Simplify.
x to the 4 power x z to the 5 power over xz to the 6 power

Answer:

below

Step-by-step explanation:

-14y = 28 - 10x

10x - 14y - 28 = 0.

a = 10

b = -14

c = -28

Answer:

a = 10

b = -14

c = 28

Step-by-step explanation:

Goal form: Standard form

ax + by = c

Given form: linear form (not fully simplified)

-14y = 28 - 10x

Add 10x on both sides (to move the x-value to the left-hand side of the equation)

-14y + 10x = 28 - 10x + 10x

-14y + 10x = 28

10x - 14y = 28

Determine [ a ], [ b ], [ c ]

ax + by = c

10x - 14y = 28

[tex]\Large\boxed{a=10}[/tex]

[tex]\Large\boxed{b=-14}[/tex]

[tex]\Large\boxed{c=28}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

eight and thirty-seven fiftyths

Step-by-step explanation:

6 and 4/100 + 2 and 5/10

6 and 1/25 + 2 and 1/2

156 / 25 + 5 / 2

312 / 50 + 125 / 50

437 / 50

400 / 50 = 8

8 and 37 / 50

The  techniques that can be used to best explain for each equation that I have created are:

A)  For  graphing -  This is often used in checking if your answer is correct, if the math is known to be a little tedious, graphing is recommended

(b) For factoring:  x^2 -3x +4 '

Where: (x-4)(x+1)=0

Then x=-1, 4

(c) For  square root method:   x^2 = 64

Therefore x = + or - [tex]-\sqrt{64}[/tex] = + or - 8

(d) For  completing the square:  x^2 + 4x = 11 and x^2 +4x + 4

Note that:  x^2 +4x + 4

= x^2 + 4x = -4

= x^2 +4x + 4 = -4 + 4

= (x+2)^2 = 0

So, x = -2

(e) For quadratic formula: 6x² + 7x -19 =0  

x= [-b + or - sqr(b² - 4ac)]/2a

Note that b=7

a=6

c=-19

Therefore

x= [-7+ or - sqr(49+4(6)(9)]/2

2.  if the discriminant is said to be negative,   then the equation is one that is made up of two imaginary or complex solutions.

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See full question below

You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.

a. graphing

b. factoring

c. square root method

d. completing the square

e. quadratic formula

2. What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?

The measure of the unknown angles are as shown below;

m<2 = 128 degrees = m<4

m<5 = 128 degrees

m<6 = 52 degrees

m<3 = 52 degrees = m<8

m<7 = 128 degrees

An angle is the point where the two lines meet. From the given diagram, the lines B and D are parallel to each other with a transversal.

Given the following parameters

m<1 = 52 degrees

From the given diagram, the following are true

m<1 = m<3 (corresponding angle)

m<3 = m<8 (vertical angles)

m<1 = m<6 (vertical angles)
m<2 = m<5 (vertical angles)

m<4 = m<7 (vertical angles)

Also;

m<1 + m<2 = 180

m<2 = 180 - m<1

m<2 = 180 - 52
m<2 = 128 degrees = m<4

m<5 = 128 degrees

m<6 = 52 degrees

m<3 = 52 degrees = m<8

m<7 = 128 degrees

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Answer:

x = 52

Step-by-step explanation:

Since the inscribed angle measures 64 degrees, the minor arc is 64*2 = 128 degrees. Therefore the major arc is 180-128 = 232 degrees. Angle X is the difference of major and minor arc divided by 2, so X = (232-128)/2 = 52 degrees.

Answer:

None of these

Step-by-step explanation:

[tex]\frac{360}{n}=24 \implies n=15[/tex]

This is called a pentadecagon.

Answer:

See below

Step-by-step explanation:

Distance = rate * time

              = 65 m/hr * 2 1/4 hr = 146.25 miles

rate = distance / time

for Declan :   rate =  146.25 miles / (2 hrs + 35/60 min) = 56.61 mph

See attachment for the graph of the inequality expression x + 2y > 6

The condition is given as:

{(x, y): x + 2y > 6}

This means that

x + 2y > 6

The above is an inequality expression, where the variables are x and y

So, we simply plot the graph of the inequality expression x + 2y > 6

See attachment for the graph of the inequality expression x + 2y > 6

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The probability of being dealt no pair is 0.5011 or 50.11% if the tandard deck of playing cards has 52 cards-4 suits.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

In 5-card poker, find the probability of being dealt the following hand. Refer to the table.

From the table:

Total number of outcomes = 2598960

Total number of favourable outcomes = 1302540

The probability of being dealt no pair:

P(no pair) = 1302540/2598960

P(no pair) = 0.5011

In percentage:

P(no pair) = 50.11%

Thus, the probability of being dealt no pair is 0.5011 or 50.11% if the tandard deck of playing cards has 52 cards-4 suits.

