Answer:
an = 36 + -4(n - 1)
Step-by-step explanation:
Explicit formula:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
an = nth terma1 = first termd = common differenceHere, we are given the following:
Sequence: 36, 32, 28The first term is 36
To get to the next term, 4 is subtracted from the previous term so the common difference is -4.
So we have:
First term(a1) = 36Common difference = -4By plugging this into [tex]a_n=a_1+(n-1)d[/tex]
We acquire : [tex]a_n=36+(n-1)(-4)[/tex]
Select the correct answer.
What is the simplest form of this expression?
(2x-3)(3x²+2x-1)
O A 6x³-5x²²-8x+3
OB. 6x³-5x² - 6x + 2
OC. 6x³-9x² - 4x +3
OD. 6x³-2²-8x+3
The simplest form of the expression (2x-3)(3x²+2x-1) is 6x³ - 5x² - 8x + 3.
What is the simplest form of this expression?Given the expression in the question:
( 2x - 3 )( 3x² + 2x - 1 )
To simplify the expression (2x-3)(3x²+2x-1), we need to use the distributive property of multiplication,
which states that: a(b+c) = ab + ac
Using this property, we can expand the expression as follows:
(2x-3)(3x²+2x-1)
2x(3x²+2x-1) - 3(3x²+2x-1)
6x³ + 4x² - 2x - 9x² - 6x + 3
Add like terms
= 6x³ - 5x² - 8x + 3
Therefore, the simplest form is 6x³ - 5x² - 8x + 3.
Option A) 6x³ - 5x² - 8x + 3 is the correct answer.
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A triangle with an area of 0.45m squared and a perimeter of about 325cm?
pls help meee
Answer:To solve this problem, we need to use the formulas for the area and perimeter of a triangle.
Let's start by using the formula for the area of a triangle:
Area = (base x height) / 2
where base and height are the length and height of the triangle's base, respectively.
Let's assume that the base of the triangle is x meters, and the height is y meters. Then we have:
Area = (x*y)/2 = 0.45 m²
Solving for y, we get:
y = (2*0.45)/x
y = 0.9/x
Now, let's use the formula for the perimeter of a triangle:
Perimeter = a + b + c
where a, b, and c are the lengths of the three sides of the triangle.
Since we know that the perimeter is about 325 cm, we can assume that the three sides are close to each other in length. Let's assume that each side has a length of 325/3 = 108.33 cm.
Converting to meters, we get:
a = b = c = 108.33/100 = 1.0833 m
Now, we can use the formula for the area of a triangle again to solve for x:
Area = (base x height) / 2
0.45 = (x * 0.9/x) / 2
0.9 = x²
x = √0.9 = 0.9487 m
Therefore, the base of the triangle is approximately 0.9487 meters, and the height is approximately 0.9/0.9487 = 0.9487 meters.
So the triangle has sides of length 1.0833 meters and a base of length 0.9487 meters, which gives us a perimeter of approximately 3.215 meters (rounded to three decimal places).
Step-by-step explanation:
find the volume of the image below.
The volume of the image is given as follows:
10626 ft³.
How to calculate the volume of a prism?The volume of a prism is calculated as the multiplication of the base area of the prism by the height of the prism.
The bottom of the prism in this problem square base of side length 23 ft, along with height of 18 ft, hence:
Bottom volume = 18 x 18 x 23
Bottom volume = 7452 ft³.
The top of the prism also has square base of side length 23 ft, along with triangular height of 12 ft, hence:
Top volume = 0.5 x 12 x 23 x 23 (multiplies by 0.5 as the top is a triangle).
Top volume = 3174 ft³.
Hence the total volume of the prism is given as follows:
7452 + 3174 = 10626 ft³.
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IXL PLEASE HURRY FAST
The triangles are not similar. Triangle EFG and Triangle QRS are not similar. ΔEFG not ~ ΔQRS
Similar triangles: Determining if the triangles are similarFrom the question, we are to determine if the given triangles are similar
From one of Triangle similarity theorems, AA (or AAA) or Angle-Angle Similarity theorem.
