The explicit rule for the sequence -2, 5, 12, 19 is
-2 + (n - 1) 7.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
We have,
-2, 5, 12, 19
This is an arithmetic sequence.
The first term.
a = -2.
The common difference.
d = 5 - (-2) = 7
= 12 - 5 = 7
= 19 - 12 = 7
Now,
The nth term of an arithmetic sequence.
= a + (n -1)d
= -2 + (n - 1)7
Thus,
The explicit rule is -2 + (n -1) 7.
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Simplify algebraic expression
Answer:
1
Step-by-step explanation:
To start, we will substitute 8 in for w. So, we get:
[tex]5 - \frac{32}{8}[/tex]
Then, we simplify our fraction, giving us:
5 - 4
Then, 5 - 4 = 1. So our answer is 1.
Hope this helped!
Answer:
5 - (32/w) = 1
Step-by-step explanation:
Given expression,
→ 5 - (32/w)
Now we have to use,
→ w = 8
Let's solve the expression,
→ 5 - (32/w)
→ 5 - (32/8)
→ 5 - (4)
→ 5 - 4
→ 1 => final value
Therefore, the answer is 1.
How do you calculate undefined FG?
To calculate undefined FG, subtract the original gravity (OG) from the final gravity (FG) of the beer. This will give you the amount of sugar that has been fermented and, therefore, the amount of alcohol produced. The formula is:
Undefined FG = OG – FG
In order to calculate the undefined FG of a beer, the original gravity (OG) and the final gravity (FG) of the beer must first be determined. The OG is a measure of the sugar content of the wort before fermentation, while the FG is a measure of the sugar content of the beer after fermentation. To calculate the undefined FG, the OG is then subtracted from the FG. This calculation provides the amount of sugar that has been fermented by the yeast, and therefore the amount of alcohol produced. This calculation is important for brewers, as it provides a quick and easy way to determine the ABV of a beer. In addition, the undefined FG can be used as a measure of the fermentation efficiency of the yeast, as a higher undefined FG indicates that more sugar has been fermented than a lower undefined FG. Understanding the undefined FG of a beer can help brewers make informed decisions about their brewing process and the quality of their beers.
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What does FG mean mass?
FG is an abbreviation for "Femtogram," which is a unit of mass equal to one quadrillionth of a gram (10^-15 g).
An exclamation is an emphatic expression of emotion or emphasis. It is often used to express strong feelings such as surprise, joy, excitement, anger, or disbelief. Exclamations are also used to emphasize a point or give an opinion. Exclamations are most commonly used in spoken language, particularly in informal conversations. They can also be used in written language, but they should be used sparingly. Exclamations are often followed by an exclamation point, although they can also be followed by a question mark or an ellipsis. Exclamations can be used to add emphasis or emotion to a statement, making it more powerful and memorable.
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what is the vertex and solutions for y=x^2+5x-7 and y=-x^2+3x+8
The vertex for the given equation [tex]y=x^2+5x-7 is (-2.5,-4.25)[/tex] and the solution to the equation is x = -5,7/1. Similarly , the vertex for the given equation [tex]y=-x^2+3x+8\ is\ (-3/2,1/4)[/tex] and the solution to the equation is [tex]x = -2,4[/tex].
What is parabola?The graph of a quadratic function is a symmetrical, U-shaped geometric form known as a parabola. It is the collection of all points that are equally spaced apart from a fixed point (referred to as the focus) and a fixed straight line (called the directrix).
What is vertex of a parabola?A parabola's vertex is the location where its symmetry line and parabola intersect.
