list two ways you can tell if a pair of numbers is a solution to an equation

Answer:[tex]\sqrt{303.51}[/tex]

Step-by-step explanation:

The difference in the radii of the two circles is [tex]4.3-1.8=2.5[/tex] inches.

Since the tangent has a length of 2.5 inches, by the Pythagorean theorem, the required distance is

Answer: [tex]8\pi[/tex]

Step-by-step explanation:

The period is [tex]\frac{2\pi}{1/4}=8\pi[/tex].

Answer:

Discount: $30 off

New Sale Price: $270

Step-by-step explanation:

$300*10% =

30

$300-30=

$270

or

$300*.1=

30

$300-30=

$270

The rise is the difference in y-coordinates:

The run is the difference in x-coordinates:

The slope is the quotient of rise over run:

========================

If two points on a line are A(10, −3) and B(12, 9), the rise is 12, and the run is 2, so the slope of the line is 6.

Answer:

-5

Step-by-step explanation:

The y coordinate of the vertex is -5.

Answer:

[tex]\frac{15}{2}[/tex]

Step-by-step explanation:

The absolute value of a number is just its distance from zero. In other words, if it's negative, the absolute value would make the number positive. This makes the absolute value [tex]\frac{45}{6}[/tex]. Now, reduce to get[tex]\frac{15}{2}[/tex].

It's 4 buns & 5 cakes

Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.

E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p

Answer:

a) 10/21 b) 5/21 c)1/21

Step-by-step explanation:

a) your have 7 choice and 5 or them or red, 5/7.  You do not replace the red marble, so for your second draw, you now only have 6 choices and of those 6 choices only 4 of them are now red or 4/6 or 2/3.  We multiple these two numbers together:

5/7(2/3) = 10/21

b) For the first draw, you have 5 red marbles available out of a total 7 marbles or 5/7.  The second draw now only has 6 marbles and 2 of them or yellow to make 2/6 or 1/3 (simplified).  We multiply these together.

5/7(1/3) =5/21

c)  I am assuming that you are still selecting 2 marbles.  The first draw would be 2/7.  This time I am selecting yellow and there are only 2 choices for yellow.  My next draw will only have 6 marbles and only 1 of them will be yellow, so 1/6.  We multiply these together

2/7(1/6) = 2/42 or 1/21

The domain of the function is the set of all real numbers and the range of the function is the set of all values greater than -2

The function is given as:

f(x) = 2(x -4)^2 - 2

A quadratic function can take any real number as its input.

So, the domain of the function is the set of all real numbers

The vertex of the above function is:

Vertex = (4, -2)

And the leading coefficient is:

a = 2

The y value of the vertex is;

y = -2

Because the value of a is positive, then the vertex is a minimum.

This means that the range of the function is the set of all values greater than -2

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The experiment is illustrated below.

A. The type of experimental design is a completely randomized design experiment where experimental units of 200 female subjects which are allocated randomly to say 4 treatment groups with each treatment group consist of 50 female patients.

Here the treatment used is low-intensity shock therapy which is also factor or explanatory variable. After administrating above treatment for a period of say 2-3 weeks, the response in pain reduction can be measured among all patients in 4 treatment groups by comparing their earlier pain level for reduction in pain.

If the study consist of 100 male and female patients, the experimental design can be changed into randomized block design by blocking subjects by gender.

The above design can be double blinded by not letting either the patients or lab technicians aware about which treatment groups, each of these subjects are experimented against to keep the data confidential.

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The algebraic expression is 20b

The statement is given as:

$20 a ticket

This means that the cost of 1 ticket is $20.

So, the cost of b tickets is

Cost = 20 * b

Evaluate

Cost = 20b

Hence, the algebraic expression is 20b

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From the given information,

a. The length of the belt is 180.28 ft

b. The height of the window from the ground is 100 ft

c. The length of the ramp needed is 141.42 ft

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the triangle. I.e., (hypotenuse)² = (opposite)² + (adjacent)²

It is given that,

The height of the silo is 150 feet

The distance from the belt to the silo is 100 feet

With the given measurements, a right-angled triangle is formed.

a. Finding the length of the belt:

From the diagram,

The height of the silo, sh = 150 ft

The base distance, sb = 100 ft

So, the length of the conveyor belt is the hypotenuse (bh) of the triangle formed.