The Angle-Angle similarity theorem states that If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other
In the given diagram,
In triangle EFG
m ∠E = 104°
m ∠F = 45°
m ∠G = 180° - (104° + 45°) = 31°
In triangle QRS
m ∠R = 100°
m ∠Q = 45°
m ∠S = 180° - (100° + 45°) = 35°
Since no two angles of one of the triangles are equal to any two angles of other triangle, the triangles are not similar
Hence,
ΔEFG not ~ ΔQRS
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A fireworks mortar is launched straight upward from a pool deck platform 6 m off the ground at an initial velocity of 48 m/sec.
The height of the mortar can be modeled by h(t)=-4.9t^2+48t+6, where h(t) is the height in meters and t is the time in seconds after launch. What is the maximum height? Round to the nearest meter.
Check the picture below.
so the maximum height will occur at its vertex y-coordinate.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+48}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 48}{2(-4.9)}~~~~ ,~~~~ 6-\cfrac{ (48)^2}{4(-4.9)}\right) \implies \left( - \cfrac{ 48 }{ -9.8 }~~,~~6 - \cfrac{ 2304 }{ -19.6 } \right)[/tex]
[tex]\left( \cfrac{ 48 }{ 9.8 } ~~~~ ,~~~~ 6 +\cfrac{ 2304 }{ 19.6 } \right) ~~ \approx ~~ (4.89~~,~~\text{\LARGE 124})[/tex]
Answer both please
Find the domain of the function. (Enter your answer using interval notation.)
f(x) =
4x³-3
x² + 4x - 5
7. [-/3 Points]
f(-8)
=
Evaluate f(-8), f(0), and f(4) for the piecewise defined function.
f(x) =
x+4 if x < 0
2-x if x 20
f(0) =
f(4) =
The solution is, the domain is: x ∈ (-∞, ∞).
Here, we have,
When we have two functions, f(x) and g(x), the composite function:
(f°g)(x)
is just the first function evaluated in the second one, or:
f( g(x))
And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:
f(x) = 1/(x + 1)
where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.
Now, we have:
f(x) = x^2
g(x) = x + 9
then:
(f ∘ g)(x) = (x + 9)^2
And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:
x ∈ (-∞, ∞)
(g ∘ f)(x)
this is g(f(x)) = (x^2) + 9 = x^2 + 9
And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:
x ∈ (-∞, ∞)
(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4
And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:
x ∈ (-∞, ∞)
(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18
And again, there are no values of x that cause a problem here,
so the domain is:
x ∈ (-∞, ∞)
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complete question:
Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat
Solve the following equation exactly on the interval [0,2π).
3cos2θ−2cosθ−2=0
Select all correct answers, assuming they are rounded to two decimal places.
Select all that apply:
θ≈1.24
θ≈2.15
θ≈2.41
θ≈3.55
θ≈4.13
θ≈5.36
Answer:θ≈2.15
θ≈4.13 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
3u^2 - 2u - 2 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3, b = -2, and c = -2. Substituting these values, we get:
u = (2 ± sqrt(4 + 24)) / 6
u = (2 ± 2sqrt(7)) / 6
Simplifying this expression, we get:
u = (1 ± sqrt(7)) / 3
Therefore, either:
Which function is a translation one unit right of the function f(x) = log x?
Answer:
Step-by-step explanation:The function y=log(x) is translated 1 unit right and 2 units down.
rancher wants to enclose a rectangular plot of land, but have a divider in the middle. There is 240 feet of fencing available. What dimension will produce the largest area the rancher can make? What is the max area? Dimensions: __________________ Area:___________ --------------------------------------------------------------------------------------------------------- 2. (10 points) From a thin square piece of cardboard 20 in. per side, square corners (x) are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Dimensions: __________________ Volume:___________ ----------------------------------------------------------------------------------------------------------- 3. (10 points) During a recent oil spill in the gulf, the radius of the spill was increasing at a rate of 10 feet per second. How fast is the circular area of the spill increasing at the moment that the radius is 80 feet? dA = dt __________
The solution is the two dimensions will be 2121.32 by 1414.2.
Here, we have,
let X and Y be the two dimensions.
Area will be X times Y.