The vertex of a parabola is the highest or lowest point on the graph of the parabola. In the case of a parabola in the form of [tex]y = ax^2 + bx + c[/tex], the vertex is the point (h, k), where:
[tex]h = -b / 2a\\k = f(h) = a(h^2) + bh + c[/tex]
For the first equation: [tex]y = x^2 + 5x - 7[/tex]
The vertex would be:
[tex]h = -b/2a = -5/2 = -2.5\\k = f(h) = a(h^2) + bh + c = (1)((-2.5)^2) + (5)(-2.5) - 7 = 6.25 - 12.5 - 7 = -4.25[/tex]
So the vertex is [tex](-2.5,-4.25)[/tex]
For the second equation:[tex]y = -x^2 + 3x + 8[/tex]
The vertex would be:
[tex]h = -b/2a = -3/2(1) = -3/2\\k = f(h) = a(h^2) + bh + c = (-1)((-3/2)^2) + (3)(-3/2) + 8 = -9/4 + -9/2 + 8 = 1/4[/tex]
So the vertex is [tex](-3/2,1/4)[/tex]
To find the solutions or roots of the equation, you can set the equation equal to zero and solve for x.
[tex]y = x^2 + 5x - 7 = 0\\x^2 + 5x - 7 = 0\\x^2 + 5x - 7 + 7 = 0 + 7\\x^2 + 5x = 7\\x(x+5) = 7\\x = -5,7/1\\y = -x^2 + 3x + 8 = 0\\x^2 - 3x - 8 = 0\\(x-4)(x+2) = 0\\x = -2,4[/tex]
Solutions for first equation are x = -5 and x = 7/1 and for the second equation are x = -2 and x = 4
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DIG DEEPER! A cube is removed from a rectangular prism. Find the surface area of the figure after removing the cube.
A rectangular prism with length 9 feet, width 8 feet, and height 5 feet. A cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet.
The surface area is ______ square feet
The surface area of the figure after a cubic hollow runs to the height of the rectangular prism is 364 square feet.
The surface area is 364 square feet.
Find the surface area of the rectangular prism.
To do this, use the formula for the surface area of a rectangular prism:
(2 x length x width) + (2 x width x height) + (2 x length x height)
In this case, the length is 9 feet, the width is 8 feet, and the height is 5 feet. Plugging these values into the formula gives:
= (2 × 9 × 5) + (2 × 8 × 5) + (2 × 9 × 8)
= 314 square feet
When a cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet, 2 cubic faces is removed and 4 cubic faces added to the surface area of the resultant solid. So
surface area = 314 - 2×5² + 4×5²
= 314 + 2×5²
= 314 + 50
= 364 square feet
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Matthew's total points scored in basketball this season were 168 points. He scored 147 of those points in the regular season and the rest were scored in his only playoff game. What percent of his total points did he score in the playoff game?
Answer:
12.5%
Step-by-step explanation:
He scored [tex]168-147=21[/tex] points in the playoff game.
This is equal to [tex]\frac{21}{168}(100)=12.5\%[/tex].
Maria is using a coordinate plane with the axes labeled only with integers. She says that the point (-0. 5, 2) cannot be plotted because halves are not numbered on the x-axis. Write a note to explain how to plot the point.
Someone pls help?
Therefore , As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).
Definition of a scatter plot.Several dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).
Here,
Maria You've erred, you know that. You don't understand the points at all. The attachment can be used to your advantage.
The property of rational numbers, according to which there are an endless number of terminating decimals between any two terminating decimals, must be used in order to plot any terminating decimal on the coordinate plane.
On the X axis, indicate -0.5 between 0 and -1.
Mark integer 2 on the Y axis in a similar manner.
Draw a line perpendicular to the Y axis, passing through (-0.5,0), and a line perpendicular to the X axis, passing through (0,2).
These two lines must cross at the specified position (-0.5,2).
As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).
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If the scale of a map is 1:32000 then what will be the actual distance of 20 cm on the map?
Therefore, By using the formula actual distance = (Map distance) x (Scale ratio) the actual distance of 20 cm on the map of 1:32000 is 0.000625 km or 625 meters.
Define Scale ratio.A ratio scale is a numerical scale with a genuine zero and uniform distances between adjacent points. The Kelvin scale is an illustration of a ratio scale. The actual zero point exists on a Kelvin scale.
What are adjacent points?Two locations that are close to one another are said to be adjacent points.
A scale of 1:32000 means that one unit of measurement on the map represents 32000 units of the same measurement in the real world.
To calculate the actual distance of 20 cm on the map,
We know,
Actual distance = (Map distance) x (Scale ratio)
Actual distance = (20 cm) x (1/32000)
Actual distance= 20/32000
Actual distance = 0.000625 km or 625 meters.
