If the triangles below are similar, determine which of the statements below are TRUE. (There may be more than one correct answer.)


Similar Triangles


Question 5 options:


A.) BC¯¯¯¯¯≅YZ¯¯¯¯¯


B.) BC¯¯¯¯¯≅XY¯¯¯¯¯¯


C.) Side XY = 26



D.) Side BC = 48



E.) ∠A≅∠X

V = 2176/3 or approximately 725.30 m³

1) Since this figure is made of a pyramid and a cube then let's find the Volume of the Cube, by plugging the measure of its side into the formula:

2) Let's proceed with the Pyramid's volume, note that we have to calculate the area of the base (in this case a square) times the height times 1/3

3) Finally, we can add them up:

Hence the answer is V = 2176/3 or approximately 725.33 m³

We can identify the sequence, since Lanie starts with 5 min and increases by 2 every week, therefore, a possible sequence identification would be:

Evaluating the sequence for the week number 10 (n = 10):

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

$ 6.20 Cents

Step-by-step explanation:

17 - 5.50= 11.5

11.50 - 5.30= 6.2

Add A Zero at the end

You Get 6.20

Answer:

c

Step-by-step explanation:

Based on the fact that the cross-country course is shaped like a parallelogram, the total length of the cross-country course is 10 miles.

The total length of the cross-country course will be the perimeter of the shape that the course is shaped like.

As this course is shaped like a parallelogram, the total length would therefore be:

= Base + Base + Length + Length

Solving gives:
= 3 + 3 + 2 + 2

= 6 miles

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Answer:

754 cm²

Step-by-step explanation:

The total surface area of a cylinder
= Lateral Surface Area + Top surface area + Bottom Surface Area

Top and Bottom surfaces are both circles

Given radius r and height h

Lateral surface area = 2πrh

Top surface area = Bottom surface area = πr²

Top + Bottom surface area = πr²  + πr²   = 2πr²

With r = 6 and h = 14 cm

Total surface area
= 2πrh + 2πr²
= 2πr(h + r)

= 2π · 6(14 + 6)

= 12π (20)

= 240 π

≈ 754 cm²

Answer:

  D'E' = 4/5

Step-by-step explanation:

Corresponding sides have the same scale factor (the dilation factor).

  D'E'/DE = E'F'/EF

  D'E' = (DE)(E'F'/EF) = 8((3/5)/6) . . . multiply by DE; substitute given values

  D'E' = 4/5

Answer:

y = 480 + 1.5 (x-40)

Step-by-step explanation:

sometimes its better to answer the question and make the formula from that

40 x 12 = 480

1.5 for overtime

x

y = 480 + 1.5 (x-40)

When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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Answer:

The perimeter of the enlarged rectangle is 36 inches.

Step-by-step explanation:

Perimeter of an enlarged figure:

To find the perimeter of an enlarged figure, we multiply the perimeter of the original figure by the scale factor.

In this question:

Perimeter of the original rectangle: 12 inches

Scale factor: 3

Perimeter of the enlarged rectange:

12*3 = 36 inches

The area of the circle is approximately 78.5 square meters.

To determine the area of a figure, we need to know what type of figure it is and what its dimensions are. The formulas for finding the areas of different types of figures are as follows:

Rectangles: Area = length x widthSquares: Area = side x sideTriangles: Area = 1/2(base x height)

Circles: Area = πr² (where π is pi and r is the radius)Problem 1:Let's say we have a rectangle with a length of 6 cm and a width of 4 cm.

To find its area, we use the formula Area = length x width. Substituting in our values,

we get:Area = 6 cm x 4 cm = 24 cm²Therefore, the area of the rectangle is 24 square centimeters.Problem 2:Next, let's look at a circle with a radius of 5 meters.

