Find the four terms of the arithmetic sequence given the 13th term (a_{13}=-60) and the thirty third term (a_{33}=-160).Given terms: a_{13}=-60 and a_{33}= -160Find these terms:a_{14}= Answera_{15}= Answera_{16}= Answera_{17}= Answer

The equations of the parallel and perpendicular lines are y = −x−7 and y = x−13, respectively.

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Add both the equations

Substitute 2 for x in x+2y =8 to find y

The solutions to the equations are x=2 and y=3.

In order to add these two numbers, we need to add the algarisms that are in the same position.

Since the first number has 7 zeros and the second one has 8 zeros, the numbers 2 and 3 will not be added, since they are in different positions (the number 3 has more "value", since it's in a higher position).

So, adding these two numbers, we have:

Therefore the result of this sum is 320,000,000 (three hundred and twenty million).

The equation is (x+1)²-4.

Here the graph is in the form parabola, where the parabola is basically a graph for a quadratic function which is a  curve in such an order that a point on it is equidistant from a fixed point called the focus of the parabola,  and a fixed line called the directrix of the parabola. The general formula for a parabola is: y = a(x-h)² + k , where (h,k) signifies the vertex whereas the standard equation of a  parabola is y² = 4ax.

For the given graph the vertex is  (h,k)=(-1,-4)

so the equation for the parabola  is

=>y= a(x+1)^²-4 .......1

Since we can see the parabola intercept  at the x-axis at point (1,0), putting those in the above equation :

=>0=a(1+1)^2-4

=>4=a(2)^2

=>a=1

So, substituting the value of an in equation 1, we get

=>y= (x+1)^2-4

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Answer: (40, 28)

Step-by-step explanation:

(42+(-2), 33+(-5))=

(42-2, 33-5)=(40, 28)

The Solution:

Required:

To use the three theorems of similarity:

There are 3 theorems for proving triangle similarity:

AA Theorem

SAS Theorem

SSS Theorem

SAS Theorem

What happens if we only have side measurements, and the angle measures for each triangle are unknown? If we can show that all three sides of one triangle are proportional to the three sides of another triangle, then it follows logically that the angle measurements must also be the same.

SSS Theorem

Or what if we can demonstrate that two pairs of sides of one triangle are proportional to two pairs of sides of another triangle, and their included angles are congruent?

AA Theorem

As we saw with the AA similarity postulate, it’s not necessary for us to check every single angle and side in order to tell if two triangles are similar. Thanks to the triangle sum theorem, all we have to show is that two angles of one triangle are congruent to two angles of another triangle to show similar triangles.

If the volume of a rectangular prism with a height of 8 inches is 200 cubic inches and the base of the prism is a square, then the width of the rectangular prism is 5  inches

The volume of the rectangular prism = 200 cubic inches

The height of the rectangular prism = 8 inches

We know the volume of the rectangular prism = l×w×h

Where ls if the length of the base

w is the width of the base

h is the height of the rectangular prism

Given that the base of the prism is a square, then the length of the base is equal to width of the base

Consider

l = w = x

Substitute the values in the equation of volume

x × x × 8 = 200

[tex]x^{2}[/tex] × 8 = 200

[tex]x^{2}[/tex]  = 25

x = 5 inches

Hence, if the volume of a rectangular prism with a height of 8 inches is 200 cubic inches and the base of the prism is a square, then the width of the rectangular prism is 5 inches

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Answer:5.50 & $6

Step-by-step explanation:

Each bag of popcorn is $5.50 and the drink is $6.

Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks costing a total of $97.50. This will be:

9p + 8d = 97.50

Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of $51.50. This will be:

5p + 4d = 51.50

where P = popcorn

d = drink

The equations will be:

9p + 8d = 97.50

5p + 4d = 51.50

Multiply equation i by 5

Multiply equation ii by 9

45p + 40d = 487.50

45p + 36d = 463.50

Subtract

4d = 24

Divide.

d = 24/4

d = 6

Drink = $6

Since 9p + 8d = 97.50

9p + 8(6) = 97.50

9p + 48 = 97.50

9p = 97.50 - 48

p = $5.50

Popcorn cost $5.50.

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The expression given as [x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] simplifies to 0

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16]

Factorize the expression

So, we have

[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] = [(x + 4)(x + 1)]/[(x + 4)(x + 4)] - [(x - 4)(x + 1)]/[(x + 4)(x - 4)]

Simplify the common factors

So, we have

[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] = [(x + 1)]/[(x + 4)] - [(x + 1)]/[(x + 4)]

The terms of the above equation are the same

So, the result of subtracting one from the other is 0

This gives

[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] = 0

Hence, the value of the expression is 0

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Answer:

b

Step-by-step explanation:

The root at [tex]x=1[/tex] has a multiplicity of 1, and corresponds to a factor of [tex](x-1)[/tex].