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Put one pair of bracket into this calculation to make it correct.
7 x 5 - 2 + 3 = 42
The equation becomes true if we put brackets in the following way:
7x(5 - 2 + 3) = 42
Where do we need to put the bracket?Here we have the expression:
7x5 - 2 + 3 = 42
And we want to find where we need to put brackets in such a way that the equation becomes true.
If we solve the equation as it is, we will get:
7x5 - 2 + 3 = 42
35 - 2 + 3 = 42
36 = 42
Now, let's return to the equation:
7x5 - 2 + 3 = 42
If we put one pair of brackets that includes from the 5 to the 3, we will get:
7x(5 - 2 + 3) = 42
7x(4) = 42
42 = 42
So the equation becomes true.
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Which shows that the set of irrational numbers under addition is not closed?
3+3
π + π
π +3
3π + (−3π)
The option that shows that the set of irrational numbers under addition is not closed is B. π + π.
What is an irrational number?All real numbers that are not rational numbers are referred to as irrational numbers in mathematics. In other words, it is impossible to express an irrational number as the ratio of two integers. The collection of real numbers known as irrational numbers, where p and q are integers, are those that cannot be expressed as fractions, such as p/q.
The example of "π + π" shows that the set of irrational numbers under addition is not closed, because the result of adding two irrational numbers (π + π) is an irrational number (2π) which is not included in the set of irrational numbers.
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360 multiplied by 420
the answer is 151200
Answer the following as the website for my hwk says I am incorrect:
a) 6/24 as its simplest form (I put 1/4)
b) 52.491 to 2 decimal places (I put 52.49)
c)how many 0.125m drinking straws are needed for a bridge which is 0.85m long (I put both 6.8 and 7)
d) 756.985 × 45 - 14.325 ( I put 34,050)
Please help!
ponential functions are in the form y = a(b)'.
What values of b make it an exponential growth function?
What values of make b it an exponential decay function?
solve x^2-4x=0 by factoring
[tex]\huge\text{Hey there!}}[/tex]
[tex]\mathsf{x^2 - 4x = 0}[/tex]
[tex]\text{Factor the LEFT side of your given equation to make it easier to solve}[/tex]
[tex]\mathsf{x(x - 4) = 0}[/tex]
[tex]\text{Set the factors to equal to the number 0}[/tex]
[tex]\mathsf{x - 4 = 0\ \& \ x = 0}[/tex]
[tex]\text{Simplify find and you should be able to have your answer to the given equation}[/tex]
[tex]\mathsf{x = 4 \ \& \ x = 0}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 4\ or \ x = 0}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Samera placed the congruent sides of these two triangles together to form a quadrilateral.
2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.
Which statements are true of the quadrilateral she constructed? Select three options.
It is a rectangle.
It is a trapezoid.
It has only one right angle.
It has two right angles.
It has two sides that are parallel.
The correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.
What is a trapezoid?A quadrilateral with at least one pair of parallel sides is called a trapezoid.
Given that, Samara placed the congruent sides of these two triangles together to form a quadrilateral.
2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.
If we construct such quadrilateral, we will get a trapezoid with one angle a right angle.
Hence, the correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.
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Answers:
1. B its a trapezoid
2. D it has two right angles
3. E it has 2 sides that are parallel
Step-by-step explanation:
Graph the line that passes through the points (9, 4) and (9, 1) and
determine the equation of the line.
Answer:
x = 9
Step-by-step explanation:
The equation is y = mx + b
m = The slope
b = y-intercept
The slope here is undefined, and there is no y-intercept, so the equation is
x = 9
PLS HELP ASAP 50 POINTS!!!!
Triangle ABC is congruent to triangle PDF. Dude AC corresponds to what side in triangle PDF
Answer:
PF
Step-by-step explanation:
Since the triangles are congruent, meaning they are the same shape, we can just match the lines between the two triangles. In triangle ABC, the line AC is the hypotenuse of the triangle. So, we need to find the hypotenuse of the triangle PDF. Looking, we can see the hypotenuse of the triangle PDF is the line, or side, PF.
