Shape A is Convex and Hexagon.
Shape B is Concave and Hexagon.
Shape C is Convex and Pentagon.
Shape D is Concave and Hexagon.
Shape E is Concave and Pentagon.
Shape F is Convex and Pentagon.
What is a Polygon?Polygons are closed figures which has at least three set of line segments joined together.The polygon with the least number of sides is a triangle.
As per the given data:
The shape of the figures is given.
The shapes can be classified as:
Concave, Convex, Hexagon, Pentagon.
Concave polygons are the one with alteast one of the vertices pointing inwards toward the shape.
Convex polygons are the one with all the vertices pointing outwards from the shape.
A Hexagon can be defined as a closed two-dimensional polygon with six sides.
A Pentagon can be defined as a closed two-dimensional polygon with five sides.
Consider the shape A:
It has 6 sides and all vertices pointing outwards.
Shape A is Convex and Hexagon.
Consider the shape B:
It has 6 sides and some vertices pointing inwards.
Shape B is Concave and Hexagon.
Consider the shape C:
It has 5 sides and all vertices pointing outwards.
Shape C is Convex and Pentagon.
Consider the shape D:
It has 6 sides and one vertice pointing inwards.
Shape D is Concave and Hexagon.
Consider the shape E:
It has 5 sides and one vertice pointing inwards.
Shape E is Concave and Pentagon.
Consider the shape F:
It has 5 sides and all vertices pointing outwards.
Shape F is Convex and Pentagon.
Hence, Shape A is Convex and Hexagon. Shape B is Concave and Hexagon. Shape C is Convex and Pentagon. Shape D is Concave and Hexagon. Shape E is Concave and Pentagon. Shape F is Convex and Pentagon.
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LM is tangent to the circle at N. Find the value of x.
L
N
M
(5x − 12)
0
283⁰
Answer:
x = 10.1
Step-by-step explanation:
You want the value of x in the given secant-tangent geometry.
Secant-Tangent angleThe angle between the secant ON and the tangent MN is half the measure of arc ON. The measure of arc ON is the remainder of the circle after long arc ON = 283° is subtracted:
arc ON = 360° -283° = 77°
(5x -12)° = 1/2(77°) . . . . . relation of angle to arc
10x -24 = 77 . . . . . . . . divide by °, multiply by 2
10x = 101 . . . . . . . . . . add 24
x = 10.1 . . . . . . . . . . divide by 10
Simplify, leaving as little as possible inside absolute value signs. |(5t^(3))/(-25t)|
Simplified expression of (5t^(3))/(-25t)| is (1/5)( [tex]t^{2}[/tex] ).
To simplify the expression |(5[tex]t^{(3))}[/tex]/(-25t)|, we need to follow these steps:
1. Start by simplifying the fraction inside the absolute value signs.
2. The 5 in the numerator and the 25 in the denominator can be reduced to 1/5.
3. The t in the denominator can be reduced with one of the t's in the numerator, leaving us with [tex]t^{2}[/tex] in the numerator. This gives us |(1/5)( [tex]t^{2}[/tex]))|.
5. The absolute value signs mean that we need to take the positive value of whatever is inside.
6. Since both 1/5 and [tex]t^{2}[/tex] are positive, we can remove the absolute value signs.
This leaves us with (1/5)( [tex]t^{2}[/tex])) as our simplified expression.
So the final answer is (1/5)( [tex]t^{2}[/tex] ).
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An object with negligible air resistance is dropped from a plane. During the first second of fall, the object falls 4.9 meters; during the second second, it falls 14.7 meters; during the third second, it falls 24.5 meters; during the fourth second, it falls 34.3 meters. If this arithmetic pattern continues, how many meters with the object fall in 10 seconds?
i know the answer is 490 meters but i don’t know how to get there. PLEASE HELP!!
Answer:
The object falls 4.9 meters in the first second, 14.7 meters in the second second, 24.5 meters in the third second, and 34.3 meters in the fourth second. We can see that the object is falling 9.8 meters per second per second, which is the acceleration due to gravity.
