The number is 63. The difference between the digits of a two-digit number is 1.
What is number?Number is a mathematical object used to count, measure, and label. Numbers can be represented in a variety of forms, such as numerals, symbols, or words. Numbers are fundamental to mathematics, and all other areas of science and technology. They are used to represent amounts of money, measurements, dates, and amounts of time. Numbers are also used to identify objects and people, and to create equations and formulas. Number is essential for understanding the world around us.
To solve this, the first thing to do is find the sum of the digits. Since the number is one more than five times the sum of its digits, the sum of the digits is (63/5)-1=12.5-1=11.5. This means that the tens digit is 11 and the unit digit is 11 + 1 = 12. Therefore, the two-digit number is 63.
To know more about number click-
https://brainly.com/question/24644930
#SPJ1
I'd really like some help with this. Please...Please! What's the probability that the point ends in the shaded region?
Answer: 29%
Step-by-step explanation:
109/360=.294 Then move the decimal to make it a percent
DOES ANYONE KNOW THE ANSWER PLEASE
Answer:
Step-by-step explanation:
45 points for signing up.
2.5 points for each visit [tex]=2.5v[/tex]
Needs to total 75 points.
So [tex]45+2.5v=75[/tex] is the solution.
This is shown by option [tex](D)[/tex].
Cornidegretting marching all de What is the probably going to the A Ched Comider gering a randonner including devine What is the probability of generating av in bad to the decimal ? A Ched Assume 20.1). What is the probability z = 1.842 Answer Find the proportion of obsertions from the STANDARD NORMANDSTRIBUTION et les than -0.9900 Armer Check Find the proportion of observations from the STANDARD NORMAL DISTRIBUTION that we than 2.9000 Araw r Check Feel the proportion of brunetices from the SACARD NORMAL ISRAENUD-2-4200 me 2.400 me 20.1) Ung the STANDARDNENDETALLE band the LOWER w
The probability of generating a value between -0.9900 and 2.9000 from a standard normal distribution is 0.4781. The probability of generating a value between -2.4200 and 2.4200 from a standard normal distribution is 0.9804. The probability of generating a value between -0.9900 and 20.1 from a standard normal distribution is 1.0000.
The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1. Any normal distribution can be standardized by converting its values into z scores.The standard normal distribution is one of the forms of the normal distribution. It occurs when a normal random variable has a mean equal to zero and a standard deviation equal to one. In other words, a normal distribution with a mean 0 and standard deviation of 1 is called the standard normal distribution.
To know more about standard normal distribution refer here:
https://brainly.com/question/29509087
#SPJ11
What is the pattern of _15,25,_45,55,65
Answer:
5 and 35
Step-by-step explanation:
It's going up in tens so it must start from 5, therefore the one between 25 and 45 must be 35.
Does someone mind helping me with this problem? Thanks!
Answer:
8183.27
Step-by-step explanation:
Answer:
8183.3
Step-by-step explanation:
500(1+0.15)20=8183.27 round it to become 8183.3
At the same time a 612 -ft teacher casts a 9-ft shadow, a nearby flagpole casts a 3112 -ft shadow. How tall is the flagpole?
The height of the flagpole is approximately 23,047.11 feet.
To resolve this issue, we can make use of the similar triangles property. The teacher, the flagpole, and each of their corresponding triangles are similar because they have the same angles.
Let h be the height of the flagpole. Then, we can set up the following proportion:
h / 3112 = 612 / 9
When we simplify this ratio, we obtain:
h = (3112 x 612) / 9
h = 207424 / 9
h ≈ 23,047.11 feet
Hence, the flagpole is roughly 23,047.11 feet tall.
To know more about Feet visit:
https://brainly.com/question/15658113
#SPJ1
Score: 8 Penalty: None Singleton tic Operations on Functions 11:58:12 PM hat f(x)=x^(2)+5x-36 and g(x)=x-4, find f(x)+g(x) an the result as a polynomial in simplest form.
The final answer sum of f(x) and g(x) is [tex]x^2 + 6x - 40[/tex], which is a polynomial in simplest form.
To find the sum of two functions, we simply need to add their respective terms together.
In this case, we have:
f(x) = [tex]x^2 + 5x - 36[/tex]
g(x) = x - 4
So, f(x) + g(x) = [tex](x^2 + 5x - 36)[/tex] +[tex](x - 4) = x^2 + 6x - 40[/tex]
Therefore, the sum of f(x) and g(x) is [tex]x^2 + 6x - 40[/tex], which is a polynomial in simplest form.