XY = 3000000
Y = 3000000 / X
Perimeter = 2x + 3y
substituting the values:
Perimeter = 2x + 3*3000000 / x
= 2x + 9000000 / x
so, we get,
2 = 9000000 / x^2
x^2 = 9000000 / 2 = 4500000
x = sqrt(4,500,000)
= 2121.32
= 1000 sqrt (4.5)
y = 3000000 / 2121.32
= 1414.2
= 1000 sqrt(2)
so the dimensions will be 2121.32 by 1414.2 .
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complete question:
A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
Which of the following expressions are equivalent to the expression below? 8 x + 32 y 4 ( 4 x + 8 y ) − 2 ( 4 x ) 8 ( x + 4 y ) ( 2 x + 12 y ) + ( 6 x + 18 y )
The expressions that are equivalent to the expression 8x + 32y are:
4(4 x + 8y) − 2(4x)
8(x + 4y)
How to write equivalent expressions?Equivalent expressions are expressions that work the same even though they look different.
If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).
Let's simply the options to see if they are equivalent to the expression 8x + 32y:
4(4 x + 8y) − 2(4x) = 16x + 32y - 8x
= 8x + 32y
8(x + 4y) = 8x + 32y
(2x + 12y) + (6x + 18y) = 2x + 6x + 12y + 18y
= 8x + 30y
Therefore, only 4(4 x + 8y) − 2(4x) and 8(x + 4y) are equivalent to the expression below.
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Complete Question
Which of the following expressions are equivalent to the expression below?
8x + 32y
4(4 x + 8y) − 2(4x)
8(x + 4y)
(2x + 12y) + (6x + 18y)
Find the perimeter of the
similar figure.
24cm
Perimeter = 72cm
32cm
Perimeter = [?]cm
The value of the unknown perimeter is derived to be 96 cm using the ratio of the known side of the similar figures.
What is ratioA ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.
By comparison using the variable x to represent the unknown perimeter, and the ratio of the known side lengths;
24/32 = 72cm/x
x = (32 × 72cm)/24 {cross multiplication}
x = 2304cm/24
x = 96 cm
Therefore, the value of the unknown perimeter is derived to be 96 cm using the ratio of the known side of the similar figures.
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Use the equation to answer ALL of the questions below.
f(x) = 2x² + 8x - 4
What is the axis of symmetry? You can use the equation
What is the vertex of the parabola (x, y)?
What is the y-intercept of the parabola?
Answer:
see explanation
Step-by-step explanation:
given a parabola in standard form
f(x) = ax² + bx + c ( a ≠ 0 )
then the equation of the axis of symmetry is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = 2x² + 8x - 4 ← is in standard form
with a = 2, b = 8 , then equation of axis of symmetry is
x = - [tex]\frac{8}{2(2)}[/tex] = - [tex]\frac{8}{4}[/tex] = - 2
that is equation of axis of symmetry is x = - 2
the axis of symmetry passes through the vertex of the parabola
substitute x = - 2 into f(x) for corresponding y- coordinate
f(- 2) = 2(- 2)² + 8(- 2) - 4 = 2(4) - 16 - 4 = 8 - 20 = - 12
vertex = (- 2, - 12 )
the y- intercept is on the y- axis, where the x- coordinate is zero
substitute x = 0 into f(x)
f(0) = 2(0)² + 8(0) - 4 = 0 + 0 - 4 = - 4
y- intercept = - 4
Two cars left Sunnyside City at the same time and traveled for 5 hours. The average speed of the faster car was 10 kilometers per hour greater than the average speed of the slower car. In the 5 hours, the two cars traveled a total of 550 kilometers
The velocity of the two cars are 50km/hr and 60km/h
What is velocity?Velocity is the rate of change of distance with time. it is measured in meter per second and it is a vector quantity.
let the faster car be A and slower car be B
V(A) = V(B) +10
S( A) = v × t
S(B) = v(b) × t
S( A) = 5( v(b) +10)
S(A) +S(B) = 550
5v(b) +50+5vb = 550
10v(b) = 550-50
v(b) = 500/10
v(b) = 50km/h
v(a) = 50 +10
v(a) = 60km/h
Therefore the velocity of the two cars are 50km/h and 60 km/h
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1. Quadrilateral LBMN is the result of a 180 degree rotation of Quadrilateral ABCD around point B, write the corresponding angles and segments in the table below.