To find how far the object falls in 10 seconds, we can use the formula for the sum of an arithmetic sequence:
S = n/2(2a + (n-1)d)
where S is the sum of the sequence, n is the number of terms, a is the first term, and d is the common difference between the terms.
In this case, we have:
n = 10 (since we want to find the total distance in 10 seconds)
a = 4.9 (the first term is the distance fallen in the first second)
d = 9.8 (the common difference is the acceleration due to gravity)
Plugging in these values, we get:
S = 10/2(2(4.9) + (10-1)9.8) = 10/2(9.8 + 88.2) = 10/2(98) = 490
Therefore, the object will fall a total of 490 meters in 10 seconds.
The object will fall 495 meters in 10 seconds.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
We can see that the object is falling with a constant acceleration of 9.8 meters per second squared (which is the acceleration due to gravity near the surface of the Earth).
Each second, the distance the object falls increases by an additional 9.8 meters.
So, during the fifth second, the object will fall 44.1 meters (34.3 + 9.8), during the sixth second it will fall 53.9 meters, during the seventh second it will fall 63.7 meters, during the eighth second it will fall 73.5 meters, during the ninth second it will fall 83.3 meters, and during the tenth second it will fall 93.1 meters.
The total distance the object will fall in 10 seconds is:
= 4.9 + 14.7 + 24.5 + 34.3 + 44.1 + 53.9 + 63.7 + 73.5 + 83.3 + 93.1
= 495 meters
Thus,The object will fall 495 meters in 10 seconds.
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Find the area of the shaded segment of the circle.
The area of the shaded segment is:= 16π - 32 cm² (exact value)
= 30.849 cm² (approximate value, rounded to three decimal places)
Define the term area?Area is the measurement of the surface inside a two-dimensional figure. It is expressed in square units, such as square meters or square inches.
To find the area of the shaded segment, we need to subtract the area of the triangle formed by the two radii and the chord from the area of the sector.
formula:
A = (θ/360)πr²
where A is the area of the sector, θ is the central angle in degrees, π is pi (approximately 3.14), and r is the radius of the circle.
Here, the central angle is 90 degrees and the radius is 8 cm.
area of sector is:
sector = (90/360)π(8)²
= 16π cm²
To find the area of the triangle, we need to find its base and height. The base is the chord, which is also the diameter of the circle and has a length of 16 cm (twice the radius). The height is half of the length of the chord (since the central angle is 90 degrees), which is 4 cm.
So the area of the triangle is:
A_triangle = (1/2)bh
= (1/2)(16)(4)
= 32 cm²
the area of shaded segment is:
shaded = sector - triangle
= 16π - 32
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CRB of variance estimation(20 pts.).. Suppose that we have a system that is zero mean and a variance o2 +0 with a known baseline variance o?, X~N(0,02 +0) with 0 > 0. This type of system is important for real world application when a system is known to be noisy with minimum variance o2. For n i.i.d. samples derive the CRB for estimating the parameter 8.
The CRB (Cramér-Rao Bound) of variance estimation is a lower bound on the variance of an unbiased estimator of a parameter. The CRB of variance estimation for this system is (02 +0)^2/(02 +0 + (02 +0)^2). This is the minimum variance that an unbiased estimator of the parameter 8 can achieve.
In this case, the parameter we are trying to estimate is 8. To derive the CRB for estimating the parameter 8, we first need to find the Fisher Information matrix, which is defined as:
I(8) = E[(d log f(X; 8)/d8)^2]
where f(X; 8) is the probability density function of X and E is the expectation operator.