To know more about polynomial refer here:
https://brainly.com/question/11536910#
#SPJ11
Marcus can choose between a monthly salary of $1,750 plus 6% of sales or $2,000 plus 3% of sales. He expects sales between $5,000 and $10,000 a month. Complete the explanation to show which salary option he should choose based on how much he could make. He should choose the option that pays (select) With option 1 he would make $ With option 2 he would make $ to $ to $
Answer:
Step-by-step explanation:
1500 + 5000x 0.055 - $1775
1500 + 10000 x 0.055 = $2050
with option 1 he would make 1775 to 2050
2400 + 5000 x0.04 =2600
2400 + 10000 x 0.04 = 2800
With option 2 hw would make $2600 to $2800
simple calculation :)
Indigo built a toy box in the shape of a rectangular prism with an open top. The diagram below shows the toy box and a net of the toy box. What is the surface area, in square centimeters, of the toy box? (Lengths are 9cm, 5cm and 10cm)
The surface area, in square centimeters, of the toy box is 370 cm²
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area. Surface area is measured in cm².
Given, the lengths are 9 cm, 5 cm, and 10 cm.
To calculate the surface area, the formula is2(h × W) + 2(h × L) + 2(W × L)
2 x 9 x 5 + 2 x 9 x 10 + 2 x 5 x 10
90 + 180 + 100
370
Therefore, the surface area of the box is 370 cm²
Learn more about surface area, here:
https://brainly.com/question/29298005
#SPJ1
The question is incomplete, the image of the box is attached below:
What is (z^(2)+10z+25)/(z^(2)-3z-40) in simplest form? State any restrictions on the variable.
The expression (z²+10z+25)/(z²-3z-40) in simplest form is (z+5)/(z-8), with the restriction that z cannot be equal to 8.
The expression (z²)+10z+25)/(z²-3z-40) can be simplified by factoring both the numerator and denominator.
First, factor the numerator:
(z²+10z+25) = (z+5)(z+5)
Next, factor the denominator:
(z²-3z-40) = (z-8)(z+5)
Now, the expression can be simplified by canceling out the common factor of (z+5):
(z+5)(z+5)/(z-8)(z+5) = (z+5)/(z-8)
Therefore, the expression in simplest form is (z+5)/(z-8).
There are restrictions on the variable in this expression. The denominator cannot be equal to zero, so we must exclude any values of z that would make the denominator zero.
The denominator is (z-8), so the restriction is:
z-8 ≠ 0
Solving for z, we find that the restriction is:
z ≠ 8
To know more about simplest form click on below link:
https://brainly.com/question/290068#
#SPJ11
Consider the function f : R→R
given by f(x) = x^(4) - 32 x^(2)
Find the minimum and and maximum values (absolute) of f over the interval [3,5]. Provide the exact values. Minimum value a Maximum value.
The minimum value of f(x) over the interval [3,5] is -512 and the maximum value is 225.
To find the minimum and maximum values of the function f(x) = x^(4) - 32 x^(2) over the interval [3,5], we can use the following steps:
1. Find the first derivative of the function: f'(x) = 4x^(3) - 64x
2. Set the first derivative equal to zero to find the critical points: 4x^(3) - 64x = 0
3. Solve for x to find the critical points: x = 0, x = 4√2, x = -4√2
4. Check the value of the function at the critical points and at the endpoints of the interval to find the minimum and maximum values.
5. The minimum value occurs at x = 4√2, where f(4√2) = (4√2)^(4) - 32(4√2)^(2) = -512
6. The maximum value occurs at x = 5, where f(5) = 5^(4) - 32(5)^(2) = 225
7. Therefore, the minimum value is -512 and the maximum value is 225.
The least value of f(x) over the interval [3,5] is -512 and the largest value is 225.
Learn more about function at https://brainly.com/question/29129022
#SPJ11
What is the total surface area of the rectangular prism shown?
Answer:
128 in^2
Step-by-step explanation:
L * W
16 * 8 = 128 in^2
3 halves of a cupcake for my family plus some extra for my 2 friends. They will each want a quarter of a cupcake.
15 quarters of a cupcake, which is equivalent to 3.75 cupcakes in total.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
5 halves of a cupcake for your family, which is equivalent to 2.5 cupcakes.
