13. In the figure, PSR is a straight line. Find RSQ and PQS.

The equation of the parabola is f(x) = 7(x-3)^2+5.

Given:

The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.

If the parabola has same shape then its a values are same.

so f(x) = 7x^2

here a = 7

so the equation with vertex (3,5) also has a value is 7.

(h,k) = (3,5)

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

= 7(x-3)^2 + 5.

Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.

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Answer:

t=0

Step-by-step explanation:

Your equation would be 324=-16t^2+324 since 370-46 is 324. subtract each side by 324 and you get 0=-16t^2. t=0

The total cost of his order of DVDs will be $32.23.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Samuel orders four DVDs from an internet-based music store. Every DVD costs $9.97. He has a 25% markdown code, and the deal charge is 7.75%.

The cost of DVDs after discount will be given as,

⇒ 4 x $9.97 x (1 - 0.25)

⇒ $29.91

The cost of DVDs after tax will be given as,

⇒ $29.91 x (1 + 0.0775)

⇒ $32.23

The total cost of his order of DVDs will be $32.23.

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Answer:

Yes it is

Step-by-step explanation:

Every new number is 3 less than the last number

n-3

Answer:

Yes, -3

Step-by-step explanation:

An arithmetic sequence is when the numbers in the sequence are subtracted or added by the same value everytime to get the next number. (NOT multiplied or divided, if it's that then it's a geometric sequence)

from 36 to 33, we can see the change is -3
from 33 to 30, it's also -3
from 30 to 37, it's also -3

The common difference is the difference between the two consecutive terms in the sequence, which is -3

Since it's subtracting or adding by the same value everytime to obtain the next value, this sequence is an arithmetic sequence, and the common difference is -3

The value of x is 25

What is congruent polygons ?

A polygon is said to be congruent if it has the same shape as the polygon it is compared to, as well as the identical side lengths and interior angles. In order to meet the condition, congruent shapes must all have the same kind of shape. Because they are different shapes, a rectangle and a pentagon cannot be congruent.

Two squares or two hexagons can be considered congruent polygons since they both have equal-length sides and angles. However, it's crucial to keep in mind that the length of the sides must also be equal. A square is not congruent if it is larger than another square.

1. Pairs of congruent corresponding parts

 ∠A = ∠C     AB = CD

 ∠B = ∠D    AH = CF

 ∠H = ∠F    HG = FE

 ∠G = ∠E    GB = ED

To find the value of x

4x + 5 = 105

4x = 105 - 5

4x = 100

 x = [tex]\frac{100}{4}[/tex]

    = 25

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Based on the amount that she paid in the first month, the amount Ronda will pay for the next month is $396.

When a loan is amortized, it means that one can pay it off by paying the same amount every period until they would have paid off both the loan and the associated interest.

The amortized amount contains:

A portion going towards the principal(debt )

A portion going towards the interest accumulated.

In conclusion, as the amount is the same every time, Ronda will have to pay the same amount of $396 the next month.

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Answer: m (slope) = 3

Step-by-step explanation: Slope Solution

m=rise run=ΔyΔx

m=y2−y1x2−x1

m=8−53−2

m=31

m = 3

Point Slope Form

y−y1=m(x−x1)

y−5=3(x−2)

Slope Intercept Form

Find the Equation of the Line:

y=mx+b

by solving for y using the Point Slope Equation.

y−y1=m(x−x1)

y−5=3(x−2)

y−5=3x−(3×2)

y−5=3x−6

y=3x−6+5

y=3x−1

m=3

b=−1

Hope this helps :)

The standard form of  (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

The expression given is (3x10^199)+(2*10^201) we need to write it in the standard form

Take 10^199 from the equation

=10^199((3x1)+(2x10^2))

=10^199(3+(2x100))

=10^199(3+200)

=10^199(203)

=203x10^199

2.03 x 10^201

1. there are 201 zeros after 2 and 199 zeros after 3

2. difference  between  201 and 199 is 2

3. on adding both of them the 3 will come 2 spaces to the right of 2

The value of (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201

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An equation for the nth term of the arithmetic sequence is aₙ=a+(n-1)d and a₁₀ of sequence -3,-1,1,3 is 15.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given,

-3,-1,1,3 is a sequence.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

We know that nth term of arithmetic sequence is aₙ=a+(n-1)d

-3,-1,1,3

First term a=-3

Common difference d=-1-(-3)=-1+3=2

We need to find the 10th term

a₁₀=-3+(10-1)(2)

a₁₀=-3+9(2)

a₁₀=-3+18

a₁₀=15

Hence,  an equation for the nth term of the arithmetic sequence is aₙ=a+(n-1)d and a₁₀ of sequence -3,-1,1,3 is 15.