In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,
∠A = ∠L, ∠D =∠M , ∠C = ∠N , and
AB = LB , CD = NM , DA = ML.
Quadrilateral ABCD rotates 180 degrees around point B,
New quadrilateral formed named LBMN
The corresponding angle after rotation of 180 degrees around B is equals to,
B remain at same position.
A rotates and point L take the position of A.
D rotates and point M take the position of D.
C rotates and point N take the position of C.
Corresponding angle to A is angle L.
Corresponding angle to D is angle M.
Corresponding angle to C is angle N.
Similarly corresponding segments are of ABCD and LBNM are
Line segment AB corresponds to line segment LB.
Line segment CD corresponds to line segment NM
Line segment DA corresponds to line segment ML.
Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.
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f(x)=5x+4, g(x)= x+7 find f(g(3))
Answer: 54
Step-by-step explanation:
Start from the middle of the equation and work your way out.
First find g(3) :
g(3) = 3+7 = 10
Then plug g(3) into the f equation:
f(g(3)) = 5(10) + 4 = 54
find the surface area of the pyramid. round to the nearest whole number. a=20 b=20 c=7 d=7
Answer:
569 square units
Step-by-step explanation:
You want the surface area of the 8-sided shape that has a square "base" 7 units on a side, and a "height" of 20 units.
Slant heightThe slant height of each triangular face is the hypotenuse of a right triangle with legs 7/2 units and 20 units. That height is ...
h = √(3.5² +20²) = √412.25 ≈ 20.304 units
Surface areaThe area of one triangular face is ...
A = 1/2bh
A = 1/2(7)(20.304) . . . one face
There area 8 congruent triangular faces, so the total area is ...
A = 8(1/2)(7)(20.304) = 8(7)√412.25 ≈ 568.51 ≈ 569
The total surface area is about 569 square units.
<95141404393>
The number 0 is a solution to which of the following inequalities? Select all that apply. x – 5 ≤ -3 x/-2 ≥ 0 x + 11 > 12 4x < 0
Answer: the inequalities for which 0 is a solution are x - 5 ≤ -3 and x/-2 ≥ 0.
Step-by-step explanation: x - 5 ≤ -3 (0 is less than or equal to 2)
x/-2 ≥ 0 (0 is greater than or equal to 0)
In mathematical form, this can be written as:
0 ≤ x - 5 ≤ -3 or x - 5 ≤ 0 and x ≤ -3
This is for math nation unit 1 please help!!
Answer: it’s C, cubic
Step-by-step explanation:
Answer:
[C] Cubic
Step-by-step explanation:
Let find define all the answer choices:
Linear- Straight Line
Quadratic - shape of a U or an upside down U
Cubic - trivalent graphs, are graphs all of whose nodes have degree 3
Exponential- curve that has a horizontal asymptote and it either has an increasing slope or a decreasing
As a result, the graph given is a Cubic graph.
RevyBreeze
For the ordered stem-and-leaf plot given, find:
a. the minimum value
b. the maximum value
c. the number of data with values greater than 25.
d. the number of data with values of at least 40.
e. the percentage of the data with value less than 15.
From a stem-and-leaf plot,
1. The minimum value = 13
2. The maximum value = 62
3. The number of data with values greater than 25 = 16
4. The number of data with values of at least 40 = 4
5. The percentage of the data with value less than 15 = 6.25%
We know that on a stem and leaf plot, the minimum is the first value and the maximum is the last value.
From the stem-and-leaf plot,
a) the minimum value is 13
b) the maximum value is 62
c) the number of data with values greater than 25:
26, 27, 28, 28, 31, 31, 32, 34, 34, 35, 38, 39, 42, 43, 47, 62
So, the number of data with values greater than 25 = 16
d) the number of data with values of at least 40:
42, 43, 47, 62
So, the required number = 4
e) the percentage of the data with value less than 15:
the data with values less than 15 are: 13, 14
So, the number of the data with values less than 15 are: 2
The total number of data values = 32
So, the required percentage would be,
P = (2/32) × 100
P = 6.25%
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Find the remainder when f(x) is divided by x-k, ( SYNTHETIC DIVISION)
[tex]f(x)=2x^3 +5x^2 -12x ; k=-1[/tex]
Explain well, please.
