Select the correct answer.
Solve the following equation by completing the square.
4z²-16z +8=0
O A z = 2 + √2 orz = 2-√2
OB.
z = 2 + √2 or z = − 2 + √2
z = −2+ √2 orz = -2-√2
z = 4 or z = 0
O C.
O. D.
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The polynomial function to find the volume of the tray is [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches.

According to the question,

We have the following information:

Christina cuts 4 squares with side length x inches from the corners of a 5 inch by 10 inch cardboard rectangle. She folds the remaining cardboard to make a tray that is x inches high.

Now, the length of the tray will be (10-2x) inches and the breadth of the tray will be (5-2x) inches.

Volume of tray = length*breadth*height

Volume of tray = (10-2x)(5-2x)x

Volume of tray = x(50-20x-10x+4[tex]x^{2}[/tex])

Volume of tray = x(4[tex]x^{2}[/tex]-30x+50)

Volume of tray = [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches

Hence, the polynomial function to find the volume of the tray is [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches.

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The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Solve for x.

3 < -5x + 2x

3 < -3x

Divide both sides by 3.

1 < -x

Change sign.

x < -1

18 ≥ 5x  + 4x

18 ≥ 9x

Divide both sides by 9.

2 ≥ x

-6x - 16 < 2x

Add 16 on both sides.

-6x < 2x + 16
Subtract 2x on both sides.

-6x - 2x < 16

-8x < 16

Divide both sides by 8.

-x < 2

Change sign.

x > -2

(1/2)x - 4 > -4

1/2x > -4 + 4

1/2x > 0

x > 0

Code = 4776

Thus,

The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

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Answer: 74

Step-by-step explanation:

Lets say the four even numbers are 2x - 4, 2x - 2 , 2x , 2x + 2

The sum would be

8x - 4 = 284

x = 36

Therefore, the smallest number is 2 * 36 - 4 = 68

The consecutive even numbers are 68, 70, 72, 74 and 74 is the largest.

9,603.75 cm² is the area of the given triangle.

So, the perimeter of the triangle is 392 cm.

Then, let the rest 2 sides be x, where x = x.

Now, we know that the rest 2 equal sides are of length 98.5 cm.

Now, calculate the area as follows:

Therefore, 9,603.75 cm² is the area of the given triangle.

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The total number of members there is 199

Two kinds of logical reasoning are often distinguished in addition to formal deduction: induction and abduction. Given a precondition or premise, a conclusion or logical consequence and a rule or material conditional that implies the conclusion given the precondition, one can explain the following.

Since the number of members of the band is <200. the members are arranged in rows and 3 will be left out

therefore assume the members on row are 200- 3= 197, but 197 is a prime number ,therefore we choose the closet number to 197 which is 196.

therefore the total number of members = 196+3= 199.

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Answer: -1

Step-by-step e

Answer:

-6n-4+3<17

-6n-1<17

-6n<17+1

-6n<18

DIVIDE BOTH SIDE WITH THE COEFFICIENT OF n WHICH IS (-6)

-6n =18

-6 -6

n= -3

The greatest number of rectangles 6cm×4cm that can be cut from a metal that measure 16cm×20cm is 13 rectangles.

A rectangle is a plane shape that has pair of opposite sides equala and parallel.

To calculate the greatest number of rectangles, we use the formula below.

Formula:

Where:

Ferom  the question,

Given:

Substitute these values into equation 1

Hence, the greatest number of rectangles is 13 rectangles.

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Answer:no image I can’t see on mobile

Step-by-step explanation:

h

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]6x-2y=25\implies -2y=-6x+25\implies y=\cfrac{-6x+25}{-2} \\\\\\ y=\cfrac{-6x}{-2}+\cfrac{25}{-2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{3}x-\cfrac{25}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}[/tex]

App inventor's random integer block test is sufficient for app inventor's prng . but to increase our confidence in app inventor's prng we can do other tests like random fraction test and random set speed test.

The Coin Flip Experiment app allows you to run experiments aimed at determining how "good" the App Inventor PRNGs are. The app allows the user to "flip a coin" her N times and the results are displayed. They should record and count the results and calculate the average head percentage. The expectation of should reach 50% on average as N increases.

To properly test an App Inventor PRNG, you must test both the Random Integer and Random Fraction blocks along with the Random Fraction and Random set speed to blocks. Create dice simulations to get better than 50/50 predictions and reuse dice simulators for all combinations of different App Inventor random blocks. If such a combination yields the same results, then you can be confident that her PRNG in App Inventor provides a good model of randomness from all angles.

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The graph of the function is y - 1 = x, not y = x - 1.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, y = (x - 1).

When x = 1, y = 0 ⇒ (1, 0).

When x = 2, y = 1 ⇒ (2, 1).

When x = 3, y = 2 ⇒ (3, 2).

When x = 4, y = 3 ⇒ (4, 3).