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The solution to the inequality 4x + 6 ∠ -6 is x ∠ -3

inequality shows the relationship between two values in an algebraic expression that are not equal. Inequality signs can indicate that one variable of the two sides of the inequality is greater than, greater than or equal to, less than, or less than or equal to another value.

4x + 6 ∠ -6

taking 6 to the right hand side of the inequality

4x < -6 -6

4x < -12

divide both sides by 4

x < -12/4

x < -3

In conclusion, x < -3 is the solution to the Algebraic expression above.

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For 8 pounds of weight, the charges be the same for both the companies.

Given, that To ship an overnight package

Shipping Company A charges $14 plus $2.25 per pound

Shipping Company B charges $20 plus $1.50 per pound

Let, the weight be w

And the cost of shipment by company A & B be A(w) & B(w) respectively.

According to the question,

A(w) = 14 + 2.25w

B(w) = 20 + 1.50w

Now, when charges be the same

A(w) = B(w)

14 + 2.25w = 20 + 1.50w

On subtracting 1.50w on both the sides, we get

14 + 2.25w - 1.50w = 20 + 1.50w - 1.50w

14 + 0.75w = 20

Now on subtracting 14 on both the sides, we get

14 + 0.75w - 14 = 20 - 14

0.75w = 6

On dividing both the sides by 0.75, we get

0.75w/0.75 = 6/0.75

w = 8

Hence, weight = 8 pounds.

For 8 pounds of weight, the charges be the same for both the companies.

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The graph of the quadratic equation with axis of symmetry x = - 2 is shown in figure.

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The function is,

⇒ f (x) = - 3 (x + 2)² + 1

Now,

We know that;

If the function is of the form y = a (x - h)² + k;

Then, The vertex = (h, k)

And, Axis of symmetry is, x = h

Here, The function is,

⇒ f (x) = - 3 (x + 2)² + 1

⇒ f (x) = - 3 (x - (- 2))² + 1

By comparing we get;

h = - 2 , k = 1

So, Vertex of the function = (- 2, 1)

And, Axis of symmetry is;

⇒ x = - 2

Thus, The graph of the quadratic equation with axis of symmetry x = - 2 is shown in figure.

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Answer:

0.302

Step-by-step explanation:

Answer: 0.302

Step-by-step explanation:

The solution set for the pair of inequalities as given in the task content is; (-∞, -4) U (11, ∞).

It follows from the task content that the solution set of the pair of inequalities is to be determined.

Therefore, each inequality can be solved as follows;

-13 > 2x - 5;

-13 + 5 > 2x

-8 > 2x

-4 > x.

Also, the inequality 2x - 5 > 17 can be solved as follows;

2x > 17 + 5

2x > 22

x > 11.

Therefore, the solution set of the inequalities as given in the task content in interval notation is;

(-∞, -4) U (11, ∞).

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The expression that is equivalent is y(x + 2) and xy + 2y and x(x + y + 2) and  x² + xy + 2x

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Now, let's check if the expression are equivalent by simplifying it.

y(x + 2) and xy + 2y

xy + 2y and xy + 2y

Therefore, the expressions are equivalent.

x(x + y + 2) and  x² + xy + 2x

x² + xy + 2x and x² + xy + 2x

They are equivalent expression.

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Answer:

x,y [tex]( \frac{2}{61})(\frac{91}{61} )[/tex]

The required equation for height H of the plant t months after Angel bought the plant is,

H = 15 + 3t

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

t = time in months

H = total height

H= initial height+ rate of growth * time

H = 15 + 3t

So, the required equation for height H of the plant t months after Angel bought the plant is,

H = 15 + 3t

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An equation for a line that is parallel to the y - axis, based on the options, is B.x = −8.

The y - axis is a vertical line which runs straight through the x - axis. This means that the coordinates of the y - axis are expressed in terms of 0. The y - axis intercepts the x - axis at point 0 which is why the coordinates are:

x = 0

Any line that is parallel to the y - axis will therefore be expressed in terms of x as well. The equation for a line that is parallel to the y - axis is therefore:
x = -8

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Domain of the function is,  (0, ∞).

