Which postulate proves the two triangles are congruent

The side lengths of RS and PR are 12 units

Similar triangles are triangles whose corresponding sides are in proportion to one another.

In most cases, one triangle is dilated to form the other triangle

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The corresponding triangles are given as:

PQR and PSQ

This means that

PQ corresponds to PS

PR corresponds to PQ

QR corresponds to QS

Where

PQ = 18

QR = 14

QS = 21

So, we have:

PR : QR = PQ : QS

This gives

PR : 14 = 18 : 21

Express as fraction

PR / 14 = 18 / 21

Multiply through by 14

PR = 14 * 18 / 21

Evaluate

PR = 12

The corresponding triangles are given as:

PQR and PSQ

This means that

PQ corresponds to PS

PR corresponds to PQ

QR corresponds to QS

Where

PQ = 18

QR = 14

QS = 21

So, we have:

RS = PR

This gives

RS = 12

Hence, the side lengths of RS and PR are 12 units

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[tex]a)2x - 3 = 19 \\ = > 2x = 19 + 3 \\ = > x = \frac{22}{2 } \\ = > x = 11 \\ b)3x + 2 = 18 \\ = > 3x = 18 + 2 \\ = > 3x = 20 \\ = > x = \frac{20}{3} \\ = > x = 6.66666667 \\ c)4x - 4 = - 4 \\ = > 4x = - 4 + 4 \\ = > x = \frac{0}{4} \\ x = 0 \\ d)5x + 1 = 10 \\ = > 5x = 10 - 1 \\ = > 5x = 9 \\ = > x = \frac{9}{5} \\ x = 1.8[/tex]

therefore 1.8 =2 or x is not equal to 2

A scale factor of 2 would be the perfect scale for the scale drawing.

We are given original dimensions of  tech fingerboard as;

Length = 100 mm

Width = 25 mm

Now, from conversions we know that;

1 inch = 25.4 mm

Since Giovanni wants to make a larger scale drawing on an 8 1/2 inch by 11-inch piece of paper, then we can say that;

11-inch = 25.4 * 11 = 279.4 mm

8 1/2 inch = 8 1/2 * 25.4 = 215.9 mm

Thus;

New Length/old length = 279.4/100 = 2.794

Since that is the maximum scale for the drawing paper, then we can say that something lesser like a scale factor of 2 would be the perfect scale for the scale drawing.

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Median, mean, mode, first and third quartiles describe a statistical distribution because these are the measures of central tendency and dispersion of a distribution.

Median, mode and mean are known as the measures of central tendency of a statistical distribution. Because these three can even represent the whole data and its properties. Mean, median and mode gives the central value around which the whole distribution lies or its representative value.

Mean: It gives the average value of the distribution. That is the Total value/ Total number of values.

Median: It is a positional average and it is the middle value of the observations in a distribution.

Mode: Mode is also a positional average which gives the most repeated or frequent observation from the distribution

Now the first and third quartiles are measures of dispersion. It gives the variation of data values from the central value. It gives an idea of the scattering of the distribution around the central value.

First quartile: If the n observations are arranged in ascending order, then the n/4th value is the first quartile.

Third Quartile: It is the 3n/4th value in the ordered n observations.

These two are used to measure the quartile deviation from the central value. If the dispersion is large, then the measures of central tendency cannot be a representative value of the distribution.

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Answer:

5 trips

Step-by-step explanation:

330 people / 68 spots = 4.853

Because passengers cannot take 0.853 of a bus, it rounds up to 5.

With regard to all the different sources of caffeine, it really is estimated that 80 percent of Americans frequently consume caffeine in some way, with an average daily intake of 200–250 mg.

A methylxanthine class stimulant, caffeine stimulates the central nervous system. It is employed as a cognitive enhancer to improve alertness and attentional function. In order to increase the release of the neurotransmitters acetylcholine, caffeine works by preventing adenosine from binding to the adenosine A1 receptor.

Because caffeine is a stimulant, it makes your nervous system and brain work harder. Additionally, it causes a greater flow of hormones like cortisol and adrenaline throughout the body. Caffeine can help you feel energized and alert in small doses.

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I understand that the question you are looking for is:

Considering all the various sources of caffeine, it is estimated that 80 percent of Americans regularly use caffeine in some form, and that the average intake is ______ per day.

Answer:

2 is the factor i think

Step-by-step explanation:

can i get a brainlist?

Applying the exterior angle theorem, the value of s in the triangle is: 74.

In the image shown above, the angles, s - 44° and s° are interior opposite angles to the exterior angle of the triangle that is given as s + 30°.

Based on the exterior angle theorem, the sum of s - 44° and s° is equal to s + 30°.