The root at [tex]x=-2[/tex] has a multiplicity of 1, and corresponds to a factor of [tex](x+2)[/tex].

The root at [tex]x=3[/tex] has a multiplicity of 2, and corresponds to a factor of [tex](x-3)^2[/tex].

We will investigate how to determine the amount of money Mark started off with at the beginning off the day.

We will assume and declare a variable to Mark's bank balance at the beginning off the day:

Then mark sets out for movies and gets himself snacks to enjoy along his movies. The total receipt charged for his excursion is:

After his day expenses he will be left with a closing balance for the day. The closing balance of the day is expressed as:

We are given that mark was left with $12. This means:

Using the expression above we can write:

We will solve the above expression for initial balance ( P ) as follows:

Therefore, the answer is:

Let k be the number in the blank, so that:

Substract 7x from both sides:

These two equations are equivalent regardless the value of x. We can change the conclusions that we may obtain by choosing different values for k.

Then, the equation:

Is true for no values of x.

If we want the equation to be false regardless of the value of x, then set k so that -k is different from 3. For example, set k=0:

Since this is contradictory, then there are no values of x that make the equation true.

If we want the equation to be true for all values of x, then 3=-k must be an identity. Then, let k=-3:

Then, the equation:

Is true for all values of x.

If we want the equation to be true for only one value of x, we have to bring back x into the equation 3=-k. So, we can take k=x. This way, we would have:

In three dimensions, the cross product of two vectors is defined as shown below

Then, solving the determinant

In our case,

Where we used the formula for AxB to calculate ixj.

Finally,

Thus, (i+j)x(ixj)=i-j

We are given the following two functions

Recall that the rule for reflection over the y-axis is given by

As you can see, the graph of g(x) will be a reflection over the y-axis of the graph f(x).

Recall that the rule for vertical translation (upward) is given by

The above translation will shift the graph vertically upward by d units.

For the given case, d = 1

As you can see, the graph of g(x) will be a vertical translation of the graph f(x)

Therefore, we can conclude that the graph of g(x) will be a reflection over the y-axis and a vertical translation of the graph f(x).

1st option is the correct answer.

For a 90 degrees counterclockwise rotation of a point, (x, y) about the origin, the new position would be (- y, x)

Thus,

For A', it becomes (- - 1, 1) = (1, 1)

For B', it becomes (- - 2, 4) = (2, 4)

For C', it becomes (- - 4, 2) = (4, 2)

we have the expression

we know that

Applying PEMDAS

P ----> Parentheses first

E -----> Exponents (Powers and Square Roots, etc.)

MD ----> Multiplication and Division (left-to-right)

AS ----> Addition and Subtraction (left-to-right)

solve Multiplication First

5x5x6x8=1,200

9x524x8x6=226,368

725x6=4,350

substitute

1,200-6x226,368+9-4,350

solve

6x226,368=1,358,208

1,200-1,358,208+9-4,350

Solve the addition and subtraction

1,200-1,358,208+9-4,350=-1,361,349

The image of the point (5, 4) after being rotated 270 degrees clockwise around the origin is (- 4, 5).

In this problem we find the case of a point to be rotated by a rigid transformation, represented by a rotation around the origin. The transformation rule is defined by the following expression:

P'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

If we know that P(x, y) = (5, 4) and θ = - 270°, then the coordinates of the image are, respectively:

P'(x, y) = (5 · cos (- 270°) - 4 · sin (- 270°), 5 · sin (- 270°) + 4 · cos (- 270°))

P'(x, y) = (- 4, 5)

The image of the point (5, 4) is (- 4, 5).

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First, let's find the measure of the third side, using the law of cosine:

Now, let's use Heron's formula to calculate the area:

The smallest positive integer Joelle could have multiplied 756 by

15876

This is further explained below.

Generally, A perfect square number is a number in mathematics that, when its square root is calculated, yields a natural number.

To solve this problem we can do:

[tex]\sqrt{756}[/tex]

By properties of roots

[tex]\begin{aligned}&\sqrt{756}=\sqrt{6\cdot126} \\&=\sqrt{6 * 6 * 21} \\\\ =\sqrt{6^2 * 21} \\&=6 \sqrt{21}\end{aligned}[/tex]

So, so that the multiplication of 756 by an integer becomes a perfect square, you have to multiply it by 21 to make $21^2$ and thus "eliminate" the root.