Range of the function is, (-∞, ∞).

x - intercept of the function is, (1, 0).

Vertical asymptote of the function is,  None.

What is domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

First to find the domain of the function,

Since, all input values shown on the x-axis make up a graph's domain.

We can see that values of x values are from 0 to ∞.

Hence, the domain is (0, ∞).

Now to find the range.

Since, the y-axis on a graph represents the possible output values, or range.

The y - axis having the values from -∞ to ∞.

Hence, the range of the function is, (-∞, ∞).

x - intercept is the point where function crosses the x - axis.

Here function crosses x - axis at (1, 0).

Hence, the x - intercept is (1, 0).

A graph's vertical asymptote is the vertical line at x = a where the graph trends toward positive or negative infinity as the inputs go closer to a.

So, the vertical asymptote is x = 0.

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The mean number of new subscribers per month during that year is 242000.

A mean simply means the average of the numbers given.

The number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003.

The mean number of new subscribers will be:

= Change in numbers / Number of years

= (1393000 - 1151000) / 1

= 242000 / 1

= 242000

Therefore, the mean is 242000.

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Answer: Part A : it is a function

Step-by-step explanation: once its on a graph it will only cross the line once

The ratio of 2 meters to 76 centimetres is 50: 19.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

In simpler terms, a ratio compares values.

Let's find the ratio of 2 meters to 76 centimetres as follows:

We have to first convert the units so they will be same.

Hence,

1 cm = 0.01 m

76 cm = ?

cross multiply

length in metres = 76 × 0.01

length in metres = 0.76 metres

Therefore, let's multiply the 2 units by 100.

0.76 × 100 = 76 metres

2 × 100 = 200 metres

In ratio, 200 : 76 will be simplified as 50 : 19

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The probability that a woman has a malignant tumor in her breast is 7.5%. ie 75

Let  + = mammogram result is positive

B = tumor is benign

M = tumor is malignant.

Note that Bc = M.

given that P(M) = .01,

so P(B) = 1 − P(M) = 0.99.

We are also given the conditional probabilities

P(+ | M) = .80 and

P(− | B) = .90, where the event − is the complement of +

P(+ | B) = .10

Bayes’ formula:-

P(M | +) = P(+ | M) P(M) / (P(+ | M)P(M) + P(+ | B)P(B))

= 0.80 × 0.01 / (0.80 × 0.01 + 0.10 × 0.99)

=0.075

So the chance would be 7.5%. ie 75

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Answer:-10.25

Step-by-step explanation:

Just because ;) -10.25= -10.00

Answer:

-10

Step-by-step explanation:

Estimate between the two numbers?

Add them together first

Which equals -10.25

The closest would be -10

Answer:

Step-by-step explanation:

Answer: The paintbrush will be your magic wand for weaving colors across the canvas. Artist paint brushes become beloved tools the more you use them! As you paint, you will become increasingly familiar with the way the brushes handle the paint and what they can accomplish for you. Pretty soon the paintbrush will become a part of you that you intuitively know how to maneuver.

If you're just starting out in acrylics, it can be a bit overwhelming standing in the paintbrush aisle at the art store, with a vast sea of artist paint brushes spread out before you. The wide selection even makes me dizzy sometimes!

Step-by-step explanation:

Answer: ∠B≈39.81°

Step-by-step explanation:

[tex]\displaystyle\\tg\angle B=\frac{AC}{BC} \\\\tg\angle B=\frac{5}{6} \\\\\angle B=arctg\frac{5}{6} \\\\\angle B\approx39.81^0[/tex]

To find: Equation of line parallel to 5x + 3y = -21 and passes through the point (-9, -3)

Solving the given 5x + 3y = -21 for 3y yields  3y = -5x - 21.  

Dividing all three terms by 3, we get:

y = (-5/3)x - 7, indicating that the given line has slope -5/3.

The slope of a line perpendicular to this y = (-5/3)x - 7 is 3/5, the negative reciprocal of -5/3.

Start with y = mx + b

Substitute -3 for y, -9 for x, and 3/5 for m

We get,

-3 = (3/5) (-9)  + b

∴  b   = 5/9

Thus, the equation is y = (3/5)x + 5/9 is the required equation of a line parallel to 5x+3y=−21 that passes through the point (-9,-3)

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The perimeter of the rectangle is =  48cm

Acc to our question-

Hence,The perimeter of the rectangle is =  48cm.

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