Therefore:

s - 44 + s = s + 30 [exterior angle theorem]

Combine like terms

2s - 44 = s + 30

2s - 44 - s = s + 30 - s [subtraction property of equality]

s - 44 = 30

s - 44 + 44 = 30 + 44 [addition property of equality]

s = 74

Therefore, applying the exterior angle theorem, the value of s in the triangle is: 74.

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Answer:

student is not correct

Step-by-step explanation:

3 1/5 ÷ 1/7 = 22/5

the mistake the student made was multiplying rather than dividing

Answer: 14 ==> 3rd option

Step-by-step explanation:

The median is the middle value of a set of ordered numbers. Since this set of numbers from 8 to 20 are already ordered, the median would be the average number between 8 and 20.

(8+20)/2=

28/2=14 ==> 3rd option

Answer:

[tex]\mathsf e^{t-1}[/tex]

Step-by-step explanation:

Definition of an inverse function

[tex]\textsf {A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\:[/tex]

In order to find the inverse of p(t) = 1 + ln(t)...

The odds against selecting an ace when a card is drawn from a standard deck of cards is 12:1.

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Using composition formula we get the value of x is 9/16 for G(H(X)) = 32x - 18

In mathematics, composing a function is the process by which two functions, f and g, produce a new function, h, such that h(x) = g(f(x)). This indicates that the function of g is being applied to the function of x. In essence, a function is then applied to the outcome of another function.

We F (2x-18) and G (4x)

By using the composition formula

H(x) = g(f(x))

That is

H(x) = g(2x-18)

      = 2(4x) - 18

      = 8x - 18

If H(x) = 8x - 18

Then, G(H(x))

⇒ G(8x - 18)

⇒ 8(4x) - 18

⇒ 32x - 18

Now, we find x in G(H(x))

⇒ 32x - 18 = 0

⇒ 32x = 18

⇒ x = 18/32

⇒ x = 9/16

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Applying the tangent ratio, the length of side x, in simplest radical form is: 8√3.

The tangent ratio is: tan ∅ = opposite side length / adjacent side length of the right triangle.

Given the following:

Reference angle (∅) = 30 degrees.

Opposite side length = 8

Adjacent side length = x = ?

Using the tangent ratio, we have: tan 30 = 8/x

x(tan 30) = 8

Divide both sides by tan 30

x(tan 30)/tan 30 = 8/tan 30

x = 8/tan 30

x = 8/1/√3

x = 8 × √3

x = 8√3

Therefore, applying the tangent ratio, the length of side x, in simplest radical form is: 8√3.

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The slope of the line shown is -2/5

The formula for calculating the slope of a line is expressed according to the formula

Slope = Rise/Run

Slope = y₂-y₁/x₂-x₁

Using the coordinate point (0,7) and (5, 5)

Slope = 5-7/5-0
Slope = -2/5

Hence the slope of the line shown is -2/5

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Step-by-step explanation:

2 hours a day for M-Th would be 8 hours. Sunday >up to< 3 hours. In 1 week, you'd have the 4 days ×2hrs ea day plus the 3hrs from Sunday... In one week she (assuming she did the full 3hrs) would have done 11hrs of piano practice. Not sure completely what to do but that's my first part that I do to figure it out if that helps any...

Answer:

1. 3

2. 42.9

Step-by-step explanation:

1. 180 - 177 = 3

2. 90 - 47.1 = 42.9

Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. Anais uses 58 inches of ribbon to trim the curtains.

Given that:

Anais bought  of ribbon

And she had 2 feet 8 inches left after trimming some curtains.

The first thing to do is to convert all units to inches;

From standard conversion rate.

1 yard  = 36 inches

As such   of ribbon in inches will be:

= 5 × 18 inches

= 90 inches of ribbon bought.

Similarly, since 1 foot  = 12 inches.

The amount of curtains left after trimming is:

= ( ( 2 × 12 ) + 8 )inches

= (24 + 8) inches

= 32 inches

If Anais bought 90 inches of ribbon and she had 32 inches of ribbon left after trimming some curtains.

It implies that the number of inches of ribbon that Anais used is:

= 90 inches - 32 inches

= 58 inches

Answer:

y = - 2x + 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x - 1 ← is in slope- intercept form

with slope m = - 2

• Parallel lines have equal slopes , then

y = - 2x + c ← is the partial equation of the parallel line

to find c substitute (4, 3 ) into the partial equation

3 = - 8 + c ⇒ c = 3 + 8 = 11

y = - 2x + 11 ← equation of parallel line

Answer:

x = 5

Step-by-step explanation:

7/17 = x/12

17x = (7)(12)

17x/17 = 84/17

     x = 5

The volume of the Parallelepiped with adjacent edges pq, pr,and ps = 136

Geometrically, the Scalar triple product:

[tex]{\displaystyle \mathbf {a} \cdot (\mathbf {b} \times \mathbf {c} )} \mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})[/tex]

is the (signed) volume of the parallelepiped defined by the three vectors given. Here, the parentheses may be omitted without causing ambiguity, since the dot product cannot be evaluated first. If it were, it would leave the cross product of a scalar and a vector, which is not defined.

Given three vectors, there is a product, called scalar triple product, that gives , the volume of the parallelepiped that has the three vectors as dimensions.

So,

Given : p(-2,1,0) , q(3,4,3), r(1,4,-1), s(3,6,4).

pq =  ( -2-3 ,1-4 ,0-3) = (-5,-3,-3)

pr= (-2-1, 1-4, 0+1) = (-3,-3,1)

ps= ( -2-3, 1-6, 0-4) = (-5,-5,-4)

pq = (-5  ,  -3  , -3)

pr = (-3,  -3,  1)

ps= (-5,  -5,  -4)

The scalar triple product is given by the determinant of the matrix (3×3)

that has in the rows the three components of the three vectors:

[tex]\left[\begin{array}{ccc}-5&-3&-3\\-3&-3&1\\-5&-5&-4\end{array}\right] \\\\-5(12+5)-3(12+5)-3(15-15)\\-5(17)-3(17)-3(0)\\-85-51\\-136\\[/tex]

So, The volume never be negative then by applying vector

v = |-136|

v= 136

the volume of the parallelepiped with adjacent edges pq, pr,and ps = 136

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Answer: k(8z - 2)=448z^2-224z+35

z(q^2)​=-10q^4 - 5

Step-by-step explanation:

k(z) = 7z^2 + 7

k(8z - 2)=7(8z - 2)^2 + 7

k(8z - 2)=7(8z - 2)(8z - 2) + 7

k(8z - 2)=7(64z^2-16z-16z+4) + 7

k(8z - 2)=7(64z^2-32z+4) + 7

k(8z - 2)=7(64z^2-32z+4+1)     ==> 7*1=7, so +1 is added in parentheses while +7 is removed outside of parentheses.

k(8z - 2)=7(64z^2-32z+5)

k(8z - 2)=448z^2-224z+35

z(q) = -10q^2 - 5

z(q^2)​=-10(q^2)^2 - 5

z(q^2)​=-10(q^(2*2)) - 5

z(q^2)​=-10q^4 - 5

The final step of the given inequality is x < 3. Therefore, option C is the correct answer.

The given inequality is -2(5 - 4x) < 6x - 4.

We need to solve and write the final step of the given inequality.

Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The inequality -2(5 - 4x) < 6x - 4 can be solved as follows:

⇒ -10 + 8x < 6x - 4

⇒ -10 + 8x-8x < 6x - 4-8x (Subtract 8x on both the side of the inequality)

⇒ -10 < -4 -2x

⇒ -10+4 < -4 -2x+4 (Add 4 on both the side of the inequality)

⇒ -6 < -2x

⇒ -6 < -2x (Divide -2 on both the side of the inequality)

⇒ x < 3

The final step of the given inequality is x < 3. Therefore, option C is the correct answer.

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The slope of the line in the given graph = rise/run = 3.

To determine the value of the slope of a line on a coordinate plane, we can find the ratio of the rise of the line to that of its run. This means that, the formula for calculating the slope of a line would be:

Slope = rise/run.

Vertical distance across the line is the rise of the line

Horizontal distance across the line is the run of the line

In the graph given, we have:

The rise is labelled as the blue line = 9 units

The run is labelled as the red line = 3 units

Slope of the line (m) = 9 units/3 units

Slope (m) of the given line = 9/3 = 3

Therefore, the slope of the line in the given graph = rise/run = 3.

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The desired odd function is sketched at the end of the question.

An odd function is a function in which the following statement is true for all values of x.

f(-x) = -f(x).

The domain of a function is the set that contains all possible input values for a function. In a graph, it is the set that contains the values of x for which the function is defined.

The domain of a function is the set that contains all possible output values for a function. In a graph, it is the set that contains the values of y for which the function is defined.

Looking at the graph, we get that a function f(x) is decreasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y decreases.

Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.

Considering these definitions, the function with the desired characteristics is plotted at the end of the answer.

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Answer:

8000

Step-by-step explanation:

800 × 10 = 8000

--------------

Answer:

8000

Step-by-step explanation:

= 800 × 10 ( adding 800 ten times )

= 8000 ( and got 8000)

Answer:

 [tex]\frac{x-7}{4} =f^{-1}( x)[/tex]

Step-by-step explanation:

→ Replace f(x) with y

y = 4x + 7

→ Minus 7 from both sides

y - 7 = 4x

→ Divide both sides by 4

[tex]\frac{y-7}{4} =x[/tex]

→ Replace y's with f⁻¹(x)

[tex]\frac{x-7}{4} =f^{-1}( x)[/tex]