To divide this evenly among your two friends who each want a quarter of a cupcake, we can start by converting the amount of cupcakes you have to quarters:
2.5 cupcakes × 4 quarters/cupcake = 10 quarters of a cupcake
Now we can divide the 10 quarters of a cupcake equally between your two friends:
10 quarters of a cupcake / 2 friends = 5 quarters of a cupcake per friend
Hence, a total of 5 + 5 + 5 = 15 quarters of a cupcake, which is equivalent to 3.75 cupcakes in total.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
17. Find the coordinates of the image of EB given E(2, -1) and B(0, 5) after a dilation with center
(3,-1) and scale factor of 3.
The coordinates of the image of EB are (0, -1) and (-6, 18).
What is dilation?Dilation is a process for creating similar figures by changing the dimensions.
The center of dilation is given as (3, -1) and the scale factor is 3.
The distance between the center of dilation and point E is:
d = √((3-2)² + (-1-(-1))²) = 1
The distance between the center of dilation and point B is:
d = √((3-0)² + (-1-5)²) = sqrt(65)
To find the new distance, we multiply the distance by the scale factor:
For point E: 3 × 1 = 3
For point B: 3 × √(65)
Now, we can find the coordinates of the image:
For point E:
x = 3 × (2 - 3) + 3 = -3 + 3 = 0
y = 3 × (-1 -(-1)) -1 = 0 - 1 = -1
So the image of E is (0, -1).
For point B:
x = 3 × (0 - 3) + 3 = -9 + 3 = -6
y = 3 × (5 -(-1)) -1 = 18
So the image of B is (-6, 18).
Therefore, the coordinates of the image of EB are (0, -1) and (-6, 18).
Learn more about the dilation here:
brainly.com/question/13176891
#SPJ1
M6U3L15: Representing ratios using tables
Set of practical problems
Complete the table to show the amounts of yellow and red paint needed for different numbers of batches of the same shade of orange paint.
Yellow paint (quarts)
Red paint (quarts)
5
6
Explain how you know that these amounts of yellow paint and red paint will give the same shade of orange as the mixture in the first row of the table.
A car is traveling at a constant speed, as shown by the double number line.
How far does the car travel in 14 hours? Explain or demonstrate your reasoning.
The olive trees in an orchard produce 3000 pounds of olives per year. It takes 20 pounds of olives to produce 3 liters of olive oil. How many liters of olive oil can this orchard produce in a year? If you get stuck, consider using the board.
Olives (pounds)
Olive oil (litres)
20
3
100
3000
More about this source textSource text required for additional translation information
Send feedback
Side panels
History
Saved
Contribute
1)The completed table is
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
2) The car travels 98 miles in 14 hours.
3) The orchard can produce 450 liters of olive oil in a year.
What is a ratio?
A ratio is a quantitative comparison between two or more quantities, indicating how many times one quantity contains another. It is expressed as the quotient of the two quantities or in the form of a fraction. Ratios can be represented in various ways, including as decimals, percentages, or fractions.
Complete the table to show the amounts of yellow and red paint needed for different numbers of batches of the same shade of orange paint.
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
To get the same shade of orange paint, we need to mix yellow and red paint in a certain ratio. This ratio will determine the hue, saturation, and brightness of the final color. In this case, we can see that the ratio of yellow to red paint is 5:3 in the first row of the table, and 6:3.6 (which simplifies to 5:3) in the second row. This means that we need the same amount of yellow and red paint for each batch of orange paint, in a 5:3 ratio.
A car is traveling at a constant speed, as shown by the double number line.
The distance traveled by the car is directly proportional to the amount of time it travels. This means that the ratio of distance to time is constant. From the given double number line, we can see that the car travels 21 miles in 3 hours. Therefore, the ratio of distance to time is 21:3 or 7:1. To find how far the car travels in 14 hours, we can set up a proportion:
distance/time = 7/1
distance/14 = 7/1
distance = 7 x 14
distance = 98 miles
Therefore, the car travels 98 miles in 14 hours.
The olive trees in an orchard produce 3000 pounds of olives per year. It takes 20 pounds of olives to produce 3 liters of olive oil.
To find how many liters of olive oil the orchard can produce in a year, we need to divide the total weight of olives by the amount of olives needed to produce one liter of oil, and then multiply by the conversion factor:
Liters of oil = (Pounds of olives / Pounds per liter) x Conversion factor
Liters of oil = (3000 / 20) x 3
Liters of oil = 150 x 3
Liters of oil = 450
Therefore, the orchard can produce 450 liters of olive oil in a year.
