Solve the inequality 1/4 (x-20)<-6 or -6x+5≤-1. Write your solution in algebraic form, interval notation, and graphed on a number line.

In the picture, the polynomial equation is (3x-k)². The values of k=4 and p=-24.

Given that,

In the picture, the polynomial equation is (3x-k)²

We have to find the k value and p value if (3x-k)²=9x²+px+16

Polynomial means polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

We get,

(3x-k)²=9x²+px+16

9x²-6xk+k²=9x²+px+16

We get,

p=-6k and k²=16

k²=16

k=4

Substitute in p=-6k

p=-6×4

p=-24

Therefore, the values of k=4 and p=-24.

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5 square root - 2 square root is 0.821854415 and it is rational.

Given,

5 square root - 2 square root

That is,

√5 - √2

We have to find this is rational or not.

First we have to solve the equation:

√5 - √2 = 0.821854415

Irrational numbers cannot be stated as a fraction, although rational numbers can be expressed as ratios (such as P/Q and Q0). However, both of the numbers are genuine and can be shown on a number line.

So, here 0.821854415 is a rational number.

That is, 5 square root - 2 square root is  rational.

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Answer:

It requires no energy from the cell.

Step-by-step explanation:

Answer:

44.8 inches

Step-by-step explanation:

5.6x8

need to write something to let me answer

Answer:

44.8 inches

Step-by-step explanation:

Hope this helps

387.869911589 to 3 decimal places is 387.870.

A decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.

In order to round off a number to 3 decimal places, there must be 2 numbers to the right of the decimal point.

In order to round off a number to 3 decimal places, if the ten thousandth figure is equal to five or greater than 5, one is added to the thousandth figure. If the ten thousandth figure is less than 5, there is no change in the thousandth digit.

The ten thousandth is greater than 9, so one is added to the thousandth digit. The number becomes 387. 870

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The constant of proportionality is 12.75

The constant of proportionality is the ratio of the constant values of two proportional quantities.

The direct variation is given by y = k x where k is the constant of proportionality.

Now the cost of 6 tickets is $76.50

76.50 = k × 6

or, k = 12.75

Therefore the constant of proportionality is 12.75

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Answer:

. .........................

Answer:

Perpendicular lines: When a line intersects another line at exact 90 degrees the lines are said to be perpendicular to each other.

Parallel lines: When two lines are formed such that the two lines are never intersecting and no angle is formed is known as parallel lines.

Answer:

20/3 batches of cookies can be made with 5 pounds of flour.

Step-by-step explanation:

given-

A recipe calls for 3/4 of a pound of flour to make 1 batch of cookies

asking-how many batches of cookies can be made with 5 pounds of flour

3/4 pound of flour=> 1 batch of cookies

then,

1 pound of flour=> 4/3 batch of cookies

so, required answer---

5 pound of flour=>5*( 4/3) batch of cookies

  =>20/3=6.66  batch of cookies

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Fractions into Decimals-

15/5 = 3

Decimals into Fractions-

0.5 = 5/10

Place the decimal number above its place value to convert it to a fraction.

For instance, since the number six is in the tenths place in the fraction 0.6, we multiply it by 10 and get the comparable fraction 6/10.

Simplify the fraction if necessary.

The division is shown by the fractional bar between the "part" and the "whole."

By dividing the numerator by the denominator, any fractions can be transformed into decimals.

For instance, the fraction 45 denotes the ratio of 4 to 5, or 4/5.

By dividing 4 by 5, this fraction can be changed into a decimal.

Fractions into Decimals-

15/5 = 3

Decimals into Fractions-

0.5 = 5/10

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Isolate the variable by dividing each side by factors that don't contain the variable.

[tex]-2.29(d+1)=-6.87[/tex]

[tex]d=2[/tex]

^Hence, our solution

________________________________________________

Hope this helps!

The form:

y = a(x-h)^2 + k

Is the vertex form of the quadratic equation, by finding the vertex, we conclude that k = -1.

For any quadratic equation of the form:

y = a*x^2 + b*x + c

With a vertex (h, k), we can rewrite the equation as:

y = a*(x - h)^2 + k

And the value h of the vertex is given by:

h = -b/(2a)

In this case, the quadratic equation is:

y = 2x^2 - 8x + 7

Then the value h of the vertex is:

h = -(-8)/(2*2) = 2

Evaluating the quadratic equation in x = 2 we will get the value of k, so we have.

y = 2*(2)^2 - 8*2 + 7 = -1

Then the vertex is (2, -1), which means that the value of K is -1.

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Answer:

the x = 0  and y = 1

so start off at the zero on the x-axis, and move up to the 1 on the y- axis

By  Side - Angle - Side congruency (SAS) rule, ΔDFC is congruent to ΔAEB as shown below.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Given is a geometrical diagram as shown in the image.