On applying the Pythagorean theorem,

bh² = sb² + sh²

⇒ bh² = (100)² + (150)²

⇒ bh² = 32500

⇒ bh = √32500 = 50√13

∴ bh = 180.28 ft

Thus, the length of the belt is 180.28 ft.

b. Finding the height of the window from the ground:

It is given that the angle of elevation from the lower end of the belt(b) to a window(w) on the side of the silo is 45°.

This creates a special right-angled triangle. I.e.,

The angles of the new triangle are 90°- 45°. So, the third angle also becomes 45° (Since the sum of angles in a triangle is 180°)

So, the new triangle has angles of 90°- 45°- 45°

Thus, the new triangle is said to be an isosceles right angled triangle.

So, the two legs of the triangle are equal. I.e., sb = sw = 100 ft

Therefore, the height of the window from the ground(sw) is 100 ft

c. Finding the length of the ramp(bw) to the window:

Since we have

sw = 100 ft and sb = 100 ft

On applying Pythagora's theorem,

bw² = sb² + sw²

⇒ bw² = (100)² + (100)²

⇒ bw = √20000 = 141.42 ft

Therefore, the length of the ramp to the window is 141.42 ft.

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Answer:

-24

Step-by-step explanation:

-6 × f(3) - 6 × g(-1) = ?

to answer this we need to find the functional values of the functions at the specified points.

f(3) = -2

we find this easily : we go to x = 3 on the x-axis, and then see there at what y value a vertical line is intersecting the functional graph. the intersection is below the x-axis, so the y value is negative.

g(-1) = 6

we go to x=-1, and we find that a vertical line there will intersect the g curve at y = 6.

and that's really it.

now we need to calculate it all in the main expression :

-6 × -2 - 6 × 6 = 12 - 36 = -24

you remember, that multiplications and divisions have to happen before any addition of subtraction ?

The solution of the given expression is 9*[tex]x^{4}[/tex]/100.

GIven an expression equal to 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].

We have to simplify the expression in which variable comes only once.

Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.

The given fraction is 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].

When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.

=27[tex]x^{4}[/tex]/300

Now divide numerator an denominator by 3.

=9[tex]x^{4}[/tex]/300

Hence the expression 27[tex]x^{12} /300x^{8}[/tex] will look like [tex]9x^{4} /100[/tex] after simplifying.

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Answer:

[tex]Simplify:\sqrt\frac{27x^{12} }{300x^{8} }[/tex]

[tex]O \frac{9}{100}x^{4}[/tex]

✔ [tex]\frac{3}{10} x^{2}[/tex]

[tex]O \frac{27}{300} x^{4}[/tex]

[tex]O\frac{9}{10} x^{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x^2+3x+2}{x^2-4x-5}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x^2+2x+x+2}{x^2-5x+x-5}[/tex]

[tex]\\ \rm\Rrightarrow {(x+2)(x+1)}{(x-5)(x+1)}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x+2}{x-5}[/tex]

And

[tex]\\ \rm\Rrightarrow \dfrac{x^2+7x+12}{x^2-3x-28}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x^2+4x+3x+12}{x^2-7x+4x-28}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{(x+4)(x+3)}{(x-7)(x+4)}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x+3}{x-7}[/tex]

The inequality graphed is the one in the first option.

On the graph we can see a solid parabola, the parabola opens downwards, and we can see that the vertex of the parabola is on the point (-1, 5).

And the shaded region is above the parabola.

Then the inequality is of the form:

y  ≥  parabola.

By knowing where is the vertex, we know that:

parabola = -a*(x + 1)^2 + 5

Then the correct option is the first one.

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Answer: A shift 16 units down

Step-by-step explanation:

See attached image.

The transformation of the function f(x) = x is (x, y) → (x + 16, y). This transformation is said to be the translation rule and the translation is 16 units towards the right.

The translation rule for a function f(x) is given by

(x, y) → (x + a, y + b)

Where a, and b are constant.

(x, y) → (x + a, y); translation towards right

(x, y) → (x - a, y); translation towards left

It is given that the function f(x) = x and g(x) = x - 16

So, the variation is

x - a = x - 16

⇒ - a = x - x - 16

∴ a = 16

Thus, the transformation is (x, y) → (x + 16, y)

Therefore, the transformation of the function f(x) = x is (x, y) → (x + 16, y) i.e., the translation of 16 units towards the right .