Answer:
15
Step-by-step explanation:
You want the remainder from division of f(x) = 2x³ +5x² -12x by x -(-1).
Synthetic divisionThe table used for synthetic division is built by listing the zero of the divisor at upper left, and the coefficients of the polynomial across the top to the right of that. They are listed in order of decreasing degree, with any necessary zero coefficients put in the appropriate place(s).
The attachment shows the table and the instructions for filling it out. The value at the bottom in the rightmost column is the remainder from the division.
The remainder theorem tells you that is also the value of the function for x = k.
The remainder from f(x) ÷ (x +1) is 15.
<95141404393>
If 2:3 is expressed in the form x: 12, what is the value of x?
Answer:
If 2:3 = x:12, then:
2/3 = x/12
Multiplying both sides by 12, we get:
x = 2/3 x 12 = 8
Therefore, the value of x is 8.
Nine to the second power +4 to the second power
Answer:
Step-by-step explanation:
9 * 9 = 81
4 * 4 = 16
81 + 16 = 97
Question 1 (Multiple Choice Worth 6 points)
(02.08 MC)
The table of values forms a quadratic function f(x)
x f(x)
-5-28
-40
-3 20
-2 32
-1 36
0 32
1 20
What is the equation that represents f(x)?
Of(x)=x²-2x+8
Otx) = 4x² + 8x-32
Of(x)=x²+2x-8
Of(x)=-4x2²-8x+32
Answer:
The answer to this question is --> f(x) = -4x^2-8x+32
Hope this helps
What is 0.3 x 0.5? Show me work
Answer: 0.15
I don't really know how to show you work on here but you can think about it like this. if 5 x 3 is 15, and if there is a decimal like 0.3 x 0.5 it would result in the answer getting smaller as you're multiplying decimals if that makes sense... so it would result in the answer being 0.15. Sorry if it wasn't a good explanation.
The line 3x+5y = 10 is dilated by a scale factor of 3. What is the equation of the dialted line
The equation of the dilated line is 9x + 15y = 10.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge (increase) or reduce (compress) a function representing their size.
Generally speaking, the transformation rule for the dilation of a geometric object or equation based on a specific scale factor of 3 is given by this mathematical expression:
(x, y) → (SFx, SFy)
Where:
x and y represents the data points.SF represents the scale factor.Therefore, the transformation rule for this dilation is given by;
(x, y) → (3x, 3y)
3(3x + 5y) = 10
9x + 15y = 10.
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Michel-Eugène Chevreul found that the greatest intensity came from placing ________colors next to each other.
tertirary
analogous
complementary
arbitrary
Answer:
C. complementary
Michel-Eugène Chevreul discovered that placing complementary colors next to each other can create the greatest contrast and vibrancy in color perception. This is because complementary colors are located opposite each other on the color wheel and, when placed side by side, they enhance each other and create a strong visual impact. For example, placing yellow next to violet or blue next to orange can create a dynamic and eye-catching effect. In contrast, placing tertiary colors (colors made by mixing primary and secondary colors) or arbitrary colors next to each other may not create as much contrast or visual interest. Overall, understanding color theory and the relationships between different colors can be helpful for creating visually appealing designs, artworks, or other color-based projects.
(Time limit) Tell if the graph is a function or not.
Give me the domain and range.
The graph is a function: yes.
The domain of this function is: x ≥ -3.
The range of this function: all real numbers.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.
Range = {-∞, ∞} or all real numbers.
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solve each rational equation. list excluded values
x+4/x+5=6/x^2+10+25
A restaurant serves a 20 ounce steak. How much does the steak weigh in ponds and ounces?
Find the volume of the following Cylinders Diameter 150mm, height 100m
Answer:
I am not sure if you wanted the answer in mm or m. I gave the answer is m
v = 0.58875[tex]m^{3}[/tex]
Step-by-step explanation:
v = 1/3[tex]\pi r^{2} h[/tex]
v = 1/3 (3.14)([tex].075^{2}[/tex])(100) The diameter 150mm is .0150m Take have of that to find the radius
v = 0.58875[tex]m^{3}[/tex]