We can prove ΔDFC ≅ ΔAEB as follows -

AE = CF       [Given]

Add length EF on both sides of the equation, we get

AE = CF                                   ...[1]

∠ 1 = ∠ 2             [Given]                  ...[2]

Given is ∠ 1 = ∠ 2. Than the tangent of both angles will be same. On solving the tangent ratio, we get -

BE = FD                  ...[3]

From equation 1, 2 and 3, we can say that

ΔDFC ≅ ΔAEB

Therefore, by Side - Angle - Side congruency (SAS) rule, ΔDFC is congruent to ΔAEB.

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Duval Street between latitudes (3,1) and (7,5). Val resides between coordinates (2, 15) and (-6, 3). Braxton Lane and Duval Street are not parallel or perpendicular.

Given that,

Mary resides on Duval Street between latitudes (3,1) and (7,5). On Braxton Lane, Val resides between coordinates (2, 15) and (-6, 3).

We have to find is Braxton Lane and Duval Street parallel or perpendicular.

To find the lines are parallel or perpendicular we have to find the slope of those points.

If slopes are equal then the lines are parallel.

If slopes are negative reciprocal then the lines are perpendicular.

We find the slope of Mary resides on Duval Street between latitudes (3,1) and (7,5).

m₁=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m₁=[tex]\frac{5 -1 }{7-3 }[/tex]

m₁=4/4

m₁=1

The slope of the Mary resides on Duval Street between latitudes (3,1) and (7,5) is 1.

We find the slope of Braxton Lane, Val resides between coordinates (2, 15) and (-6, 3).

m₂=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m₂=[tex]\frac{3 -15 }{-6-2 }[/tex]

m₂=-12/-8

m₂=3/2

The slope of the Braxton Lane, Val resides between coordinates (2, 15) and (-6, 3) is 3/2.

m₁≠m₂

Therefore, Braxton Lane and Duval Street are not parallel or perpendicular.

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The next term would be 3 then 1 in the sequence 243, 81, 27, 9,... by the term of sequence and series through mathematical sequencing.

A grouping of numbers in a kind of a specific order is known as a sequence. On the other hand, a series can also be described as the accumulation of a kind of a sequence’s constituent parts.

Basically, the sequence proceeds with a dividing term of 3. The sequence will go on with the square root of the previous number. Basically, from backward, the sequence is an exponential multiple of 3.

Mathematical sequence and series formulas pertain to several kinds of sequences and series. A series is the accumulation of elements in a sequence, which is a group of arranged elements that follow a pattern.

The formulas for the nth term and the sum are typically included in the sequence and series formulas.

A series is made up of all the elements in a sequence, while a sequence is a certain arrangement of elements in a specific order.

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The solution to the given exponential equation is; x = 6.48

We want to solve the exponential equation;

4^(x) = 7 - (3^x)

We can use logarithm or inverse of logarithm to solve this but in this case we will use the logarithm to get;

x log 4 = 7 - (x log 3)

x log 4 + x log 3 = 7

x(log 4 + log 3) = 7

1.08x = 7

x = 7/1.08

x = 6.48

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Answer:

177

Step-by-step explanation:

5(54 − 6 − 3) + (6)(2) − 60

= 177

The answer in simplest form is [tex]20\frac{30}{11}[/tex] .

Given fraction is [tex]5*4\frac{6}{11}[/tex].

So we convert the mixed fraction into an improper fraction to calculate further.

[tex]4\frac{6}{11} =\frac{50}{11}[/tex]

Next, we calculate the above fraction given in the question

[tex]5*\frac{50}{11}[/tex] = [tex]\frac{250}{11}[/tex]

So now we convert obtained improper fraction to mixed fraction which is its simplest form,

[tex]\frac{250}{11} = 20\frac{30}{11}[/tex]

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Answer:

-8

Step-by-step explanation:

A= - 48

B= 6

-48/6

= 8

Negative x Negative = Positive

Negative x Positive = Negative

Positive + Positive = Positive

Answer: 0.700

0.699 is the closest to 0.700, the hundredth would go up by one creating 0.700 hope this helps

Answer:

y+5 = 1/5 (x+6)

Step-by-step explanation:

The point slope form looks like this.

y - y1 = m (x - x1)

the m represent slope and (x1, y1) are the coordinates of the point that the line passes through.

Answer:

Correct answer should be x= -6

Step-by-step explanation:

prove me wrong

Answer:

X=17/24

Step-by-step explanation:

first you need to find common denominators. To find it, you would multiply the denominator of the 1 2/3 and the 2 3/8.8*3=24, which means the denominator is 24. For 1 2/3, we multiplied 3*8 so we also have to do it for 2. The new equation is x+1 16/24=2 3/8. But remember, we still have to multiply 8*3, which means we have to multiply 3*3 too.

New equation:x+1 16/24=2 9/24

Now we can subtract 1 16/24 from each side

X=17/24

well, the amount paid was "x", which oddly enough is 100%, but we also know that 6% of that is $1.80, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1.80& 6 \end{array} \implies \cfrac{x}{1.80}~~=~~\cfrac{100}{6} \implies 6x=180\implies x=\cfrac{180}{6}\implies x=30[/tex]