Since X~N(0,02 +0), the probability density function of X is:
f(X; 8) = (1/sqrt(2*pi*(02 +0)))*exp(-X^2/(2*(02 +0)))
Taking the derivative of the log of this function with respect to 8, we get:
d log f(X; 8)/d8 = -(1/(02 +0))*((X^2)/(02 +0) - 1)
Squaring this and taking the expectation, we get:
I(8) = E[(1/(02 +0))^2*((X^2)/(02 +0) - 1)^2]
Simplifying and using the fact that E[X^2] = 02 +0, we get:
I(8) = (1/(02 +0))^2*(02 +0 + (02 +0)^2)
Finally, the CRB for estimating the parameter 8 is given by the inverse of the Fisher Information matrix:
CRB(8) = 1/I(8) = (02 +0)^2/(02 +0 + (02 +0)^2)
Therefore, the CRB of variance estimation for this system is (02 +0)^2/(02 +0 + (02 +0)^2). This is the minimum variance that an unbiased estimator of the parameter 8 can achieve.
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A grocery store baked three different types of
cookies to sell. The number of each type of cookie
is described below.
120 chocolate chip cookies
42 fewer oatmeal than chocolate chip cookies
3 times as many peanut butter than oatmeal cookies
What is the total number cookies that the grocery store
baked?
A 198
B 354
C 396
D 432
Answer:
D. 432
Step-by-step explanation:
To find out this question you need to find out how many cookies you have of each type. we know we have 120 chocolate chip cookies. There are 42 fewer oatmeal cookies than chocolate chip cookies so we take 120 and minus 42.
120 - 42 = 78
There are 78 oatmeal cookies. now we want to find out how many peanut butter cookies we have. There are 3 times as many peanut butter cookies than oatmeal cookies so we times 77 with 3.
78 × 3 = 234
Now we know how many cookies are in all the types, we need to find the total number of all cookies in the grocery store.
120 + 78 + 234 = 432
therefore the answer will be D. 432
Hope this helps :)
What is the volume of the rectangular prism?
Responses
1214
cubic inches
12 and 1 fourth cubic inches
1034
cubic inches
10 and 3 fourths cubic inches
914
cubic inches
9 and 1 fourth cubic inches
734
cubic inches
The volume of a rectangular prism is -
V = Length x width x height
V = L x B x H
What is volume?Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -
V = ∫∫∫ F(x, y, z) dx dy dz
Given is a rectangular prism.
The volume of a rectangular prism is the measurement of the total space inside it. Since the image of the prism is not given, we can write the volume of a rectangular prism as -
V = Length x width x height
V = L x B x H
Therefore, the volume of a rectangular prism is -
V = Length x width x height
V = L x B x H
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A stone is thrown into a pond, creating a circular ripple that spreads over the pond in such a way that the radius is increasing at a rate of 4 flsec. Complete parts a through c. a) Find a function for the radius in terms of t. r(t)= (Use integers or decimals for any numbers in the expression.) b) Find a function A(r) for the area of the ripple in terms of the radius r. A(r)= (Type an exact answer, using π as needed.) c) Find (A∘r)(t). (A∘t)(t)= Complete parts a through c. Choose the correct answer below. A. The function gives the area of the ripple in terms of t. B. The function gives the square of the area of the ripple in terms of L. C. The function has no specific meaning. D. The function gives the perimeter of the ripple in terms of t
terms of time t.
A. The function A(r)=πr2 gives the area of the ripple in terms of the radius r, and (A∘r)(t)=πr(t)2=π(4t)2=16πt2 gives the area of the ripple in terms of time t.
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Make sure to do all the steps because there is a Part A, Part B, & a Part C
Answer: 54 cups of sugar
Step-by-step explanation:
part A add 3 each time
1=3
2=6
3=9
4=12
5=15
6=18
Part B
1x3 per pie
so if there is 70 pies do 70x3
Part C]
if you do 18 and since you need 3 cups of sugar per pie
do 18 times 3 to get a total of 54 cups of sugar
18x3=54
The distance a person falls on a bungee chord in
metres, h may be mod- elled with time, t in seconds according to: h
= 2 * (t - 5) ^ 2 - 50
a) What is the height of a person after 4 seconds?