Hope this helped!
Hello- some help please!! I will give you brainlist :]
Answer:
standard form
= x⁶ + 53x⁵ + 2x⁴ -2
Step-by-step explanation:
the degree is 6.
leading coefficient is 1
this is called a polynomial.
it has 4 terms
How do you solve a 2 step equation 7th grade?
The Two steps equation in mathematics can be solved within exactly two steps by performing operation on both sides of the equation .
What is a Two Step Equation ?
The Two Step Equation can be defined as the equations that can be solved exactly within two steps.
When solving the two step equation, we have to perform the operation on both sides of equals to sign.
To solve the equation we need to perform same operation on both sides of equation.
For Example ⇒ Solve [tex]3x+3=12[/tex] ;
Step1 : we Subtract 3 from both sides to isolate the variable x.
⇒ [tex]3x + 3 - 3 = 12 - 3[/tex]
⇒ [tex]3x = 9[/tex]
Step2 : We Divide both the sides of equation by 3 and solve for x.
⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]
⇒ [tex]x = 3[/tex] ;
Therefore , the given equation is solved in two steps .
The given question is incomplete , the complete question is
How do you solve a 2 step equation ?
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Lori's bookcase has 5 mystery novels and 8 romance novels. She randomly picks out 2 mysteries and 3 romances. How many different sets of 5 novels could Lori pick out?
Answer:
I would say 6 sets
Step-by-step explanation:
Mystery = 5 | Romance = 8
0 5
1 4
2 3
3 2
4 1
5 0
each time she picks out 5 novels. There is only 5 mystery novels so you cant go past that
....but that's just me personally
Answer:
Step-by-step explanation:
560
Find the value of y
Answer:
y = 4
Step-by-step explanation:
The triangles are congruent.
8y = 6y + 8
2y = 8
y = 4
please help quickly
If UY=13p-1 and VX=20p-95 than what is UY
Viewing the given triangle, the information given helped to determine side UY to be 90
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
WX and WY, XV and YU
The solution is worked out using sides WX and XV, WY and YU
WX / WY = XV / YU
WX / WY = 1/2 since it is a mid segment
1 / 2 = (20p - 95) / (13p - 1)
13p - 1 = 2 * (20p - 95)
13p - 1 = 40p - 190
190 - 1 = 40p - 13p
189 = 27p
p = 7
solving for UY
= 13p - 1
= 13 * 7 - 1
= 90
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What is the difference between the high and low temp in the thermometer?
*
Captionless Image
The difference between the two given temperature values is 24 °F
How are Kelvin, Celsius, and Fahrenheit related?We have got an equation that can relate these three units of measurement of temperature, as given below:
c/5 = (F - 32)/9= (K - 273)/5
where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.
The given parameter the lowest temperature = -3 °F
the highest temperature = 21 °F
To determine the difference between the two given temperature values.
The range or difference between the two given temperature values is calculated as follows;
Range = highest - lowest
Range = 21 °F -(-3 °F)
Range = 24 °F
Thus, the difference between the two given temperature values will be 24 °F
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HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
x-5 that is the answer na
The total number of laps anitia swims, d, is proportional to the total timethat she swims, t, at constant pace, r. Which of the following equations best represents this situation.?
A bag contains:
1 red beads
2 yellow beads
2 green beads
1 blue bead
A bead is chosen at random.
What is the probability that it is green?
What is the probability that it is green or yellow?
Pls pls help!
I'll give you brainliest answer!
Thx!
The probability to draw a green bead is 1/3 and the probability to draw a green or yellow bead is 2/3
It is given that the bag contains 1 red bead, 2 yellow beads, 2 green beads, and 1 blue bead.
Hence the total no. of beads in the bag = no. of red + yellow + green + blue beads
= 1 + 2 + 2 + 1 beads
= 6 beads.