When x = 5, y = 4 ⇒ (5, 4)

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The expression that gives the volume of the Sphere with radius 7  is  (4/3)π(7³) , the correct option is (a) .

In the question ,

it is given that

the radius of the sphere is 7 .

we need to find the expression that represents  the Volume of the Sphere when radius is 7 .

the formula for the Volume of the Sphere is (4/3)π(r³) .

Substituting the value of radius = 7 , in the formula ,

we get ,

Volume = (4/3)π(7³)

Therefore , The expression that gives the volume of the Sphere with radius 7 is  (4/3)π(7³) .

The given question is incomplete , the complete question is

Which expression gives the volume of a sphere with radius 7 ?

(a) (4/3)π(7³)

(b) (4/3)π(7²)

(c) 4π(7²)

(d) 4π(7³)

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Answer:

the correct answer is -32+43

Step-by-step explanation:

I just know

The side lengths of the fence he can build with the greatest area inside are of:

75 yards and 75 yards.

Considering a rectangle of length l and width w, we have that the area and the perimeter of the rectangle are given as follows:

A farmer has 300 yards of fencing, hence the perimeter is:

P = 300.

Then:

2(l + w) = 300

l + w = 150

l = 150 - w.

Then the equation giving the area of the fence is:

A = lw

A = w(150 - w)

A = -w² + 150w.

Which is a quadratic equation with coefficients given by:

a = -1, b = 150.

The width that will give the highest possible area is the x-coordinate of the vertex, hence:

w = -150/(2(-1)) = 75 yards.

The length is of:

l = 150 - w = 150 - 75 = 75 yards.

Which means that the third option is correct.

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The completion for the row of the table will be:

Grade 8

Dance club: 0.25

Hiking club: 0.75

Total : 1

Grade 9:

Dance club: 0.40

Hiking club: 0.60

Total : 1

The dance club for grade 8 will be calculated as:

= Number of dancers / Total number

= 5/20

= 0.25

The hiking club will be:

= 15/20

= 0.75

The dance club for grade 9 will be calculated as:

= Number of dancers / Total number

= 20/50

= 0.4

The hiking club will be:

= 30/50

= 0.6

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Answer:

add 54 to the numerator and 61 to the denominator because after you add it the fraction, it should be 60/90: simplified to 2/3 if you divide the numerator and denominator by 30.

The number that must be added to the numerator and denominator is 40.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Fraction = 6/29

The new fraction = 2/3

Now,

(6 + x)/(29 + x) = 2/3

3(6 + x) = 2(29 + x)

18 + 3x = 58 + 2x

3x - 2x = 58 - 18

x = 40

Thus,

The number x is 40.

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The slope of the graph above is [tex]-\frac{4}{3}[/tex]

The slope of a line is the change in the dependent variable with respect to the change in the independent variable. The slope of a line is rise over run.

Therefore,

slope = m = y₂ - y₁ / x₂ - x₁

Hence, using the coordinates on the graph let's find the slope of the graph.

(-2, 1)(1, -3)

Therefore,

x₁ = - 2

x₂ = 1

y₁ = 1

y₂ = - 3

Hence,

[tex]slope = \frac{-3-1}{1-(-2)}[/tex]

[tex]slope = \frac{-4}{1+2}[/tex]

[tex]slope = \frac{-4}{3}[/tex]

Therefore, the slope of the line is [tex]-\frac{4}{3}[/tex]

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The height of the sunflower after 9 weeks is 52 inches and the function that represent the height of the sunflower after w weeks = 25 + 3w weeks.

Sophia planted a tiny sunflower in her backyard at the start of spring.

When she planted the sunflower,

The height of the sunflower = Initial height of the sunflower = 25 inches.

Now, The sunflower then began to grow at a rate of 3 inches per week.

Thus, the growth rate of the sunflower = 3 inches/week

The growth in 9 weeks = 3*9 = 27 inches,

The height of the sunflower after 9 weeks = initial height + growth = 25 +27 = 52 inches.

The growth in w week = 3w inches,

The height of the sunflower after w weeks = initial height + growth = 25 + 3w inches.

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According to the circle, if 8 points in a plane are chosen to lie on or inside a circle of diameter 2cm then show that the distance between some two points will be less than 1cm.

Circle:

Circle refers the round shape that has no corners or line segments. And it is a closed curve shape in geometry.

Given,

Eight points are in/on the circle of radius 1cm.

Here we need to show that distance between some two points is less than 1cm.

Let us consider the points be p1,p2,…,p8

Noe, we have to place the point p8 at the center of the circle and placing other seven points on the periphery of the circle, at equal distances

Here we have to remember that we are required to prove that there are at least a pair of points whose distance from each-other is less than 1cm.

So, now we have one point at the center and seven at the periphery of the circle.

Based on this the heptagon which will be formed by joining the seven points on the circle will have all its side equal in length.

Then the length of the side of the heptagon is less than 2π/7 cm which is less than 1cm.