The height of the person after 4 seconds is -48 meters. Below you will learn how to solve the problem.
The height of a person after 4 seconds can be found by plugging in the value of t into the given equation and solving for h.
Step 1: Plug in the value of t into the equation:
h = 2 * (4 - 5) ^ 2 - 50
Step 2: Simplify the equation:
h = 2 * (-1) ^ 2 - 50
Step 3: Simplify further:
h = 2 * 1 - 50
Step 4: Solve for h:
h = 2 - 50
Step 5: Simplify to get the final answer:
h = -48
Therefore, the height of the person after 4 seconds is -48 meters.
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Colin is making soap for gifts. The table shows the cost of the scented oils needed to make each kind of soap. He needs 1. 5 ounces of Scented oil to make a batch of soap. If he wants to make 2 batches of lavender soap and 2 batches of vanilla soap, how much money will he need for the oils? Almond oil - $1. 23 per ounce
Lavender -$1. 54
Vanilla -$1. 65
Melon -$1. 12
If Colin wants to make 2 batches of Lavender soap and 2 batches of Vanilla soap, then he will need $9.57 for the oils
Here, Colin needs 1.5 ounces of Scented oil to make a batch of soap.
He wants to make 2 batches of Lavender soap and 2 batches of vanilla soap.
So, the amount of scented oil for 2 batches would be:
1.5 × 2 = 3 ounces
The cost of an ounce of Lavender oil is $1.54
So, using unitary method the cost of oil for the 2 batches of Lavender soap would be:
C₁ = 3 × 1.54
C₁ = 4.62 dollars
The cost of an ounce of Vanilla oil is $1.65
So, using unitary method the cost of oil for the 2 batches of Vanilla soap would be:
C₁ = 3 × 1.65
C₁ = 4.95 dollars
Thus, the total cost would be,
C = C + C
C = 4.62 + 4.95
C = 9.57 dollars
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Julie ate lunch at a deli. She ordered a turkey sandwich for $11.73 and a salad for $5.27. The tax was 9.7%. What is the amount of tax for Julie's meal?
Answer:
$1.65
Step-by-step explanation:
9.7%×(11.73+5.27)
0.097×(11.73+5.27)
=1.649
to 2d.p
=1.65
The legs of an isosceles trapezoid are 10. The bases are 9 and 21. Find the area of the trapezoid and the lengths of the diagonals.
The area of the trapezoid is 75 square units, and the lengths of the diagonals are 13 and 17 units.
Describe Isosceles Trapezoid?An isosceles trapezoid is a type of trapezoid with two parallel sides that are equal in length, and two non-parallel sides that are also equal in length. The two legs meet at an angle at the top of the trapezoid, and the bases are parallel to each other.
To find the area of the trapezoid, we use the formula:
Area = (b1 + b2) * h / 2
where b1 and b2 are the lengths of the bases, and h is the height.
In this case, b1 = 9, b2 = 21, and h is the distance between the bases. Since the trapezoid is isosceles, the height is also the length of the two diagonals minus the sum of the two bases, divided by 2:
h = (d1 + d2 - b1 - b2) / 2
we will use the Pythagorean theorem:
d1² = h² + (b2 - b1/2)²
d2² = h² + (b2 + b1/2)²
Plugging in the values we get:
h = (d1 + d2 - 9 - 21) / 2
h = (d1 + d2 - 30) / 2
d1² = h² + (21 - 9/2)²
d2² = h² + (21 + 9/2)²
Simplifying, we get:
h = (d1 + d2 - 30) / 2
d1² = h² + 225/4
d2² = h² + 529/4
Substituting the first equation into the other two, we get a system of two equations in two variables:
d1² = ((d1 + d2 - 30) / 2)² + 225/4
d2² = ((d1 + d2 - 30) / 2)² + 529/4
Simplifying and solving for d1 and d2, we get:
d1 = 13
d2 = 17
To find the area, we plug in the values of the bases and the height:
h = (d1 + d2 - 30) / 2 = (13 + 17 - 30) / 2 = 5
Area = (b1 + b2) * h / 2 = (9 + 21) * 5 / 2 = 75
Therefore, the area of the trapezoid is 75 square units, and the lengths of the diagonals are 13 and 17 units.