Let the event to draw a green bead be A
Let the event to draw a yellow bead be B
Probability of any event = no. of outcomes favorable to that event/ total number of outcomes
Hence P(A) = no. of green beads/ total no. of beads
= 2/6
= 1/3
Hence the probability that a green bead is drawn is 1/3
P(B) = no. of yellow beads/ total no. of beads
2/6 = 1/3
We need to find P(A or B)
= P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A ∩ B) = P(A and B)
Since no bead is of 2 colors, P(A ∩ B) = 0
Hence we get
P(A U B) = 1/3 + 1/3
= 2/3
Hence the probability to draw a green or yellow bead is 2/3
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Help me. The question is giving me problems help.
D/3
The real world situation that can be modelled with the given expression can be modelled as shown below.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
D/3
A real world situation that can be modelled with this expression can be written as follows -
Amanda has a total of {D} bananas. She divides the bananas into 3 of her childrens equally. Write an expression that would represent the amount of bananas recieved by each of her child.
Therefore, the real world situation that can be modelled with the given expression can be modelled as shown above.
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The ratio of the number of model cars that jim owns to the number of model cars Terrence owns is 8:6. Terrence owns 36 model cars
Part A
How many model cars does Jim own?
___
Part B
How will the ratio change if Jim and Terrence each sell ten of their model cars?
O The new ratio would stay the same
O The new ratio would be 4:3
O The new ratio would be 23:29
O The new ratio would be 19:13
When Jim's model car ownership is compared to Terrence's model car ownership, the ratio is 8:6, Jim possesses 48 model vehicles.
what is equation ?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, according to the definition given by the term in its most basic form. When two terms are placed on each side of an equal sign, a simple equation is used to show their relationship. The four mathematical operations of addition, subtraction, multiplication, and division may be used singly or in combination in simple equations.
given
You are aware that Jim and Terrence both own four model automobiles in comparison to three owned by Jim.
Let's assume that Jim owns Jim has the following number of model cars, then you can answer the task as follows:
4/3 = x/36
x = (4* 36)/ 3
x = 48
Therefore, Jims owns 48 model cars.
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simplify 2√12+3√48-√75
Answer:
11√12
Step-by-step explanation:
√12 = 2√3
2√12
= 2 * 2√3
= 4√3
√48 = 4√3
3√48
= 3 * 4√12
= 12√12
√75 = 5√3
2√12 + 3√48 - √75
= 4√3 + 12√12 - 5√12
= 16√12 - 5√12
= 11√12
Answer: My answer is 11√3
Step-by-step explanation:
Pull terms out from under the radical, assuming positive real numbers.
Exact Form:
11√3
Decimal Form:
19.05255888…
The diameters of the top and bottom of a frustum of a cone are 6cm and
15cm respectively. If the height of the frustum is 30cm, calculate (i) the
curved surface area (ii) the volume of the frustum.
Curved surface area of frustum is 1000.82 cm² and
Volume of frustum is 2756.754 cm³.
What is a conical frustum?Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum.
Frustum is a Latin word which means ‘piece cut off’. When a solid (generally a cone or a pyramid) is cut in such a manner that base of the solid and the plane cutting the solid are parallel to each other, part of solid which remains between the parallel cutting plane and the base is known as frustum of that solid.
Height of frustum = h = 30 cm
Diameter of top of frustum = 6 cm
Radius of top = R = 6/2 = 3cm
Diameter of bottom of frustum = 15 cm
Radius of bottom = r = 15/2 = 7.5 cm
Slant Height = l = √h²+ (r - R)²
⇒ l = √30² + (7.5 - 3)²
⇒ l = √900 + 20.25 = √920.25 = 30.34 cm
A) Curved surface area of frustum = π(r + R)l
= 3.1416 × (7.5+3) × 30.34
= 3.1416 × (10.5) × 30.34
Curved surface area of frustum = 1000.82 cm²
B) Volume of frustum = (πh/3)(r²+R²+r.R)
= (3.1416 × 30/3)(7.5² + 3² + 7.5×3)
= (31.416) × (56.25 + 9 + 22.5)
= 31.416 × 87.75
Volume of frustum = 2756.754 cm³
Hence, the curved surface area and volume of given conical frustum are 1000.82 cm² and 2756.754 cm³ respectively.
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