Help me with this please!

Answer:

[tex]f(x)=(x-4)^2+28[/tex]

Step-by-step explanation:

Here are the steps to convert the quadratic function [tex]f(x)=x^2-8x+44[/tex] into vertex form:

Step 1: Group the [tex]x[/tex] terms together:
[tex]f(x)=(x^2-8x)+44[/tex]

Step 2: Complete the square within the parentheses by adding and subtracting the square of half the coefficient of the [tex]x[/tex] term:
[tex]f(x)=(x^2-8x+16)-16+44[/tex]

Step 3: Rearrange the expression:
[tex]f(x)=(x^2-8x+16)-16+44[/tex]

Step 4: Factor the perfect square trinomial [tex](x^2-8x+16)[/tex]:
[tex]f(x)=(x-4)^2-16+44[/tex]

Step 5: Simplify and combine constants:
[tex]f(x)=(x-4)^2+28[/tex]

Therefore, the quadratic function [tex]f(x)=x^2-8x+44[/tex] in vertex form is [tex]f(x)=(x-4)^2+28.[/tex] The vertex of the parabola is located at the point [tex](4,28)[/tex].

Answer:

The curve could be [tex]y=-\frac{4}{x^2}+5[/tex] and [tex]y=\frac{4}{x^{2}}-3[/tex]

Step-by-step explanation:

The explanation is attached below.

To find a curve that passes through a point and has a specific arc length, we can use integration and the arc length formula.

To find a curve that passes through the point (1,1) and has an arc length on the interval [2,6] given by the integral ∫[2,6]√(1+64x^(-6)) dx, we can start by finding the equation of the curve based on the integral expression.

Let's first find the antiderivative of the integrand: ∫√(1+64x^(-6)) dx. By using the power rule of integration and substitution, we can find that the antiderivative is (√(1+64x^(-6)) + 8x^(-4)) / 2 + C.

We know that the arc length formula is given by the integral of the square root of the sum of the squares of the derivatives of x and y. By using the given integral expression, we can equate it to the arc length formula and solve for y.

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The solution to the Compound inequality 4x > -16 or 6x ≤ -48 is x > -4 or x ≤ -8, expressed either graphically or in interval notation.

The compound inequality 4x > -16 or 6x ≤ -48, we will solve each inequality separately and then combine the solutions.

1. Solving the inequality 4x > -16:

Dividing both sides of the inequality by 4 (since it is a positive number), we have:

x > -16/4

x > -4

2. Solving the inequality 6x ≤ -48:

Dividing both sides of the inequality by 6 (since it is a positive number), we have:

x ≤ -48/6

x ≤ -8

Now, let's combine the solutions:

The solution to the compound inequality 4x > -16 or 6x ≤ -48 is the combination of the individual solutions.

Since it is an "or" compound inequality, we consider the values that satisfy either of the two inequalities.

The solution is x > -4 or x ≤ -8.

Graphically, this represents two separate intervals on the number line. The interval for x > -4 is shaded to the right of -4, and the interval for x ≤ -8 is shaded to the left of -8.

In interval notation, the solution is (-∞, -8] ∪ (-4, +∞), where (-∞, -8] represents all values less than or equal to -8, and (-4, +∞) represents all values greater than -4.

the solution to the compound inequality 4x > -16 or 6x ≤ -48 is x > -4 or x ≤ -8, expressed either graphically or in interval notation.

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Given that 'd' = (n-1)/2.

This means there is a vertex 'u' at most (n-1)/2 distance away from 'v'.

A tree with 'n' vertices has the longest path of 'n-1' edges (path graph property).

Let 'd' be the maximum distance from 'v' to any other vertex.

The longest path must pass through 'v', else we could extend it by adding 'v' and a neighbor, contradicting maximality.

Thus, 'd' is at least half the length of the longest path, i.e., d >= (n-1)/2. If 'd' > (n-1)/2, then the longest path exceeds 'n-1', a contradiction.

So, 'd' = (n-1)/2.

This means there is a vertex 'u' at most (n-1)/2 distance away from 'v'.

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(a) The coordinates of K are (-4, 1) and S are (2, 4).