Hence,
1)The completed table is
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
2) The car travels 98 miles in 14 hours.
3) The orchard can produce 450 liters of olive oil in a year.
To learn more about the ratios, visit:
https://brainly.com/question/2328454
#SPJ1
Kyler designed a pool with a diameter of 25 meters. What is the area of the bottom of the pool?
Answer:
962.084375 meters² or 306.25π
Step-by-step explanation:
A diameter is a line that goes straight through the center of the circle. Since it goes through the center, it creates 2 radii. This splits the diameter into 2 separate parts, and since the diameter is 25 meters, that means that the radius will be 25/2 = 17.5 meters.
The formula for the area of a circle is pi • r²
Since we know the radius (17.5), we can solve this expression:
pi • 17.5²
pi • 306.25
If we use 3.1415 for pi, we get962.084375 meters²
If you liked this answer, please mark me brainliest!
During a rugby contest 54342 people what's the first game or 49990 people what's the second game if 156330 people watched all three games how many what's the third game
The answer would be 51,998
what is the vaule of z??
Answer:
Z= 6
Step-by-step explanation:
Z + 9 = 15
- do the inverse (opposite) operation
15 -9 = 6
9 -9 * cancel out *
Z = 6
CHECK:
6 +9 = 15
TRUE
(Please answer quickly, giving brainliest when two people answer!!)Which graph represents the inequality 2.5 is less than the product of −0.5 and a number?
number line with open circle on point 0.2 and arrow shaded to the left
number line with open circle on point negative 5 and arrow shaded to the left
number line with open circle on point negative 0.2 and arrow shaded to the right
number line with open circle on point negative 5 and arrow shaded to the right
The graph representing the inequality 2.5 is less than the product of −0.5 and a number is number line with open circle on point negative 5 and arrow shaded to the left.
What is Inequalities?Inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠.
Given inequality is,
2.5 is less than the product of −0.5 and a number.
2.5 < -0.5x
We have to isolate x on one side.
Dividing both sides by -0.5,
-5 > x
The inequality sign changes when a negative number is divided.
Or x < -5
So the solutions of the inequality are all the numbers less than -5.
So the graph of the inequality will be a number line where an open circle is at -5, since the point -5 is not included.
Since the solutions are less than -5, arrow is shaded to the left.
Hence the second option is the correct one.
Learn more about Graphing Inequalities on a Number Line here :
https://brainly.com/question/27916124
#SPJ1
Two fire towers are located 5 miles apart on a straight road. They both spot the same fire on the north side of the road and report its location in terms of angles from the road. From the tower A, the fire is 22 degrees. From the tower B (5 miles east of tower A), the fire is 37 degree. How far from tower B is the point on the road closest to the fire? Please sketch and show the fire location. The point on the road closest to the fire will be on a line to the fire directly perpendicular to the road. Round to two decimal places
Tower B is 2.34 miles far from the point on the road closest to the fire.
The point on the road closest to the fire can be found by drawing a line perpendicular to the road that passes through the fire location. Let x be the distance from tower B to this point. Then, using trigonometry, we can find that the distance from tower A to the fire location is x/tan(22) and the distance from tower B to the fire location is (5 - x)/tan(37). Since the fire location is the same from both towers, these distances must be equal, so we can set up the equation x/tan(22) = (5 - x)/tan(37) and solve for x, which is approximately 2.34 miles.
To sketch the fire location, draw a straight road with two fire towers located 5 miles apart. From tower A, draw a line at an angle of 22 degrees towards the north side of the road to represent the direction of the fire location. From tower B, draw a line at an angle of 37 degrees towards the same side of the road. The point where these two lines intersect represents the location of the fire. Draw a line perpendicular to the road passing through this point to find the closest point on the road to the fire.
For more questions like Distance visit the link below:
https://brainly.com/question/14929758
#SPJ11
Paula bought $12.74$12.74 worth of $0.49$0.49 stamps and $0.21$0.21 stamps. The number of $0.21$0.21 stamps was six less than the number of $0.49$0.49 stamps. Solve the equation 0.49s+0.21(s−6)=12.740.49�+0.21(�-6)=12.74 for s�, to find the number of $0.49$0.49 stamps Paula bought.
The number of $0.49$ stamps Paula bought is s = (1274 - 49s / 21) + 6.