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Instructions: Write the polynomial expression in Standirrd 6x-8x^(4)-x-5x^(4) Standard Form: Check
The polynomial expression in standard form is -13x^(4)+5x.
What is polynomial?A polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
The polynomial expression in standard form is -13x^(4)+6x-x. To write a polynomial expression in standard form, we need to rearrange the terms in descending order of their degree (exponent). We also need to combine any like terms.
First, we can rearrange the terms in descending order of their degree:
-8x^(4)-5x^(4)+6x-x
Next, we can combine the like terms:
-13x^(4)+6x-x
Finally, we can simplify the expression:
-13x^(4)+5x
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find the degree, end behavior, x and y-intercept s zeroes of multiplicity, and a few midinterval points of the function (1)/(2)=(x+2)(x-1)^(2)(5x-2)
The degree of the function (1)/(2)=(x+2)(x-1)^(2)(5x-2) is 4, as there are 4 total x terms in the equation.
The end behavior of the function is determined by the leading term, which is (1/2)(5x^4). As the degree is even and the leading coefficient is positive, the end behavior is that the function will rise to the right and rise to the left.
The x-intercepts of the function are the values of x that make the function equal to zero. These can be found by setting each factor equal to zero and solving for x:
x+2=0 -> x=-2
x-1=0 -> x=1
5x-2=0 -> x=2/5
The x-intercepts are -2, 1, and 2/5.
The y-intercept is the value of the function when x=0. Plugging in 0 for x gives:
(1/2)(0+2)(0-1)^2(5(0)-2) = (1/2)(2)(-1)^2(-2) = -2
The y-intercept is -2.
The zeroes of multiplicity are the values of x that make the function equal to zero and the number of times they appear as a factor in the equation. In this case, the zeroes of multiplicity are:
-2 with a multiplicity of 1
1 with a multiplicity of 2
2/5 with a multiplicity of 1
A few midinterval points can be found by plugging in values of x between the x-intercepts and solving for the function value. For example, plugging in x=0.5 gives:
(1/2)(0.5+2)(0.5-1)^2(5(0.5)-2) = (1/2)(2.5)(-0.5)^2(-0.5) = -0.3125
So one midinterval point is (0.5, -0.3125).
Another midinterval point can be found by plugging in x=-1:
(1/2)(-1+2)(-1-1)^2(5(-1)-2) = (1/2)(1)(-2)^2(-7) = -7
So another midinterval point is (-1, -7).
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A labour economist aims to estimate the variance of unemployed workers' mathematic test scores. Assume that a random sample of 18 scores had a sample standard deviation of 10.4.
Using the information above, form a 90% confidence interval for the population variance.
We can be 90% confident that the true population variance of unemployed workers' math test scores falls between 65.61 and 197.57.
The first step in finding a 90% confidence interval for the population variance is to find the degrees of freedom for the sample. In this case, the degrees of freedom is 18 - 1 = 17.
Next, we need to find the critical value for a 90% confidence interval with 17 degrees of freedom. We can do this using a chi-squared distribution table. The critical values for a 90% confidence interval with 17 degrees of freedom are 8.671 and 27.488.
Now we can use the formula for a confidence interval for the population variance:
CI = [(n-1) * s²] / X²
Where n is the sample size, s is the sample standard deviation, and X^2 is the critical value from the chi-squared distribution table.
Plugging in the values we have:
CI = [(17) * (10.4)²] / X²
For the lower bound of the confidence interval, we use the smaller critical value:
CI = [(17) * (10.4)²] / 8.671
CI = 197.57
For the upper bound of the confidence interval, we use the larger critical value:
CI = [(17) * (10.4)²] / 27.488
CI = 65.61
So the 90% confidence interval for the population variance is (65.61, 197.57).