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The amount that Ross report as taxable income will be $31965.

Taxable income refers to the base upon which an income tax system imposes the tax.

In other words, the taxable income is the income over which the government imposed tax. It includes some or all items of income and is reduced by expenses and other deductions.

From the information:

Gross salary = $56,145

Interest earnings = $205

Dividend income = $65

Standard deduction = $12,000

Itemized deductions = $11,250

Adjustments to income = $1,200

The taxable income is given by:

= Gross salary + Interest earnings + Dividend income - Standard deduction - Itemized deductions - Adjustment to income

= 56145 + 205 + 65 - 12000 - 11250 - 1200

= $31965

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The net that represents a cube is (b) net b

A cube has 6 faces

This means that the net must have 6 faces

For a net to represent a cube, there must be four adjacent faces

And 2 two adjacent faces

Where

The net that represents the above scenario is net (b)

Hence, the net that represents a cube is (b) net b

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[tex]x {}^{2} - 9 = 8x \\ x {}^{2} - 8x - 9 = 0 \\ x = \frac{ - ( - 8) + \sqrt[]{( - 8) {}^{2} - 4(1)( - 9)} }{2( {1}^{}) } [/tex]

[tex]x = \frac{8 + \sqrt{64 + 36} }{2} = \frac{8 + \sqrt{100} }{2} = \frac{8 + 10}{2} = 9[/tex]

Answer: x = 9

Step-by-step explanation:

The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.

let x = a number

[tex]x^2-9=8x\\x^2-8x-9\\(x-9)(x+1)\\x-9 = 0\\x=9\\x+1=0\\x=-1[/tex]

taking only the positive solution, we get x = 9

answer

symbolic materials ?

Answer:

x = 117

Step-by-step explanation:

Foremost, we know that the three angles of the triangle always add up to 180 degrees.

So, there are two sides which are 27 degrees and 36 degrees, we need to find the third one's degree.

Add 27 and 36 (27 + 36 = 63)

Two sides equal 63.

Then, subtract 180 - 63 = 117

So the third angle's measurement is 117 degrees. The answer is 117.

To check, add 117 + 27 + 36 = 180

Hope it helps.

Answer:

d.

Step-by-step explanation:

Given a length [tex]l[/tex] and a width [tex]w[/tex], we can express the perimeter of a rectangle as [tex]2(l+w)[/tex].

Therefore the perimeter [tex]P[/tex] can be expressed as

[tex]2\times[(x-8)+(x-9)]\\=2\times(2x-17)\\=4x-34[/tex]

See below for the algebraic expressions of the scenarios.

The given parameters are:

Scenario 1

Represent the speed with x.

So, we have:

Speed = Distance/Time

The time is given as:

Time = 10 minutes

Since he did not stop at all;

The speed is

x = 2400/10

Multiply both sides by 10

10x = 2400

The above expression represents the scenario 1.

Scenario 2

Represent the speed with x, and time with t

So, we have:

Speed = Distance/Time

The time to reach halfway is given as:

Time = 6 minutes

He stopped for 1 minute, before continuing at the same initial speed

So, the total time it 13 minutes

The speed is represented as:

x = 2400/13

Multiply both sides by 13

13x = 2400

The above expression represents the scenario 2.

Scenario 3

Represent the speed with x, and time with t

So, we have:

Speed = Distance/Time

The time to reach halfway is given as:

Time = 6 minutes

He stopped for 1 minute, before continuing at twice the initial speed

So, the total time is

t = 6 + 1 + 1/2 * 6 minutes

t = 10 minutes

The speed is represented as:

x = 2400/10

Multiply both sides by 10

10x = 2400

The above expression represents the scenario 3.

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Answer:

no

Step-by-step explanation:

Answer:

Step-by-step explanation:

6(3x-5)≤2(9x+7)+10

divide by 2

3(3x-5)≤9x+7+5

3(3x-5)≤9x+12

divide by 3

3x-5≤3x+4

-5≤4

which is true.

Considering the Central Limit Theorem, we have that:

a) The probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.

b) The probability can be calculated, as the sample size is greater than 30.

It states that the sampling distribution of sample means of size n is approximately normal has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal or the sample size is greater than 30.

In this problem, the underlying distribution is skewed right, that is, not normal, hence:

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