To solve the equation 0.49s + 0.21(s - 6) = 12.74 for s, we can multiply both sides by 100 to get:
49s + 21(s - 6) = 1274
Now, we can move the 21(s - 6) term to the left side of the equation and the 49s term to the right side of the equation. To do this, we will subtract the 49s from both sides of the equation, which yields:
21(s - 6) = 1274 - 49s
Next, we can divide both sides of the equation by 21 to isolate the (s - 6) term, resulting in:
(s - 6) = 1274 - 49s / 21
Finally, we can add 6 to both sides of the equation to solve for the number of $0.49$ stamps that Paula bought:
s = (1274 - 49s / 21) + 6
Therefore, the number of $0.49$ stamps Paula bought is s = (1274 - 49s / 21) + 6.
Learn more about equation
brainly.com/question/29657992
#SPJ11
I need help find answer for number 9
The perimeter of the given triangle MNP is 65.
What is a regular figure and its perimeter?A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthened n sides).
Suppose that length of each side of that figure be of u units, then we have the perimeter as:
P=u+u+u+u+u+u......=n*u
units.
We are given that;
Side MN=5x-34, QR=25, QS=22, RS=x+4
Now,
5x + x - 34 + 4 = 22
6x - 30 = 22
6x - 30 + 30 = 22 + 30
6x = 52
6x/6 = 52/6
x = 8.67
P= 5*8-34+25+22+8+4
=40-34+47+12
=65
Therefore, the perimeter of the triangle will be 65.
Learn more about perimeter here:
https://brainly.com/question/10466285
#SPJ1
PLEASE HELP!!!!!!! ASAP PLSSS WHICH ONE IS IT???!
Answer: y = 5/6x
Step-by-step explanation:
It is a direct variation.
Convert the following phrase into a mathematical expression. Use x as the variable. Combine like terms when possible.
A number multiplied by −8, subtracted from the sum of 5 and three times the number
The expression is ____.
The expression will be 5 + 11x.
What is an expression?
An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
It is possible to compare expressions to phrases. In English, a phrase by itself may contain an action, but it does not constitute a whole sentence.
Explanation: 3 + 7
Let the number to be "x"
Step 1 : the number is multiplied by - 8
So, -8 x
Step 2 : subtracted from the sum of 5 and 3 times the number
So, (5 +3x) - (-8x)
= 5+3x + 8x
= 5 + 11x
Hence, The final expression will be 5 + 11x.
To earn more about Expressions, visit the link:
https://brainly.com/question/723406
#SPJ1
What is the vertex form of the quadratic equation represented in the following table?
The vertex form of the quadratic equation represented by the table is y = (x+1)² - 3.
What is a quadratic equation's vertex form?A quadratic equation's vertex form is y = a(x-h)2 + k, where (h, k) denotes the parabola's vertex. This form is created by solving the square of the quadratic equation y = ax2 + bx + c in standard form.
The axis of symmetry is given by the formula:
x = -b/2a.
x = (-1 + 1) / 2 = -0.5
Substitute x = -0.5 into the given table and find the corresponding value of y:
f(-0.5) = (-0.5+1)² - 3 = -2.25
The vertex of the parabola is (-0.5, -2.25).
The vertex form of a quadratic equation is:
y = a(x-h)² + k
Find the value of a by using any of the given points on the parabola.
Substitute (1, 4):
4 = a(1 + 0.5)² - 2.25
6.25 = a(1.5)²
a = 2.78
Substituting the values of a, h, and k, we get:
y = 2.78(x+0.5)² - 2.25
y = (x+1)² - 3
Hence, the vertex form of the quadratic equation represented by the table is y = (x+1)² - 3.
Learn more about vertex here:
https://brainly.com/question/29030495
#SPJ1
FIRST OT HELP GETS BRAINLIEST! PLEASE SHOW WORK!
The table shows the value of printing equipment for 3 years after it is purchased. The values form a geometric sequence. How much will the equipment be worth after 7 years?
Geometric sequence: [tex]a_{n} = a_{1} r^{n - 1}[/tex]
Year Value $
1................12,000
2...............9,600
3...............7,680
The equipment will be worth approximately $3,145.73 after 7 years.
What is the worth of the equipment after 7 years?
To find the value of the printing equipment after 7 years, we need to first determine the common ratio (r) of the geometric sequence.