756 * 21=15876

In conclusion,  You can verify that 15876is a perfect square since root (15876)=132 and 132 is a natural number

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To create the abbreviated expression, combine similar terms by adding them all together. If the expression be [tex]$\sqrt{112 x^{10} y^{13}}$[/tex] then expression exists [tex]$4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex].

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Start by recognizing the like terms, or terms with the same variables and exponents, in algebraic formulas. Then, to create the abbreviated expression, combine similar terms by adding them all together.

Let the expression be [tex]$\sqrt{112 x^{10} y^{13}}$[/tex]

separating the roots of the expression, we get

[tex]$\sqrt{112 x^{10} y^{13}}=\sqrt{112} \sqrt{x^{10}} \sqrt{y^{13}}$[/tex]

simplifying the above equation, we get

[tex]$=\sqrt{112} \sqrt{x^{10}} \sqrt{y^{13}}$[/tex]

Simplify [tex]$\sqrt{x^{10}}= x^5$[/tex]

[tex]$=\sqrt{112} x^5 \sqrt{y^{13}}$[/tex]

Simplify [tex]$\sqrt{y^{13}}=y^6 \sqrt{y}$[/tex]

[tex]$=\sqrt{112} x^5 y^6 \sqrt{y}$[/tex]

[tex]$=\sqrt{112}=4 \sqrt{7}$[/tex]

[tex]$=4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex]

Therefore, the correct answer is [tex]$4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex].

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Based on this poll, we are 95% confident that between 23% (lower limit) and 31% (upper limit) of U.S. adults feel that access to health care is the most urgent health-related problem.

The lower limit is the lowest percentage of poll participants who choose access to health care as the most urgent health-related problem.

The upper limit is to the highest percentage of poll participants who choose access to health care as the most urgent health-related problem.

Using the lower and upper limits, the Gallup poll can confidently estimate the range of the poll participants who pin-pointed access to health care as the most urgent.

Mean responses who choose access = 27%

Margin of error = ±4

Lower Limit = µ - margin of error

= 27% - 4%

=23%

Upper Limit = µ + margin of error

= 27% + 4%

=31%

Thus, at a 95% confidence level, the Gallup poll can claim that 27% ±4% of poll participants rated access to health care as the most urgent issue.

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sin theta = -0.5 degrees

cos theta=-0.86 degrees

hope it helped

Given:

To Determine: The standard form equation of an ellipse

Solution

The required sample size, using the z-distribution, is given as follows:

n = 253.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The equation for the margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 95%, hence the critical value z has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate and the margin of error are given as follows:

[tex]\pi = 0.22, M = 0.015[/tex]

Hence the required sample size is calculated as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.015 = 1.96\sqrt{\frac{0.015(0.985)}{n}}[/tex]

[tex]0.015\sqrt{n} = 1.96\sqrt{0.015(0.985)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.015(0.985)}}{0.015}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.015(0.985)}}{0.015}\right)^2[/tex]

n = 253. (rounding up, as a sample size of 252 would result in a margin of error slightly above 1.5%).

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Answer:

12

Step-by-step explanation:

The GCF of 12 and 24 is 12. To calculate the most significant common factor of 12 and 24, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; characteristics of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the most significant factor that exactly divides both 12 and 24, i.e., 12.

The given system of equations : 6x - y = 2 and 4x - y = -8.

6x - y = 2 ( 1 )

4x - y = -8 ( 2 )

for the value of y, use substitution method:

Solve the equation (1) for y :

6x - y = 2

y = 6x - 2

Susbtitute the value of y in the equation ( 2 )

4x - y = - 8

4x - (6x - 2) = - 8

4x - 6x + 2 = - 8

4x -6x = - 8 - 2

-2x = -10

Divide both side by ( -2)

-2x/(-2) = -10/(-2)

x = 5

Substitute x = 5 in the equation ( 1 )

6x - y = 2

6( 5 ) - y = 2

30 - y = 2

y = 30 - 2

y = 28

So, the value of y is 28

Answer : y = 28

Answer: Maximum height reached is 804.88 m

Step-by-step explanation:

At maximum height velocity is zero

We have equation of motion v² = u² + 2as

    Initial velocity, u = 320 ft/s = 97.536 m/s

    Final velocity, v = 0 m/s    

    Acceleration, a = -9.81 m/s²

    Substituting

                     v² = u² + 2as

                     0² = 97.536² + 2 x  -9.81 x s

                     s = 484.88 m

   So the arrow further a height of 484.88 m

Total height = 320 + 484.88 = 804.88 m

a = 1/2bh, solve for b

that means -----> isolate the variable b

so

therefore

the answer is

General equation of line:

Where,

Slope of line is -2 then:

Equation of line is y=-2x+5