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We cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations.

By geometry we know that the area of the piece of metal is equal to the product of its length and width, then we must find two real numbers such that:

l · w = 27.75, where l, w > 0.

Unfortunately, we cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations. We need at least one equation to find an unique solution.

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Answer: If one angle of a parallelogram is a right angle, then all other angles would also be right angles and the parallelogram would be a rectangle.

The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

The optimization equation is given as

z=−3x+5y

The constraints are given as:

x+y≥−2

3x−y≤2

x−y≥−4

Next, we plot the constraints on a graph and determine the points of intersections

See attachment for the graph

From the attached graph, the points of intersections are

(-3, 1), (3, 7) and (0, -2)

So, we have:

(0, -2)

(-3, 1)

(3, 7)

Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

So, the complete parameters are:

Optimization Equation:

z=−3x+5y

Constraints:

x+y≥−2

3x−y≤2

x−y≥−4

Vertices of the feasible region

(0, -2)

(-3, 1)

(3, 7)

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If the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.

Given that height in t seconds is shown by h(t)=52t-16[tex]t^{2}[/tex].

We are required to find the time after which the ball will attain its maximum height.

The maximum height is the y coordinate of vertex of the parabola. Then we can use the following value of t.

h(t)=52t-16[tex]t^{2}[/tex]

Differentiate with respect to t.

dh/dt=52-32t

Again differentiate with respect to t.

[tex]d^{2}h/dt^{2}[/tex]=-32t

Because tim cannot be negative means the height is maximum.

Put dh/dt=0

52-32t=0

-32t=-52

t=52/32

t=1.625

Hence if the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.

Question is incomplete as the right and complete equation is

h(t)=52t-16[tex]t^{2}[/tex] .

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1 week = 7 days

10 weeks = 10×7 days

= 70 days

if Ellen reads 1 book in a day

Therefore,

1 day = 1 book

70 days = 70×1

= 70 books.

Thus Ellen reads 70 books in 10 weeks.

Hope helps

Answer:

70 books

Step-by-step explanation:

Ellen reads one book per day for 10 weeks.

All we need to do to know the number of books Ellen read overall is to multiply 1 (number of books he read each day) and 10 weeks (total number of days).

Each week is 7 days, so 10 weeks is equal to 70 days.

The equation will be: 1 x 70

We can conclude that Ellen read 70 books overall within 10 weeks.

Answer:

Step-by-step explanation:

[tex]\frac{1}{2} x=a=\frac{2}{3} y\\\frac{1}{2}x=a\\x=2a \\\frac{2}{3} y=a\\y=\frac{3}{2} a\\x+y=2a+\frac{3}{2} a=\frac{4a+3a}{2} =\frac{7}{2} a=na\\n=\frac{7}{2}[/tex]

Usando la distribución hipergeométrica,  la probabilidad de que ambas estén numeradas con el valor 1, es: 0.0222 = 2.22%.

La fórmula es:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Los parámetros son:

Los valores de los parámetros son:

N = 10, k = 2, n = 2.

La probabilidad de que ambas estén numeradas con el valor 1, es P(X = 2), entonces:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,10,2,2) = \frac{C_{2,2}C_{8,0}}{C_{10,2}} = 0.0222[/tex]

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a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is $11,949.50.

b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.

The future value can be determined using an online finance calculator.

Data and Calculations:

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Semi-Annually

Time (t in years): 8 years

Result:

A = $11,949.50

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,244.94

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,704.56(1 + 0.04/2)(2)(8)

A = 8,704.56(1 + 0.02)(16)

A = $11,949.50

Using the formula A = Pert

Principal (P):  $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Continuously

Time (t in years):   8 years

Result:

A = $11,987.29

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,282.73

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A, using the mathematical constant, e = 2.71828

A = Pert

A = 8,704.56(2.71828)(0.04)(8)

A = $11,987.29

Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is $11,949.50,  the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.

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Answer:

0.7

Step-by-step explanation:

Each increment is 0.1, so count the approximate number of increments needed to get from the orange circle on the left and the one on the right and multiply by 0.1 to get the difference.

Step-by-step explanation:

Let ABC be the equilateral triangle. Let AE, BD and CF be the medians. A meridian divides a side into two equal parts. Hence, proved that medians of an equilateral triangle are equal .

