Answer:
852
Step-by-step explanation:
You want the next number in the pattern that starts with 5, 12, 33, 96, 285.
PatternWhen looking for patterns in sequences, it is often useful to consider first differences and the relations between them.
12 -5 = 7
33 -12 = 21
96 -33 = 63
285 -96 = 189
We notice that these differences have a common ratio of 3. This suggests the next difference will be 189×3 = 567.
The next number in sequence is 285 +567 = 852.
__
Additional comment
When differences have a common ratio, an exponential sequence is indicated. These differences have a ratio of 3, but are not powers of 3, so the exponential term needs additional components to completely describe the sequence. We expect there are horizontal and vertical offsets involved.
Exponential regression gives the explicit formula as ...
y = (3 +7·3^(x-1))/2
Find an equation of the tangent line to the curve at the given point.
y = x³ - 3x + 1, (3, 19)
Answer:
y=24x-53.
Step-by-step explanation:
1) the slope-interception view of the required tangent line is
y=slope*x+interception;
2) y'=3x²-3;
3) slope=y'(3), then slope=3*3²-3=24;
4) the required equation of tangent line has the form
y=24x+interception;
5) to calculate the interception it is needed to substitute the given coordinates (3;19) into this equation:
19=24*3+interception; ⇒ interception=-53;
6) finally, the required equation is y=24x-53.
this I never got taught, need help bunch of points
Answer:
Absolute value is the distance from 0 all negative numbers become positive and positive stays positive.
Step-by-step explanation:
Solve the equation -2 =
k=
k+7
3
[tex]{ \orange{ \tt{k = 1}}}[/tex]
Step-by-step explanation:
-2 = k+7/3
cross multiply 3 with -2 then,
-6 = k+7 (OR) k+7 = -6.
k = -6+7
k = 1.
Point B is on line segment
AC
. Given AB=3x, BC=4x+8, and AC=5x+10, determine the numerical length of
AC
.
Answer:
The length of AC is 15 units
Step-by-step explanation:
Write the equation of the line in fully simplified slope-intercept form.
The equation of the line in fully simplified slope-intercept form is [tex]y=\frac{1}{4} x-1[/tex].
What is a slope intercept form?A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.
For calculating the slope, the formula used is [tex]m=\frac{x_{2} -x_{1} }{y_{2} -y_{1} }[/tex]
From the graph we see that the points are (4,0) and (0,-1).
Substituting the points in the formula,
[tex]m=\frac{x_{2} -x_{1} }{y_{2} -y_{1} }\\m=\frac{-1-0}{0-4} \\m=\frac{-1}{-4} \\m=\frac{1}{4}[/tex]
We know that, the equation of a line in point slope form, where (x₁, y₁) is the point and slope m is:
(y – y₁) = m(x – x₁)
Here, (x₁, y₁)= (4,0)
Substitute the value of m and any coordinate into the formula y−y₁=m(x−x₁)
[tex]y-0=\frac{1}{4} (x-4)\\y=\frac{1}{4} x-1[/tex]
Therefore, the equation of the line in fully simplified slope-intercept form is [tex]y=\frac{1}{4} x-1[/tex].
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find the midpoint of a line segment with endpoints A(-5,5) and B(2,-5)
Answer:
(-1.5,0)
Step-by-step explanation:
Find the average for the x and y values.
x = [tex]\frac{(-5+ 2)}{2}[/tex] = [tex]\frac{-3}{2}[/tex] or -1.5
y = [tex]\frac{(5- 5)}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
A bedroom (14 ft by 12ft) and hallway (8ft by 3ft) are getting new wood flooring. Wood flooring is priced at $6.20 per square foot. How much will it cost to add the wood flooring?
If a bedroom (14 ft by 12ft) and hallway (8ft by 3ft) are getting new wood flooring. Wood flooring is priced at $6.20 per square foot. The amount it will cost to add the wood flooring is: $1,190.40.
Cost priceFirst step is to calculate the bedroom square feet
Bedroom square feet=14ft ×12ft
Bedroom square feet= 168 sq feet
Second step is to calculate hallway square feet
Hallway square feet=8ft × 3ft
Hallway square feet=24 sq feet
Third step is to calculate the total square feet
Total square feet=168+24
Total square feet=192
Fourth step is to calculate the cost
Cost=$6.20× 192
Cost= $1,190.40
Therefore the amount it will cost to add the wood flooring is: $1,190.40.
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What is the slope of a line parallel to the line whose equation is 2x - 5y = 30. Fully simplify your answer.
Answer: [tex]\boxed{y=\frac{2}{5} x-7}\ as\ an\ example[/tex]
Step-by-step explanation:
Find the slope-intercept form:
[tex]2x-5y=30\\\\-5y=-2x+30\\\\y=\frac{-2x+30}{-5} \\\\y=\frac{2}{5} x-6[/tex]
Therefore the slope is 2/5
An example of a line parallel to this line is
[tex]y=\frac{2}{5} x-7[/tex]
Robert spends $30.45, before tax, at the bookstore. If the sales Tax rate in his city is 7.25%, and Robert started with $40, how much does Robert have left?
The amount of money Robert has left given the amount he started with and after deducting tax is approximately $7.34
How much does Robert have left after deducting tax?Tax can be defined as the compulsory levy paid by citizens of a particular country on their income, goods and be services.
Amount Robert started with = $40Amount Robert spent before tax = $30.45Tax rate = 7.25%Amount of tax = Tax rate × Amount Robert spent before tax
= 7.25% × $30.45
= 7.25/100 × 30.45
= 0.0725 × 30.45
= $2.207625
Total amount Robert spent = Amount Robert spent before tax + Amount of tax
= $30.45 + $2.207625
= $32.657625
Amount Robert has left = Amount Robert started with - Total amount Robert spent
= $40 - $32.657625
= $7.342375
Approximately,
$7.34
Therefore, the amount Robert has left after deducting tax is $7.34
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PLEASE HELP NOWW PLEASE
Answer: NOW
Step-by-step explanation:
|1/4 x +2| -3 =5 solve for x and graph on number line
The value of x on the number line is 24 and - 40
A number line in elementary mathematics is a representation of a graduated straight line that acts as an abstraction for real numbers, represented by the letter R. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
When seen as a geometric space, namely the one-dimensional Euclidean space, the number line, also known as a real line in advanced mathematics, is technically defined as the set R of all real numbers. It can be conceptualized as a linear continuum, metric space, topological space, vector space (or affine space), measure space, or topological space.
The given equation is
[tex]|\frac{1}{4}x+2 | -3=5[/tex]
Solving the equation:
[tex]or,|\frac{1}{4}x+2 | =5+3\\or,|\frac{1}{4}x+2 |=8\\or,\frac{1}{4}x+2=\pm8\\or,x+8=\pm32\\or,x=-8\pm32[/tex]
Now we take the two separate values of x:
either x=-8+32 or x=-8-32
or,x=24 or x=-40
The value of x is 24 and - 40.
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Consider the equation 5x + 8y = 24, A line parallel to the above line would have a slope of:
Answer:
Any line with a slope of -5/8 would be parallel to this line.
Step-by-step explanation:
First write this in the slope intercept form of a line
y = mx + b. The number before the x will be the slope.
5x + 8y = 24 Subtract 5x from both sides of the equation
8y = -5x +24 Divide everything by 8
y = -5/8x + 3
If f (x) = x² +4, solve f (x) = 13.
The solution of the function f(x) = 13 is x= 3
According to the question we have been the function f(x), that i s
f(x) = x² + 4
We need to find the value of x where we have been given that
f(x) = 13
Therefore, we will put the required value of function f(x) in the above condition we get
x² + 4 = 13
Subtracting 4 both the sides we get,
x² + 4 - 4 = 13 - 4
x² = 9
Taking square root both sides we get,
√x² = √9
x = 3
Hence the value of x is 3.
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the scale from a square park to a drawing is 5 m to 1 cm .the actual park has an area of 1600 m2 .what is the area of the drawing of the park
The area of the drawing of the park is 64 cm²;
Scale: Square park to Drawing = 5m:1cm
= 5m:0.01m;
Therefore; Square Park Area = 1600m²;
Drawing Area = 1600 ×(0.01/5)²
= 0.0064m² = 64 cm²
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Please HELP ME!!!! This is really confusing. HOW DO I DO THIS?!?!?!
Answer:
Flying Disc should be 72
Step-by-step explanation:
circumference = πd
HD Coin C = 3π
9.42477796077
Flying Disc. C = 23π
72.2566310326
Jar Lid C = 8π
25.1327412287
Flower Pot C = 15π
47.1238898038
consider the line y=9x-8 find the equation that is perpendicular to this line and passes through the point -8,3
The equation of line is y=-9x-69.
To solve this problem we need to know the concept of slope of line and equation of straight line.
Writing the standard form of line is in the form of y= mx+ c where m is the slope of line.
And we also know that the product of slope of a line perpendicular to the line is equal to -1.
Let us assume that the slope of required line is m'
So, m' × 9 = -1
⇒ m'= -9
Now, the equation of line will be;
[tex](y-3)=-9(x+8)[/tex]
⇒ y-3=-9x-72
⇒ y=-9x-69 is the standard equation of line perpendicular to the given line y=9x-8.
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the numbers being multiplied in a product are called
Answer:factors
Step-by-step explanation:
A square that is 7 yd on a side is placed inside a rectangle that has a width of 9 yd and a length of 14 yd. What is the area of the region inside the rectangle that surrounds the square?
Answer: 77 yd^2
Step-by-step explanation:
S=Area of Square. s=side length of square. w=width of rectangle
l=length of rectangle. R=Area of Rectangle
S=s^2
S=7^2
S=49 yd^2
R=l*w
R=9*14
R=126 yd^2
R-S=
126-49=77 yd^2
Pls help it’s due soon
Select all the triangles that have an area of 10 square units:
The triangles that have an area of 10 square units are triangles A and B
How to determine the triangles that have an area of 10 square units?The area of a triangle is calculated using
Area = 0.5 * Base * Height
Triangle 1
Base = 5
Height = 4
So, we have
Area = 0.5 * 5 * 4
Area = 10
Triangle 2
Base = 4
Height = 5
So, we have
Area = 0.5 * 5 * 4
Area = 10
Triangle 3
Base = 5
Height = 5
So, we have
Area = 0.5 * 5 * 5
Area = 12.5
Hence, the triangles that have an area of 10 square units are triangles A and B
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I need help with this rational expression
Answer:
Step-by-step explanation:
[tex]\frac{x}{y} 6x+58\\(x+3)(x+8)\\[/tex]
A plastic page designed to hold trading cards will hold up to 8 cards. How many pages will be needed to store 583 cards? Give an appropriate counting number answer to the question. (Find the least counting number that will work.)
The number of pages that would be needed to store 583 cards is (blank).
Answer:
73 pages
Step-by-step explanation:
You want the number of pages required to hold 583 cards when each page will hold 8.
Least integerThe number of pages required is ...
(583 cards)/(8 cards/page) = 72 7/8 pages
The least integer greater than this number is 73
The number of pages needed to store 583 cards is 73.
Kendra is making a large salad for a party. She buys lettuce for $2.25 per pound and tomatoes for $2.65 per pound. She spends at
least $8.
Let x represent the number of pounds of lettuce that Kendra buys. Let y represent the number of pounds of tomatoes that Kendra
buys.
Which inequality represents this situation?
Answer:
(D)
Step-by-step explanation:
Given that Kendra is making a large salad for a party. She buys lettuce for $2.25 per pound and tomatoes for $2.65 per pound. She spends at least $8.
x represent the number of pounds of lettuce that Kendra buys and y represent the number of pounds of tomatoes that Kendra buys.
We are to select the inequality that represents the situation.
We have
total amount of money that Kendra spends on lettuce is given by
and the total amount of money that she spends on tomatoes is
Therefore, the inequality can be written as
Thus, option (D) is CORRECT.
3. This diagram is a straightedge and compass construction
of the bisector of angle BAC. Only angle BAC is given.
Explain the steps of the construction in order. Include a
step for each new circle, line, and point.
A straight line that divides a given angle between two equal angles is referred to as an angle bisector. The following are the steps to constructing a bisector of angle BAC:
What is a compass construction?Construction with a straightedge and a set of compasses is a method for constructing lengths, angles, and other geometrical figures. It is also known as ruler-and-compass construction or classical construction.
These are the steps:Draw an internal arc using any radius and point A as the center to join lines BA and AC at points E and F, respectively.Draw an arc with point E as the center and a radius that is the same or different from the radius of the circle.Draw a second arc with the same radius and center point F, intersecting the first arc at point G. A thru G,Construct a straight line. This is an angle bisector of BAC.To know more about compass construction visit:
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What is 150 minus 22.37?
Answer:
Step-by-step explanation:
127.63
Express in kg the mass of 0.3 tonne
0.3 tonnne=300 kilograms
In the given question mass is given in tonne and we have to convert it into tonne.
Among the SI base units, the kilogram (kg) is the only one whose name and symbol, for historical reasons, include a prefix. "Kilo" the SI prefix for 1000 or 103. Names and symbols for decimal multiples and submultiples of the unit of mass are formed by attaching prefix names to the unit name "gram," and prefix symbols to the unit symbol "g."
To calculate a tonne value to the corresponding value in kg, just multiply the quantity in tonne by 1000 (the conversion factor). Here is the formula:
Value in kg = value in tonne × 1000
Suppose you want to convert 0.3 tonne into kg. Using the conversion formula above, you will get:
Value in kg = 0.3 × 1000 = 300 kg
final answer is 0.3 tonne=300 kilograms.
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Proportion Word Problems Maze Worksheet
One US dollar equals 0.84 euros. Margo wants to exchange $400 for euro. How many euros will she receive in exchange?
Answer:
1 us dollar =0.84 euros so,400 us dollar =084x400 so, she will receive 336 euros in exchange.
190 g = _____________ kg
Find the solutions to x² = 28.
A. x=+7√2
OB. x=+2√/14
OC. x=+14√2
X
OD. x=+2√7
X
Answer:
x=+2√7
Step-by-step explanation:
Determine if the following relations represent a function
1. {(-1, -2), (0, -2), (1, -2), (2, -2)}
2. {(1, 0), (1,1), (1, 2), (1, -2)}
1) Yes, because each value of x maps onto only one value of y.
2) No, because the x-value of 1 maps onto 4 different y values.
Answer:
yes, a function.no, not a function.Step-by-step explanation:
You want to know if the given sets of ordered pairs represent a function.
FunctionA function is a relation that maps an input value to a single output value. On a graph, this means no two points are vertically aligned. For a table or set of ordered pairs, it means no input (x) value is repeated.
1.The input (x) values are {-1, 0, 1, 2} with no repeats. This relation is a function.
2.The input values are {1, 1, 1, 1} with repeats. This relation is not a function.