In conclusion, we can be 90% confident that the true population variance of unemployed workers' math test scores falls between 65.61 and 197.57.
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Both circles have the same center. What is the area of the shaded region? Use 3.14 for pi and round to the nearest hundredth.
Step-by-step explanation:
the area of the full larger circle minus the area of the smaller circle.
the area of a circle is
pi×r²
the radius of the smaller circle is 23.1 yd.
the radius or the larger circle is 23.1 + 7.8 = 30.9 yd.
the area of the larger circle is
pi×30.9² = 3.14 × 954.81 = 2,998.1034 yd²
the area of the smaller circle is
pi× 23.1² = 1,675.5354 yd²
the area of only the ring around the smaller circle is then
2,998.1034 - 1,675.5354 = 1,322.568 yd² ≈
≈ 1,322.57 yd²
or
pi×30.9² - pi×23.1² = pi(954.81 - 533.61) =
= 421.2pi = 421.2 × 3.14 =
= 1,322.568 ≈ 1,322.57 yd²
The volume of an eraser is 9.6cm3. If its height is 0.8cm,find the area of its base.
(Quick)
Please help.
Answer:
35° and 55°
Step-by-step explanation:
(x - 20) and x form a right angle (90° ) and are complementary
complementary angles sum to 90° , then
x - 20 + x = 90
2x - 20 = 90 ( add 20 to both sides )
2x = 110 ( divide both sides by 2 )
x = 55
then the 2 angles are
x = 55°
x - 20 = 55 - 20 = 35°
Jannette says
because
's sides form a Pythagorean triple and
's side lengths are multiples of
's side lengths. Is she correct? Explain your reasoning.
The sοlutiοn tο the given prοblem οf the triangle cοmes οut tο be triangle side lengths are multiples οf triangle side lengths is untrue.
What is a triangle exactly?A triangular is a pοlygοn because it has twο οr maybe mοre additiοnal sectiοns. It has a straightfοrward square fοrm. Only the edges A, B, but alsο C distinguishes a triangular frοm a parallelοgram. When the sides are nοt exactly cοllinear, Euclidean geοmetry prοduces a singular plane instead οf a cube. If a shape has three edges and three angles, it is said tο be triangular.
Here,
A cοllectiοn οf the three pοsitive integers a, b, and c knοwn as a Pythagοrean triple fulfill the fοrmula a² + b² = c², where c is the hypοtenuse length οf a right triangle οf legs οf length a and b.
Triangle has sides that are 6, 8, and 10 in length. The Pythagοrean Theοrem is satisfied by these three numbers:
6² + 8² = 36 + 64 = 100 = 10²
Triangle is a right triangle as a result, and its side lengths make a Pythagοrean triple.
Hence, The statement that triangle side lengths are multiples οf triangle side lengths is untrue.
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How many ounces of water must be added to 95 ounces of a 27% solution of potassium chloride to reduce it to a 19% solution?
To reduce 95 ounces of a 27% solution of potassium chloride to a 19% solution, you must add 28.6 ounces of water.
To calculate this, you can use the formula M1V1 = M2V2, where M1 is the initial concentration, V1 is the initial volume, M2 is the desired concentration, and V2 is the desired volume.
So, M1 = 27%, V1 = 95 ounces, M2 = 19%, and V2 = (95 + V2) ounces.
Plugging this into the formula, you get 27(95) = 19(95 + V2). Solving for V2, you get V2 = 28.6 ounces, which is the amount of water you must add.
The equation (M1V1=M2V2) represents the dilution equation in chemistry. “Dilution is the process of decreasing the concentration of a solute in a solution, usually simply by mixing with more solvent like adding more water to the solution.”
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Explain how to convert a number of months to a fractional part of a year.Divide the number of months by 6
Hence, to convert a number of months to a fractional portion of a year, linear function divide the number of months by either 6 or 12 to get the answer in terms of half-years or complete years.