Therefore, if we replace the position of any point then too we get a pair of points whose distance from each-other is less than 1cm.

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The hour hand is 2.70 m long and minute hand is 4.50m long with mass of 60 kg and 100 kg. Therefore. Total angular momentum is 1.2 kgm²/s.

Mass of Hour hand = 60 kg

length of hour hand = 2.70 m

Now,

Moment of inertia of the hour hand is given by:

                         I = mL²/ 3

                         I = 60(2.70)²/3

                         I = 145.8 kgm²

Now,

The angular speed of hour hand is:

                           ω = 2π/ T

                          ⇒ ω = 2π / 12×3600

                          ⇒ ω = 1.45 × 10⁻¹ rad/s

Now,

Angular momentum is given as:

L₁ = Iω = 145.8 × 1.45× 10⁻¹

           = 0.021 kgm²/s

Mass of minute hand = 100 kg

length of minute hand = 4.50 m

Now,

Moment of inertia of the minute hand is given by:

I = mL²/ 3

I = 100(4.50)² /3

I = 675 kgm²

Now,

The angular speed of minute hand is

ω = 2π/ T

ω = 2π / 60× 60

ω = 1.74 × 10⁻³ rad/s

Now,

Angular momentum is given as:

L₂ = Iω = 675 × 1.74 ×10⁻³

           = 1.178 kgm²/s

Total angular momentum is given as

L = L₁ + L₂

  = 0.021 + 1.178

  = 1.2 kgm²/s

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The minimum cost will be at (2.5 , 3) and the minimum cost be $25.

Given, a landscaping contractor plans to use the least expensive combination of two brands of fertilizer.

A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates.

A package of Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates.

The lawn requires at least 60 oz of phosphates and 40 oz of nitrates.

Let the number of Brand X packages be, x

the number of Brand Y packages be, y

According to the question,

12x + 10y ≥ 60 = 6x + 5y ≥ 30

10x + 5y ≥ 40 = 2x + y ≥ 8

x ≥ 0

y ≥ 0

Z = 16x + 7y

On solving the equations, we get

6x + 5y = 30

6x + 3y = 24

On subtracting, we get

2y = 6

y = 3

and x = 2.5

So, minimum cost will be at (2.5 , 3) and the minimum cost be

Z = 16(2.5) + 7(3)

Z = 4 + 21

Z = 25

Hence, the minimum cost will be at (2.5 , 3) and the minimum cost be $25.

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The total cookies she baked altogether is 28 cookies

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

Half of the cookies is placed on the table, 6 is eaten by my dog, half is eaten by my brother and I ate the last 4, the means my brother ate 4 cookies too.

Therefore the total cookies put on the plate is 6+4+4= 14cookies

half of all the cookies were put in the plate,

therefore the total cookies made is 14×2= 28cookies.

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The values of x, y and z in the given Rhombus are

x = -98, y = 36 and z = -97/4.

Given, the figure shown is a rhombus

as, the opposite angles of the rhombus are equal

So, 3y - 1 = 107

3y = 107 + 1

3y = 108

y = 36

and (-x - 8) = (-4z - 7)

x + 8 = 4z + 7

x - 4z = -1

also, the sum of the opposite angles of the rhombus is 180°.

So, (-x - 8) + (-4z - 7) = 180

-x - 4z = 180 + 15

x + 4z = -195

On adding the equations, we get

2x = -196

x = -98

and z = -97/4

Hence, the values of x, y and z are

x = -98, y = 36 and z = -97/4.

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Solving each pair of expression shows that

(1/5)^2 + 1 ≠ 2 * 12 / 25

( 1 + 1/4 )^2 = 2 - 7/16

Putting equals sign implies that the the expression in left hand side of the equation is equal to the expression on the right hand side

If they are not equal the sigh to be used is not not equal to

(1/5)^2 + 1 & 2 * 12 / 25

1/25 + 1 & 24/25

26/25 ≠ 24/25

( 1 + 1/4 )^2 & 2 - 7/16

(5/4)^2 & 25/16

25/16 = 25/16

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Answer:1712

Step-by-step explanation:  is 1712

The inverse function of the given function will be f(x)⁻¹ = ( 10 ) / ( 9x - 99).

From the question, we have

f(x) = ( 10/9x) + 11

x = ( 10 / 9y ) + 11

x - 11 = ( 10 / 9y )

9y / 10 = ( 1 / ( x - 11 )

9y = 10 / ( x - 11 )

y = ( 10 ) / ( 9x - 99 )

Inverse function :

The expression that established the relationship between the dependent variable and the independent variable is referred to as a function. An inverse function is a function that is applied to the value of y after switching the values of two variables, x and y.

Complete question:

What is the inverse of function f?

f(x) = 10/9x+11

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Answer:

3. line XZ is congruent to line XZ | reflexive property
4. triangle WXZ is congruent to triangle YZX | HL (i think)
5. angle WXZ is congruent to angle YXZ | CPCTC

Step-by-step explanation: