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The length of TS  in ΔTRS using Similarity of triange is 12 cm .

If two items have the same shape or have the same shape as their mirror images, they are said to be Similar. One can be produced from the other more accurately by evenly scaling it, perhaps with the addition of further translation, rotation, and reflection.

If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be comparable (corresponding sides). Similar triangles may have varying individual side lengths, but they must have equal angles and the same scale factor or matching ratio of the side lengths. If two triangles resemble one another, then

In ΔTPQ and ΔTPS

∠T is common in both triangle

PQ ║ RS

∴∠TPQ = ∠TRS (Corresponding Angles)

similarly ,

∠TQP = ∠TSR

∴ Δ TPQ ~ ΔTRS

So,

PQ/ RS = TQ/ TS

⇒ 2/ 6 = 4 / TS

⇒TS = (4*6)/2  = 12

The length of TS  in ΔTRS using Similarity of triange is 12 cm .

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The length of TS  in ΔTRS using Similarity of triangel is 12 cm .

What is meant by length ?

In ΔTPQ and ΔTPS

∠T is common in both triangle

PQ ║ RS

∴∠TPQ = ∠TRS (Corresponding Angles)

similarly ,

∠TQP = ∠TSR

∴ Δ TPQ ~ ΔTRS

So,

PQ/ RS = TQ/ TS

⇒ 2/ 6 = 4 / TS

⇒TS = (4*6)/2  = 12

The length of TS  in ΔTRS using Similarity of triange is 12 cm.

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Answer:500

Step-by-step explanation:

take y + 2

x-3

Answer:

Undefined

Step-by-step explanation:

The function is defined in the domain (1, +∞)

Any value in the range of (-∞, 1] is undefined

The slope and y-intercept of the linear function y = -10x + 1 are -10 and (0,1) respectively.

The given linear function is y = -10x + 1.

The slope of a linear function is the coefficient of the x-term. In this case, the slope is -10.

The y-intercept of a linear function is the point at which the line crosses the y-axis. To find the y-intercept, we can substitute x = 0 into the equation and solve for y.

y = -10(0) + 1

y = 1

So, the y-intercept is (0,1).

Therefore, the slope and y-intercept of the linear function y = -10x + 1 are -10 and (0,1) respectively.

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The law of exponential and logarithmic function is that the logarithmic functions are the inverses of the exponential functions.

According to the first law, we can multiply two exponential functions with the same base by adding their respective exponents. According to the second law, the exponents must be subtracted in order to divide two exponential functions with the same base.

According to the third law, we must multiply the exponents in order to raise a power to a new power. According to the fourth and fifth laws, we must raise each factor to the same power in order to raise a product or quotient to that power.

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The total salary of Saul is given by the equation A = $ 1,740

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total salary of Saul be represented as A

Now , the equation will be

The basic monthly salary of Saul = $ 1,500

The total commission percentage of Saul = 4 %

The minimum amount of items to sell = $ 20,000

The amount of items worth sold = $ 26,000

So , the extra amount of items sold by Saul = 26,000 - 20,000 = $ 6,000

Now ,

The total salary of Saul A = basic monthly salary of Saul + ( commission percentage x extra amount of items sold by Saul )

Substituting the values in the equation , we get

The total salary of Saul A = 1,500 + ( 4 % x 6,000 )

On simplifying the equation , we get

The total salary of Saul A = 1500 + ( 4/100 ) x 6,000

The total salary of Saul A = 1500 + 240

The total salary of Saul A = 1,740

Hence , the total salary including the commission is $ 1,740

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A polynomial function that has zeros,

5 and -2+2i, is x² -x(3 +2i) +10(i - 1).

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

A polynomial function has zeros,

5 and -2+2i.

Firstly, we will write the zeros as factors of the polynomial,

(x-5) and (x +2 - 2i).

Now, multiply the factors,

⇒ x²+2x -2ix -5x -10 + 10i

⇒ x² -x(3 +2i) +10(i - 1)

Therefore, x² -x(3 +2i) +10(i - 1) is the required polynomial.

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b.  a = two-thirds, b = 0, c = 3 c is correct

We have to find the values of a, b, and c of the equation:

y = 2/3 x square + 3  (Given)

y = 2/3 x square + 3  which is in the form of y = ax square + bx +c

y = 2/3 x square + (0)b + 3

therefore, a = 2/3 , b = 0, c= 3

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1.59C + 2.25A = 786.75

C + A = 33    (even if all were the higher paying  adults, that would only be 33x2.25=74.25  far less than <<786.75)

1.59C + 1.59A = 33(1.59) = 52.47   subtract to eliminate C

     (2.25-1.59)A = 786.75 -52.47 = 734.28

       .66A = 734.28

            A = 73428/66 = 1112.55 = about 1113  adults

C = 33-1113 = -1080 children

which makes no sense.  over a thousand  "negative" children?  the public pool gave refunds to over a thousand prepaid children who didn't show up?  but a public swimming pool, no matter how large, probably wouldn't accomodate 1113 adults.

To calculate the mode in math is to place all the given set in order and calculate the number of times the number appears in the order, the number that appears for most of the time is the Mode.

A value or number that appears most frequently in a dataset is referred to as the mode. We might occasionally need to identify the value that appears more frequently in the dataset. In these situations, we determine the mode for the given collection of data. For a certain set of data, a modal value might or might not exist. There might not be any mode at all for data without any repeated values.

Mode = L+h [tex]\frac{(fm - f1)}{(fm - f1)+(fm - f2)}[/tex]

where,

L is the lower limit of the modal class

h is the size of the class interval

fm is the frequency of the modal class

f1 is the frequency of the class preceding the modal class

f2 is the frequency of the class succeeding the modal class

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Answer: The graph that could be the graph of f(x) is a parabola that opens upwards, with a vertex at (2,-4) and x-intercepts at x = -1 and x = 4. Since the degree of the polynomial function f(x) is 3 and the roots are -1, 0, and 4, the polynomial function is a cubic function and its graph is a parabola.

The roots of a polynomial function are the x-coordinates of the x-intercepts of the graph of the function. Therefore, since the roots of the equation f(x) = 0 are -1, 0, and 4, the graph of f(x) will have x-intercepts at x = -1 and x = 4.

The fact that the vertex is at (2, -4) mean that the parabola will open upwards and pass through the point (2, -4)

It's important to note that, if the polynomial function has a degree greater than 3, there may be multiple graphs that could represent the polynomial function, as long as they have the same roots.

Step-by-step explanation:

4(6x³ -2x² + 1) is the  polynomial expression  with GCF 4.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The polynomial expression is 24x³ - 8x² + 4

We have to write this polynomial expression in the factored from by taking GCF.

Rewrite 24 as 4×6

8 as 4×2

24x³ - 8x² + 4

4(6x³ -2x² + 1)

Hence, 4(6x³ -2x² + 1) is the  polynomial expression  with GCF 4.

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The slope of line 3x-7y=9 is 3/7.

The equation for the slope of a line and the points also called a point-slope form of the equation of a straight line is given by:

y − y₁ = m(x − x₁)

If P(x₁,y₁) and Q(x₂,y₂) are the two points on a straight line, then the slope formula is given by:

Slope,m = Change in y-coordinates/Change in x-coordinates

m=(y₂–y₁)/(x₂– x₁)

First, rewrite this to isolate y.

7y = 3x - 9

y = (3/7)x - (9/7)

In this form, the slope is given by the number multiplying the x, so the slope is 3/7

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Answer: Circle 3

Step-by-step explanation:

There are p plates, and 4 are unable to be used, so the expression is p - 4 = Circle 3

Answer:

c

Step-by-step explanation:

Because the number of plates on the table minus 4 saved for dessert mean p-4

The given expression is not an equivalent expression.

What is an equivalent expression?

An equivalent expression is a mathematical expression that has the same value as another expression, even though they may appear to be different. Equivalent expressions are obtained by using the same operations or by making substitutions that preserve the value of the expression.

The expressions -6z + (-5.5) and 3.5z - 5y - 2.5 are not equivalent. They have different coefficients for the variables z and y, and different constants. To determine if two expressions are equivalent, you need to check that they have the same value for all possible values of the variables. If the values are the same for all inputs, then the expressions are equivalent. If the values are not the same for all inputs, then the expressions are not equivalent.

Hence, the given expression is not an equivalent expression.

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It is option D (f-¹(x) = x-3/5)

The quotient of 3 and 15 is 0.2.

The division is breaking something up into equal parts. The Dividend is the whole we start with, the Divisor is what you use to divide up the whole, and the Quotient is the answer like this:

Dividend ÷ Divisor = Quotient

So if asked that, "What is the quotient of 3 and 15?" it means sense that 3 is the Dividend, 15 is the Divisor, and you want to know the Quotient. Thus, the answer is:

3 ÷ 15 = 0.2

Therefore, the quotient of the given question, 3 and 15, that is, 3 ÷ 15 is equal to 0.2.

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Answer:

Step-by-step explanation:From the issue, we may deduce that:

x + y = 50 She desires to produce 50 ounces of the combination (because to this).

(0.35x) + (0.60y) = 0.55(x+y) (because we're calculating the amount of salt in each solution and the combination contains 55% salt)

We may take the first equation and replace it in the second equation:

(0.35x) + (0.60y) = 0.55(50) (50)

0.35x + 0.60y = 27.5 when x is substituted.

A system of two equations with two variables is now available:

x + y = 50\s0.35x + 0.60y = 27.5

To determine one of the variables in terms of the other, we may utilize the first equation. Let's figure out y:

y = 50 - x

We now change y in the second equation to the following expression:

0.35x + 0.60(50-x) = 27.5

Finding the value of x:

0.35x + 30 - 0.6x = 27.5

0.25x= -2.5

x= -10

Since the number of ounces cannot be negative, the answer is illogical. As a result, you should double-check your calculations or determine if the issue statement contains a mistake.

To get the answer, you can also try an alternative approach like substitution or elimination. Then, double-check your calculations.

Answer:

  (x, y) = (2, 4)

Step-by-step explanation:

You want to solve the system of equations ...

There are numerous ways to solve this system of equations. One of the simplest is to use a graphing calculator. (See the attachment)

  (x, y) = (2, 4)

The second equation gives an expression for x that can be substituted into the first equation:

  y = -2(y -2) +8

  3y = 12 . . . . . . . . add 2y and simplify

  y = 4

  4-2 = x = 2

The solution is (x, y) = (2, 4).

The y-variable has a coefficient of 1 on the left side of the equal sign, so we can eliminate the y-variable by subtracting the second equation from the first.

  (y) -(y -2) = (-2x+8) -(x)

  2 = -3x +8 . . . . . . . . . . . simplify

  3x = 6 . . . . . . . . . . add 3x-2

  x = 2 . . . . . . . . divide by 3

  y = -2(2) +8 = 4 . . . . . substitute for x in the first equation

The solution is (x, y) = (2, 4).

Step 1: Think about this as four separate division questions:

     [tex]\dfrac{10c^3de^2}{2cde} =\dfrac{10}{2} \cdot \dfrac{c^3}{c} \cdot\dfrac{d}{d}\cdot \dfrac{e^2}{e}[/tex]

Step 2: Simplify each of the four, one at a time:

     [tex]\begin{aligned}\dfrac{10c^3de^2}{2cde} &=\dfrac{10}{2} \cdot \dfrac{c^3}{c} \cdot\dfrac{d}{d}\cdot \dfrac{e^2}{e}\\[0.5em]&=5 \cdot c^{3-1} \cdot1\cdot e^{2-1}\\[0.5em]&=5 c^{2} e\end{aligned}[/tex]

The angle between the ladder and the ground is decreasing at the rate of 1 ft/sec.

According to the question,

A sliding ladder of length let L=13ft.

Let the ladder touches the house at height h and touches the ground

x ft from the house. This is shown in the figure.

In ΔABC,

 θ = [tex]cos^{-1} \frac{AB}{BC}[/tex]

⇒ θ  = [tex]cos^{-1} \frac{x}{BC}[/tex]

⇒ dθ/dt= [tex]\frac{d}{dt} cos^{-1} \frac{x}{BC}[/tex]

⇒ dθ/dt=  [tex]\frac{-1}{\sqrt{1 - (\frac{x}{13} )^{2} } } \frac{1}{13} \frac{dx}{dt}[/tex]

substituting the value of x=12ft and [tex]\frac{dh}{dt} = 5ft/sec[/tex] , we have

⇒ dθ/dt= [tex]\frac{-1}{\sqrt{1 - (\frac{12}{13} )^{2} } } \frac{1}{13} (5)[/tex]

⇒ dθ/dt=  [tex]\frac{-1}{\frac{5}{13} } \frac{1}{13} (5)[/tex]

dθ/dt= -1

so the angle between the ladder and the ground is decreasing at the rate of 1 ft/sec.

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The complete question is:

A 13 ft. ladder is leaning against a wall when its base starts to slide away At the instant when the base is 12 ft. away from the wall, the base is moving away from the wall at the rate of 5 ft/sec. The rate at which the angle θ between the ladder and the ground is changing is -

Julio needs to prove that two sides of the two triangles are congruent, in addition to the hypotenuse and one set of legs that are already congruent, to use the SAS Triangle Congruence Theorem.

Congruence, in mathematics, a term employed in several senses, each connoting harmonious relation, agreement, or correspondence .Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout. Thus two triangles are congruent if two sides and their included angle in the one are equal to two sides and their included angle in the other.

This idea of congruence seems to be founded on that of a "rigid body," which may be moved from place to place without change in the internal relations of its parts. The position of a straight line (of infinite extent) in space may be specified by assigning four suitably chosen coordinates. A congruence of lines in space is the set of lines obtained when the four coordinates of each line satisfy two given conditions. For example, all the lines cutting each of two given curves form a congruence.

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Answer:

[tex]\boxed{41\;meters}[/tex]

Step-by-step explanation:

The flagpole, the shadow and the line connecting the tip of the shadow to the top of the flagpole construe a right-angle triangle with the flagpole and shadow being the legs of the triangle and the other the hypotenuse

Given flagpole height is 24 meters and shadow is 33 meters we can compute the third side using the Pythagorean Theorem for the hypotenuse:

[tex]c = \sqrt{a^{2} + b^{2}}[/tex]

Substituting known values we get
[tex]c = \sqrt{24^{2} + 33^{2}}\\\\c = \sqrt{576 + 1089}\\\\c = \sqrt{1665}\\\\c=40.804 \;meters[/tex]

Rounded to the nearest meter this would be 41 meters

The results of this question are listed below:

Herein we find a quadratic function that relates doll production and production cost, of which we must determine what quantity minimizes production costs. This can be done by transforming the equation into vertex form.  First, write the equation in standard form:

PC = 0.2 · t² - 8 · t + 500

Second, use algebra properties until vertex form is obtained:

PC = 0.2 · (t² - 40 · t + 2500)

PC = 0.2 · (t² - 40 · t + 400) + 0.2 · 2100

PC - 420 = 0.2 · (t - 20)²

Third, determine the critical point:

(t, PC) = (20, 420)

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The amount of money that Alex will use to purchase the 5 x 7 print would be = $11.89.

An online printing service is the service that is rendered online that helps interested individuals to prepare their printed paper works.

The number of 4 x 6 prints(X) purchased by Alex = 29

The number of 5 x 7 prints (y) purchased by Alex = 16

The total amount he paid for the whole service = $22.89

The cost of 5 x 7 prints can be calculated using this expression;

22.89 - 0.84 = 22.05/2 = 11.025

Therefore the cost of 5×7 prints = 11.05+ 0.84 = $11.89.

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Answer:

Step-by-step explanation:

y=5x(dollars per hour)+3(flat fee)

y=5x+3

Circle M has a center (h+d, k+e) and the radius is rs. Therefore, option C is the correct answer.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that, circle B has a center (h, k) and a raius of r. Circle B is translated d units to the right and e units up. Then it is dilated about its new center by a scale factor s resulting in a new circle

Translation rules:

When the shape is moved towards the right by k units, then replace x with x + k.

When the shape is moved up by k units, then replace y with y + k.

Now, (h, k)→(h+d, k+e) and the radius is rs.

Therefore, option C is the correct answer.

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Answer:

3(5a + 4)

Step-by-step explanation:

Given expression: 15a + 12

The common factor for both is 3.

Factorize:

=> 3(5a) + 3(4)

Take out the common factor: (3)

=> 3(5a + 4)

Answer:

3(5a+4)

Step-by-step explanation:

Firstly, find the highest common factor between 15a and 12, which is 3 and write it in brackets, which is:

3(5a+4)

The brackets are 5a+4 because 3×5a=15a and 3×4=12, which gives you the algebraic expression 15a+12