(b) The lengths of KL and LQ are x + 4 and 2 - x respectively.

(c) The value of x = -1.

(d) The lengths of SR and RQ are y - 4 and 1 - y respectively.

(e) The value of y = 2.5

(f) The coordinates of M are (-1, 2.5).

(a) The x coordinate of K will be equal to that of P and the y coordinate will be equal to that of Q.

So coordinates of K are (-4, 1).

Similarly, the x coordinate of S is equal to that of Q and the y coordinate will be equal to that of P.

So coordinates of S are (2, 4).

(b) The coordinates of K, L and Q are K(-4, 1), L(x, 1) and Q(2, 1).

Using distance formula,

Length of KL = √[(x + 4)² + (1 - 1)²] = x + 4

Length of LQ = √[(2 - x)² + (1 - 1)²] = 2 - x

(c) KL = LQ

x + 4 = 2 - x

2x = -2

x = -1

(d) The coordinates of S, R and Q are S(2, 4), R(2, y) and Q(2, 1).

Using distance formula,

SR = √[(2 - 2)² + (y - 4)²] = y - 4

RQ = √[(2 - 2)² + (1 - y)²] = 1 - y

(e) SR = RQ

y - 4 = 1 - y

2y = 5

y = 2.5

(f) The coordinates of M are,

M(x, y) = (-1, 2.5)

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Answer: 1250 cubes

Step-by-step explanation:

V = a x a x a

V1 = 20cm x 20cm x 20cm = 800cm³

V2 = 100cm x 100cm x 100cm = 1000000cm³

1000000cm³/800cm³=1250

The student takes 160 minutes to mow 4 lawns, which means he takes 40 minutes to mow one lawn. Therefore, the correct prediction is that it will take him 8 hours to mow 12 lawns. So, the correct answer is B).

Based on the given information, we know that the student takes 160 minutes to mow 4 lawns. Therefore, the time it takes him to mow one lawn is 40 minutes (160 divided by 4).

If the student has 12 lawns to mow, he will need to spend 12 times the time it takes him to mow one lawn.

So, the prediction is that it will take him 12 times 40 minutes, which equals 480 minutes, or 8 hours, to mow 12 lawns.

Therefore, the correct prediction is: It will take him 8 hours to mow 12 lawns. So, the correct answer is B).

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Answer:

A. The probability that both beads are red is 5/92.

B. The probability that one bead is black and the other is yellow is 6/23.

Step-by-step explanation: To find the probabilities, we need to calculate the total number of possible outcomes and the number of favorable outcomes for each scenario.

A. Both beads are red:

Total number of beads = 6 + 8 + 10 = 24

The first bead can be any of the 24 beads. After picking the first bead, there will be 5 red beads left out of the remaining 23 beads. Thus, the probability of picking a red bead is:

P(Red on first pick) = 6/24 = 1/4

For the second pick, there will be one less bead, and one less red bead. Therefore, the probability of picking another red bead is:

P(Red on second pick) = 5/23

To find the probability of both events occurring, we multiply the probabilities together:

P(Both red) = P(Red on first pick) * P(Red on second pick)

= (1/4) * (5/23)

= 5/92

Therefore, the probability that both beads are red is 5/92.

B. One bead is black and the other is yellow:

Total number of beads = 24 (same as before)

The first bead can be any of the 24 beads. After picking the first bead, there will be 8 black beads and 10 yellow beads remaining. Thus, the probability of picking a black bead is:

P(Black on first pick) = 8/24 = 1/3

For the second pick, there will be one less bead, and if the first bead was black, there will be 10 yellow beads left. If the first bead was yellow, there will be 8 black beads left. Therefore, the probability of picking a yellow bead after a black bead is:

P(Yellow on second pick after black) = 10/23

However, we also need to consider the case when the first bead is yellow and the second bead is black. In that case, the probability is:

P(Black on second pick after yellow) = 8/23

To find the probability of either event occurring (black then yellow or yellow then black), we add the probabilities together:

P(One black and one yellow) = P(Black on first pick) * P(Yellow on second pick after black) + P(Yellow on first pick) * P(Black on second pick after yellow)

= (1/3) * (10/23) + (1/3) * (8/23)

= 10/69 + 8/69

= 18/69

= 6/23

Therefore, the probability that one bead is black and the other is yellow is 6/23.

To summarize:

A. The probability that both beads are red is 5/92.

B. The probability that one bead is black and the other is yellow is 6/23.

hello

the answer to the question is:

[tex] \sin(s) = \frac{tu}{x} \\ \sin(24) = \frac{22.5}{x} \\ x = 25[/tex]

The range of the function y = ∛(x + 8) is: 0 ≤ y < ∞

The correct option is C

We have the function,

y = ∛(x + 8)

From the function , we can say that  the values of y are greater than or equal to zero but less than infinity.

In other words, the function takes on all non-negative values but does not include infinity.

Thus, the range of the function y = ∛(x + 8) is: 0 ≤ y < ∞

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The expression in ascending order is  [tex]e^{log4} < log_326 < log_233 < log_22^6[/tex].

We have,

Using a log and exponent calculator we get,

log 4 = 0.60

So,

[tex]e^{log 4}[/tex] = [tex]e^{0.60}[/tex] = 1.82

[tex]log_233[/tex] = 5.044

[tex]log_22^6[/tex] = 6

[tex]log_326[/tex] = 2.97

Now,

Arranging from least to greatest:

[tex]e^{log4} < log_326 < log_233 < log_22^6[/tex]

Thus,

The expression in ascending order is  [tex]e^{log4} < log_326 < log_233 < log_22^6[/tex].

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The correct answer is option (d). Cross-price elasticity of demand for good B is -2.

Given that A 10 percent increase in the price of good A leads to a 20 percent decrease in the quantity of good B demanded.

It appears that the cross-price elasticity of demand for good B is -2.

Elasticity of demand measures the responsiveness of the quantity demanded or supplied of a good to a change in its price.

It reflects the extent of the buyer's reaction to a change in the commodity's price.

The following can be inferred from the question:

An increase in the price of Good A leads to a decrease in the quantity of good B demanded.

Therefore, Goods A and B are complementary products.A good is considered complementary when a price increase in one product causes a decrease in the quantity demanded of the other product.

It is evident that the cross-price elasticity of demand for good B is -2.Elasticity of demand is a significant concept in economics that measures the sensitivity of a product's demand to changes in its price.

It is commonly calculated as the percentage change in the quantity demanded of a commodity when there is a one percent change in its price.

The cross-price elasticity of demand is a metric that examines the impact of price changes on one good on the quantity demanded of another good.

It is calculated as the percentage change in the quantity demanded of a product B when there is a one percent increase in the price of product A.

It reflects the relationship between the two goods.

Goods that are considered complementary products, such as goods A and B, have negative cross-price elasticity of demand.A 10 percent increase in the price of good A leads to a 20 percent decrease in the quantity of good B demanded.

This change in the quantity demanded of good B is twice as large as the percentage change in the price of good A.

Hence, the cross-price elasticity of demand for good B is negative, and its value is -2.

In conclusion, the correct answer is option (d). Cross-price elasticity of demand for good B is -2.

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complete question:

A 10 percent increase in the price of good A leads to a 20 percent decrease in the quantity of good B demanded. It appears that: a. elasticity of demand for good A 0.5 and is inelastic. b. elasticity of demand for good B is -2 and is elastic. c. cross-price elasticity of demand for good A is -0.5. d. cross-price elasticity of demand for good B is -2. e. cross-price elasticity of demand for good B is 2.

Answer:

7.3 inches

Step-by-step explanation:

Volume of cylinder = π r ² h

368 = π (4) ² h = 16π h

h = 368/(16π)

= 7.3 inches

The integral is solved where A = 2√ln(x) + c and the equation diverges.

Given data ,

Let the integral be represented as A

where the value of A is

A = ∫( 2 to ∝ ) ( 1/x√ln(x) )

Let the value of u = ln(x)

So, Taking the derivative of both sides with respect to x:

du/dx = 1/x

Rearranging the equation, we get:

dx = du / (1/x) = x du

Now, we can substitute the value of dx and the expression for u in terms of x into the integral:

∫(2 to ∞) 1 / (x * √(ln(x))) dx = ∫(ln(2) to ∞) 1 / (√u) du

On simplifying the integral , we get

∫( 2 to ∝ ) ( 1/x√ln(x) ) = 2√ln(x) + c

And , the integral diverges

Hence , the integral is A = 2√ln(x) + c

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Answer:

2144.67 m³

Step-by-step explanation:

Volume of sphere = (4/3) X π X r ³

= (4/3) π (8)³

= (2048/3) π

= 2144.67 m³ to nearest hundredth

The slope is:

Solution:

To calculate the slope, we will need to use the slope formula :

[tex]\hfill\stackrel{\tt{Slope \: Formula}}{\sf{m=\frac{y_2-y_1}{x_2-x_1}}}[/tex]

So to solve further, we plug in the values.

[tex]\sf{m=\dfrac{80-50}{12-6}}[/tex]

Simplify

[tex]\sf{m=\dfrac{30}{6}}[/tex]

Reduce the fraction

[tex]\sf{m=5}[/tex]

Star: 0.1667, 16.67%; Circle: 0.1875, 18.75%; Triangle: 0.0625, 6.25%; Cylinder: 0.1875, 18.75%; Heart: 0.5, 50%.

We have,

Fraction form: star 1/6

Decimal: 0.1667

Percentage %: 16.67%

Fraction form: circle 3/16

Decimal: 0.1875

Percentage %: 18.75%

Fraction form: triangle 1/16

Decimal: 0.0625

Percentage %: 6.25%

Fraction form: cylinder 3/16

Decimal: 0.1875

Percentage %: 18.75%

Fraction form: heart 8/16

Decimal: 0.5

Percentage %: 50%

Thus,

Star: 0.1667, 16.67%; Circle: 0.1875, 18.75%; Triangle: 0.0625, 6.25%; Cylinder: 0.1875, 18.75%; Heart: 0.5, 50%.

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Answer:

3x²-2x-8

Step-by-step explanation:

(3x+4)(x-2)=

3x²-6x+4x-8=

3x²-2x-8

The point on the y-axis is on the line that passes through point r and is parallel to line PQ is; (0, 2/3)

To find the point on the y-axis that lies on the line passing through point r and is parallel to line pq, we need to first find the slope of line pq.

Substituting the given points, we get:

slope = (-1 - (-3))/(3 - (-3)) = 2/6 = 1/3

Since the line passing through point r is parallel to line pq, it will have the same slope as line pq.

The line passing through point r with slope 1/3.

Using a point-slope form of the equation of a line;

y - (-2) = 1/3(x - 1)

y = 1/3x + 2/3

So, the line passing through point r with slope 1/3 is;

y = 1/3x + 2/3.

y = 1/3(0) + 2/3 = 2/3

therefore, the answer is (0,2/3 )

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Hello !

Answer:

[tex]\boxed{\sf x=2\ or\ x=-3}[/tex]

Step-by-step explanation:

[tex]\sf 5x^2+5x-30[/tex]

This equation is a quadratic equation in the form ax²+bx+c=0

The solution of this equation is given by the quadratic formula :

[tex]\sf x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

There are 3 cases depending on the values of the discriminant :

Let's calculate the discriminant :

[tex]\sf b^2-4ac=5^2-4\times5\times(-30)=625 > 0[/tex]

There are 2 real roots.

Now let's use the quadratic formula to find the two roots.

[tex]\sf x=\frac{-5\pm\sqrt{5^2-4\times5\times(-30)}}{2\times5}\\x=\frac{-5\pm\sqrt{625}}{10} \\x_1=\frac{-5+\sqrt{625}}{10}=2\\x_2=\frac{-5-\sqrt{625}}{10}=-3\\\boxed{\sf x=2\ or\ x=-3}[/tex]

Have a nice day ;)

Answer:

g'(1,-5)

Step-by-step explanation:

Rule

(x,y) → (y -x)

(-5,-1) → (-1,5)

Helping in the name of Jesus.

Answer:

For new coordinates of each point, we can use the following formula:

(x, y) [tex]\longrightarrow[/tex] (y, -x)

To rotate a point 90 degrees clockwise about the origin, we swap the x and y coordinates and negate the x coordinate.

Therefore, the rotated points are:

G(-5,-1) [tex]\longrightarrow[/tex] G'(-1, 5)

H(-3,-2) [tex]\longrightarrow[/tex] H'(-2, 3)

J(-3,-5) [tex]\longrightarrow[/tex] J'(-5, 3)

K(-5,-4) [tex]\longrightarrow[/tex] K'(-4, 5)

Therefore, The vertex of G is (-1,5)

The value of volume of this rectangular pyramid would be,

⇒ Volume = 504 feet³

Since, The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

We have to given that;

In a rectangular pyramid,

Length of rectangular pyramid = 9 feet

Width of rectangular pyramid = 8 feet

Height of rectangular pyramid = 7 feet

We know that;

Volume of rectangular pyramid is,

⇒ Volume = Length x width x height

Substitute all the values, we get;

⇒ Volume of rectangular pyramid = 9 × 8 × 7

⇒ Volume of rectangular pyramid = 504 feet³

Therefore, WE get;

The volume of this rectangular pyramid would be,

⇒ Volume of rectangular pyramid = 504 feet³

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The phrase "at least one set X exists" in set theory means that there is some set, which we'll label as X, that has a definite existence in the mathematical universe we're considering.

In other words, it doesn't have to be the case that X is the empty set, or that X is a set containing specific elements. It simply must be the case that there is some set X.

The line you mentioned "EX (X = X)" is a way of expressing "there exists a set X such that X equals X". This might seem obvious, but it's a fundamental assumption necessary for the development of set theory.

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Answer:

[tex]y = \dfrac{1}{4}x+9[/tex]

Step-by-step explanation:

The product of slope of perpendicular lines are (-1).

Slope intercept form: y = mx +b

Here, m is slope and b is y-intercept.

        y = -4x - 2.

Slope m₁ = -4

[tex]\text{slope of the required line = m =$\dfrac{-1}{m_1}$}[/tex]

                                           [tex]\sf m = \dfrac{-1}{-4}=\dfrac{1}{4}[/tex]

The line is passing through the point(0 , 9)

Substitute the slope and point in the equation of line in point-slope form:                        

                  [tex]\boxed{y - y_1 = m(x - x_1) }[/tex]

               [tex]y - 9 = \dfrac{1}{4}(x - 0)\\\\\\y - 9 = \dfrac{1}{4}x\\\\~~~~~~ y = \dfrac{1}{4}x+9[/tex]

The corresponding rectangular coordinates for point Q is (-3√3, 3)

To convert polar coordinates  (r, θ) to rectangular coordinates  (x, y). Use the following relations:

x = rcosθ

y = rsinθ

We have:

(r, θ) = (6, 5π/6)

x = 6 cos (5π/6)

x = 6 * -√3/2

x =  -3√3

y = 6 sin (5π/6)

y = 6 * 1/2

y = 3

Therefore, the corresponding rectangular coordinates for point Q is (-3√3, 3)

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When a number subtracted from 13 gives -15​ then the number is -2.

We have to find the number which is subtracted from 13 gives -15​.

Let x be the unknown number.

By the given information, let us form a equation:

x-13=-15

We have to solve for x:

Add 13 on both sides of the equation:

x=-15+13

x=-2

Hence, -2 is the unknown number.

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The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

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Answer:

b-3

c-40

Step-by-step explanation:

The complete values are:

1. Scale factor = 1/2

DE = 17.69

AC = 6.5 unit

AB = 8.845 unit

2.  Scale factor = 2/3

UT = 11.34 unit

YZ =  12 unit

XY =  17 unit

1. In ΔACB and ΔDFE

Using Pythagoras

DE = √13² + 12²

DE = √169 + 144

DE = √313

DE = 17.69

AC = 6.5 unit

AB = 8.845 unit

and, Scale factor = 6/12 = 1/2

2. In ΔTUV and ΔXYZ

Scale factor = 8/12 = 2/3

Using Pythagoras

UT= √64 + 64

UT = 11.34 unit

So, YZ = 8  x 3/2 = 12

and, XY = 11.34 x 3/2 = 17

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