The number -3 written as a logarithm with a base of 2 is log₂(0.125) or log₂(1/8)

As a general rule, logarithms are mathematical expressions that are written in the form log(x) or ln(x), for natural logarithms

The number is given as:

x = -3

The base of the logarithm is given as:

Base = 2

To rewrite the given number as a base of 2, we take the exponent of the number where the base is 2

This is represented as:

Number =2^-3

Apply the power rule of indices

Number =1/2^3

Evaluate the exponent

Number = 1/8

Evaluate the quotient

Number = 0.125

Hence, when the number -3 is rewritten as a logarithm with base 2, the equivalent logarithm expression is log₂(0.125) or log₂(1/8)

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The time taken for the smaller pipe to fill the pool by itself is 15.71 hours

1/6 = 1/x + 1/(x+6)

1/6 = (x+6)+(x) / (x)(x+6)

1/6 = (x+6+x) / x²+6x

1/6 = (2x+6)(x² + 6x)

1(x² + 6x) = 6(2x+6)

x² + 6x = 12x + 36

x² + 6x - 12x - 36 = 0

x² - 6x - 36 = 0

x = 9.71 or -3.71

The value of x cannot be negative

Therefore, the

Time taken for long pipe = x

= 9.71 hours

Time taken for small pipe = x + 6

= 9.71 + 6

= 15.71 hours

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The equations of the three altitudes of triangle ABC include the following:

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Also, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Assuming the following parameters for triangle ABC:

For the equation of altitude AM, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2

Slope of AM = -1/slope of BC

Slope of AM = -1/(-3/2)

Slope of AM = 2/3.

The equation of altitude AM is given by:

y - y₁ = m(x - x₁)

y - 0 = 2/3(x - (-2))

3y = 2(x + 2)

3y = 2x + 4

3y - 2y - 4 = 0.

For the equation of altitude BN, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3

Slope of BN = -1/slope of CA

Slope of BN = -1/(1/3)

Slope of BN = -3.

The equation of altitude BN is given by:

y - y₁ = m(x - x₁)

y - 8 = -3(x - 0)

y - 8 = -3x

y + 3x - 8 = 0.

For the equation of altitude CL, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4

Slope of CL = -1/slope of AB

Slope of CL = -1/4

The equation of altitude CL is given by:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 4)

4y - 2= -(x - 4)

4y - 2= -x + 4

4y + x - 2 - 4 = 0.

4y + x - 6 = 0.

In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:

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Answer:

Gradient of the line is choice D.9/5

Step-by-step explanation:

Slope between two points:slope=(y₂-y₁)/(x₂-x₁)

slope(m)=

[tex] \frac{5 - ( - 4)}{3 - ( - 2)} \\ refine \: (m )= \frac{9}{5} [/tex]

Answer:

4900

Step-by-step explanation:

When rounding a number such as 4928 to the nearest hundred, we use the following rules:

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

In this case, Rule B applies and 4928 rounded to the nearest hundred is:

4900

Answer:

Step-by-step explanation:

4,928, look at the last two numbers 28 if they are above 50 you round up, if below 50 round down,

The answer is 4,900

The correct answer for the solution of  inequality  is [tex]x\geq 8[/tex].

Let the unknown number be "[tex]x[/tex]."

The statement  "a number plus four" can be written  as "[tex]x+4[/tex]."

The phrase "is greater than or equal to twelve" can be expressed as "[tex]\geq 12.[/tex]

Put these together, the inequality becomes:

[tex]x + 4\geq 12[/tex]

solve for "[tex]x[/tex],"  isolate the variable on one side of the inequality:

Subtract -[tex]4[/tex] from both side of the expression:

[tex]x + 4 - 4 \geq 12 - 4[/tex]

[tex]x\geq 8[/tex]

The correct expression for the  inequality is  [tex]x\geq 8[/tex]

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Answer:

B

Step-by-step explanation:

The area of the triangle is half the base time the height.  The height is y sub 1.  The length is the distance between the x values.

Step-by-step explanation:

x = a + 7

y = b-a

To prove

x + y = b + 7.

=a+7+b-a

=a-a+7+b

=0 + 7+b

= b+7

Proved ✅

The experimental probability that only 2 of 4 children in a family are boys is 50%.

Experimental probability refers to the chance of an expected success being achieved in a series of experiments conducted.

Experimental probability is the number of times that the expected success occurs as a fraction of the total number of times the experiment was conducted.

Like all probabilities, the experimental probability is based on the likelihood that what the experimenter expects is achieved.

Expected number of boys = 2

The number of children in the family = 4

Experimental probability = 50% (2/4 x 100)

Thus, we can conclude, based on the experimental probability, that 50% (or 2) of the 4 children in the family are boys.

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Answer:

15%

Step-by-step explanation:

Step 1: Count samples with one H

Why; Only 1 of 4 children  in families are boys. The problem is simulated with samples.

Step 2: Count samples with only one H.

Why; The H represents the one boy in the family.

Step 3: Add the samples you counted with one H.

Answer: Your answer should be 3/20 after you change it into a percentage your final answer is 15%

What is ordinary number?

1 : a number designating the place (such as first, second, or third) occupied by an item in an ordered sequence — see Table of Numbers. 2 : a number assigned to an ordered set that designates both the order of its elements and its cardinal number.