We can do this by dividing any term by the preceding term. Let's divide the value in year 2 by the value in year 1:
r = 9,600/12,000 = 0.8
Now we can use the formula for a geometric sequence to find the value of the equipment after 7 years:
a₇ = a₁r⁶
where;
a₁ is the value in year 1 and r is the common ratio we just found.Plugging in the values we have:
a₇ = 12,000 x 0.8⁶
a₇ ≈ $3,145.73
Learn more about geometric sequence here: https://brainly.com/question/1509142
#SPJ1
The Triangle and square shown below have the same perimeter What is the length of one side of the square
The length of one side of the square is 1.5 units
What is the length of one side of the squareThe complete question is added as an attachment
From the question, we have
The triangle and the squate have the same perimeter
The perimeter is the sum of the side lengths
So, we have
Triangle = 3x + 4x + 5x
Square = 4 * (x + 1)
Evaluate
Triangle = 12x
Square = 4x + 4
So, we have
4x + 4 = 12x
Evaluate
8x = 4
So, we havr
x = 0.5
From the figure, we have
Length = x + 1
Evaluate
Length = 0.5 + 1
So, we have
Length = 1.5
Hence, the length is 1.5
Read more about perimeter at
https://brainly.com/question/24571594
#SPJ1
I need help on this asap!!
The amount in the second case is more. Then the better job is the second one.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
If he can make $2,000 worth of sales per week. Then the total amount in the first case is given as,
⇒ $31,200 + $2,000 x 0.09 x 52
⇒ $40,560
And the total amount in the second case is given as,
⇒ $26,000 + $2,000 x 0.15 x 52
⇒ $41,600
The amount in the second case is more. Then the better job is the second one.
More about the solution of the equation link is given below.
https://brainly.com/question/22613204
#SPJ1
Convert the Cartesian coordinates (1,−5) to polar coordinates
with r>0 and 0≤θ<2π. give theta answer in radiants
The Cartesian coordinates (1, -5) are equivalent to the polar coordinates (√26, 4.910188838655984) with r > 0 and 0 ≤ θ < 2π.
To convert the Cartesian coordinates (1, -5) to polar coordinates with r>0 and 0≤θ<2π, we need to use the following formulas:
r = √(x^2 + y^2)
θ = tan^-1(y/x)
First, let's find the value of r:
r = √(1^2 + (-5)^2)
r = √(1 + 25)
r = √26
Now, let's find the value of θ:
θ = tan^-1((-5)/1)
θ = tan^-1(-5)
θ = -1.373400766945016
Since we need the angle to be between 0 and 2π, we can add 2π to the negative angle to get the positive equivalent:
θ = -1.373400766945016 + 2π
θ = 4.910188838655984
Therefore, the polar coordinates of the Cartesian coordinates (1, -5) are (r, θ) = (√26, 4.910188838655984).
So the answer is:
r = √26
θ = 4.910188838655984
The Cartesian coordinates (1, -5) are equivalent to the polar coordinates (√26, 4.910188838655984) with r > 0 and 0 ≤ θ < 2π.
For more information about Cartesian coordinates, visit:
https://brainly.com/question/4726772
#SPJ11
Write an equation of the parabola in intercept form that passes through (-18,72) with x-intercepts of -16 and -2
The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).
What is Parabola?A parabola is a type of curve that is formed when a point called the focus moves along a straight line called the directrix.
In other words a parabola is defined as the set of all points in a plane that are equidistant to the focus and the directrix.
The shape of a parabola is similar to a U or a V shape, and it can either be open upwards or downwards, depending on the orientation of the curve.
The Intercept form of a parabola is given by
y = a(x - p)(x - q)
Where p and q are the x - coordinates at which the parabola crosses the x-axis (i.e, the x-intercepts).
Here we have
The parabola in intercept form that passes through (-18,72) with x-intercepts of -16 and -2
Let y = a(x-p)(x-q) is the equation of parabola
From the data, x-intercepts p = - 16 and p = -2
=> y = a(x+ 16 )(x + 2) ---- (1)
Given that the parabola passes through (-18, 72)
=> 72 = a(- 18 + 16 )(-8 + 2)
=> 72 = a(-2)(-6)
=> 72 = - 12a
=> a = - 6
Substitute a = -6 in equation (1)
=> y = -6(x+ 16 )(x + 2)
Therefore,
The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).
Learn more about Parabolas at
https://brainly.com/question/29173045
#SPJ1