What is linear function ?In mathematics, the term "linear function" is used to describe two separate but related ideas. Calculus and related fields classify polynomial functions of degree 0 or 1 as linear if their graphs are straight lines. A straight line on a coordinate plane represents any function, which is referred to as linear. Since it represents a straight line in the coordinate plane, the linear function y = 3x - 2 is an example. As the function may be connected to y, it can be represented as f(x) = 3x - 2.
You may divide a number of months by 12, which is the number of months in a year, to get a fractional portion of a year.
Consider the case when you have nine months. Nine months are equal to 0.75 years when you divide nine by twelve. But, if you divide 9 by 6, you obtain a result of 1.5, indicating that 9 months are equal to 1.5 half-years or 1 year and 6 months.
Hence, to convert a number of months to a fractional portion of a year, divide the number of months by either 6 or 12 to get the answer in terms of half-years or complete years.
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What happens to the parent graph when the equation is: y = -|x + 2| - 5
Graph opens down, it moves 2 units left and 5 units down.
Graph opens up, it moves 2 units left and 5 units down.
Graph opens down, it moves 2 units right and 5 units down.
Graph opens up, it moves 2 units right and 5 units down.
The transformation is (a) Graph opens down, it moves 2 units left and 5 units down.
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
y = -|x + 2| - 5
Where the parent function is
y = |x|
When we modify the equation to y = -|x + 2| - 5, we are applying several transformations to the parent graph:
The expression inside the absolute value brackets, x + 2, shifts the graph to the left by 2 units. The negative sign outside the absolute value brackets reflects the graph across the x-axis. i.e. the graph now opens downwards The subtraction of 5 outside the absolute value brackets shifts the entire graph down by 5 units.So the resulting graph (a)
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How to find the number of X-intercept
Answer: +-root15/2
To find the x-intercepts, set the function equal to 0 and solve for x.
0.8x^2 - 3 = 0
0.8x^2 = 3
x^2 = 15/4
x = +- root15/2
Jane is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be inches. The area of the pennant must be at most square inches. (Jane doesn't want to buy more materials.) Write an inequality that describes the possible heights (in inches) of the triangle.
Use for the height of the triangular pennant.
Answer:
h ≤ 6
Step-by-step:
Let h be the height of the triangular pennant in inches.
The formula for the area of a triangle is:
A = 1/2 * base * height
We know that the base of the triangle is 10 inches, so we can substitute this value into the formula:
A = 1/2 * 10 * h
Simplifying this equation, we get:
A = 5h
We also know that the area of the pennant must be at most 30 square inches. So we can write:
A ≤ 30
Substituting the formula for the area, we get:
5h ≤ 30
Dividing both sides by 5, we get:
h ≤ 6
Therefore, the possible heights of the triangle must be at most 6 inches in order for the area of the pennant to be at most 30 square inches.
The inequality that describes the possible heights of the triangle is:
h ≤ 6
**NEED SPSS INDEPENDANT T TEST***
I am interested in the effect of sugar on activity. To test this, I randomly form 2 groups. The control group drinks two cups of water and the experimental group drinks 2 cups of juice. I then measure activity. The data are below. Higher scores indicate higher activity. Did sugar effect activity? (α=.05, two-tailed) Control (Water) Experimental (Juice)
5 6
6 12
10 11
3 12
12 10
6 8
The results of the SPSS INDEPENDANT T TEST can help to determine whether the effect of sugar on activity is statistically significant.
Yes, sugar has an effect on activity. In order to determine this, you can use an SPSS INDEPENDANT T TEST. This is a statistical test used to determine whether there is a significant difference between two groups of data, in this case, the control (water) and experimental (juice) groups.
The T Test requires that the two data sets are of equal length and are both normally distributed. The data provided above meet these criteria. The results of the T Test will tell us if the difference between the two sets is statistically significant at the 5% level (α=.05).
