 9.51/2.74
x = 3.47 hours
3) How many counting numbers less than 50 are multiples of both 3 and 5?
Answer: 3 numbers
Step-by-step explanation:
For this questions to be solved, we need to write the multiples of both 3 abd 5 that are less than 50. This will be:
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45.
Common multiples = 15, 30 and 45
Therefore, the numbers that is less than 50 that are multiples of both 3 and 5 are 3 numbers
Find the missing side lengths leave your answerss as radicals??
Answer:
x= 3√3y= 3Step-by-step explanation:
1) Add 30+90 to get 120 and subtract 180-120= 60 as your third angle.
2) Take sin60= x/6 to get x= 3√3
3) Take sin30= y/6 to get y= 3
Here's a tip to verify this answer.
Use Pythagorean Theorem to do:
Square root of (3√3)^2 + 3^2 which equals 6 as your hypotenuse!