Therefore, the results of the SPSS INDEPENDANT T TEST can help to determine whether the effect of sugar on activity is statistically significant.
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Select all the equations that are equovalent to 52= -4 (2n +1)
The equation that is equivalent to 52 = -4 (2n + 1) is C) -52/4 = 2n + 1.
Starting with the given equation:
52 = -4 (2n + 1)
First, we can simplify the right-hand side of the equation by distributing the -4:
52 = -8n - 4
Then, we can isolate the variable (n) by adding 4 to both sides of the equation:
56 = -8n
Finally, we can solve for n by dividing both sides by -8:
-7 = n
Therefore, we have found that the solution to the equation 52 = -4 (2n + 1) is n = -7.
Now, let's check each of the answer choices to see if they are equivalent to this solution:
A) 13 = -2 (2n + 1)
If we simplify the right-hand side of this equation, we get:
13 = -4n - 2
Then, if we add 2 to both sides and divide by -4, we get:
-3.75 = n
This solution is not equivalent to n = -7, so this equation is not equivalent to the original equation.
B) -7 = -2 (2n + 1)
If we simplify the right-hand side of this equation, we get:
-7 = -4n - 2
Then, if we add 2 to both sides and divide by -4, we get:
1.25 = n
This solution is not equivalent to n = -7, so this equation is not equivalent to the original equation.
C) -52/4 = 2n + 1
If we simplify the left-hand side of this equation, we get:
-13 = 2n + 1
Then, if we subtract 1 from both sides and divide by 2, we get:
-7 = n
This solution is equivalent to n = -7, so this equation is equivalent to the original equation.
D) -13 = -4 (2n + 1)
If we simplify the right-hand side of this equation, we get:
-13 = -8n - 4
Then, if we add 4 to both sides and divide by -8, we get:
1.875 = n
This solution is not equivalent to n = -7, so this equation is not equivalent to the original equation.
Therefore, the equation that is equivalent to 52 = -4 (2n + 1) is C) -52/4 = 2n + 1.
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Two trains, Train A and Train B, weigh a total of 437 tons. Train A is heavier than Train B. The difference of their weights is 415 tons. What is the weight of each train?
Step-by-step explanation:
A + B = 437
A - B = 415 (for that sequence it is important to know that A is larger than B).
A = 415 + B
that we use now in the first equation :
415 + B + B = 437
2B = 22
B = 11
A = 415 + B = 415 + 11 = 426 tons
B = 11 tons
Find the value of x then tell whether the side lengths form a Pythagorean triple.
The value of x is approximately 7.21 and the side lengths do not form a pythagorean triple.
What is the numerical value of x?The figure in the image is a right traingle.
Measure of first leg = 12Hypotenuse = 14Measure of second leg = xWe can use the Pythagorean theorem to solve for the missing leg of the right triangle:
a² + b² = c²
Where a and b are the legs of the triangle and c is the hypotenuse.
Plugging in the given values, we get:
12² + b² = 14²
144 + b² = 196
Subtracting 144 from both sides:
b² = 52
Taking the square root of both sides:
b = 7.21
Therefore, the second leg of the right triangle is approximately 7.21 units long.
This is not a Pythagorean triple because the three sides (12, 7.21, and 14) do not form a set of integers that satisfy the Pythagorean theorem.
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Proving triangles congruent by ASA and AAS
The complete proof that ΔUWX ≅ ΔWUV is explained below.
What are congruent triangles?Congruent triangles are set of given triangles which have equal values of corresponding properties. Thus the triangles have equal dimensions and measure of internal angles.
The two column complete proof required are given below:
STATEMENT REASONS
1. WX ║ UV Given
2. < V ≅ <X Given
3. <VUW ≅ <UWX Definition of alternate angles.
4. UW ≅ UW Reflexive property of congruence
5. ΔUWX ≅ ΔWUV Angle-Side-Angle (AAS) property
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