To find its area, we use the formula Area = πr². Substituting in our values, we get:Area = π(5 m)² = π(25 m²) ≈ 78.5 m²

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Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer:

c ≈ 9.49

Step-by-step explanation:

Using the Pythagorean Theorem:

\(a^2+b^2=c^2\)

A and B are the two legs and c is the hypotenuse.

\(3^2+9^2=c^2\)

\((3*3)+(9*9)=c^2\)

\(9+81=c^2\)

\(90=c^2\)

\(\sqrt{90}=\sqrt{c^2}\)

\(3\sqrt{10}=c\)

\(c = 9.49\)

Answer:

\(c=\sqrt{90}\)

Step-by-step explanation:

When using the Pythagorean Theorem, \(a^{2}\) and \(b^{2}\) represent the horizontal and vertical sections of the triangle. The term \(c^{2}\) represents the hypotenuse. The easiest way to understand an equation is to try to explain it with a sentence or two.

Pythagorean's Theorem in English:

The horizontal length squared plus the vertical length squared equals the hypotenuse squared.  

The problem is asking for the square root of the hypotenuse squared, so the first thing to do would be solving Pythagorean's Theorem for the hypotenuse squared.

\(c^{2}=a^{2} +b^{2}\)

The given information in this problem implies that a=3 and b=9.

Using these values to calculate the hypotenuse squared:

\(c^{2}=3^{2}+9^{2} =9+81=90\)

Now that we know the value of the hypotenuse squared, take the square root of it.

\(\sqrt{c^{2} }=\sqrt{90}\)

\(c=\sqrt{90}\)

The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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Answer:

\(7x - \frac{7}{79} = 68x + 8 \\ 7x - 68x = 8 + \frac{7}{79 } \\ - 61x = \frac{639}{79} \\ x = \frac{639}{79 \times ( - )61} \\ x = \frac{639}{ - 4819} \\ = - 0.132.......\)

Answer:

x = -639 / 4819   (x = -0.1326 [rounded])

Step-by-step explanation:

7x - 7/79 = 68x + 8

{subtract 7x from both sides to begin to isolate x}

       7x - 7/79 = 68x + 8

       -7x             - 7x

            - 7/79   = 61x + 8

{subtract 8 from both sides to isolate x}

- 7/79   = 61x + 8  

- 8                   -8

{8 = 632/79}

- 639 / 79 = 61x

{divide both sides by 61 to isolate x}

-639 / 79  = 61x

÷ 61            ÷61                  \(-\frac{639}{79}\)   ÷ \(\frac{61}{1}\) =  \(-\frac{639}{79}\) * \(\frac{1}{61}\) =   \(-\frac{639}{4819}\)

-639 / 4819 = x

(-639/4819 ≈ -0.1326 [rounded] )

{updates in bold}

Based on the given values above which is 2 inches: 1 foot, given that the mantel in the room has an actual width of 8 feet, this would mean that the width of the mantel in the blueprint would be 16 inches. 8 times 2 is 16.

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Answer:

-9

Step-by-step explanation:

x+5 less than or equal -4

x lessthan orcequal -4-5

x less than or equal -9

Answer:

0

Step-by-step explanation:

By the remainder theorem, this is the same as finding f(-1/2), which is equal to 0.

Answer:

1) 0.99348

2) 0.55668

Step-by-step explanation:

Assume that men’s weights are normally distributed with a mean given by  = 172lb and a standard deviation given by  =29lb. Using the Central Limit Theorem to solve the following exercises

When given a random number of samples, we use the z score formula:

z-score is z = (x-μ)/σ/√n where

x is the raw score

μ is the population mean

σ is the population standard deviation.

(1) If 36 men are randomly selected, find the probability that they have a mean weight greater than 160lb.

For x > 160 lb

z = 160 - 172/29/√36

z = 160 - 172/29/6

z = -2.48276

Probability value from Z-Table:

P(x<160) = 0.0065185

P(x>160) = 1 - P(x<160) = 0.99348

(2) If 81 men randomly selected, find the probability that they have a mean weight between 170lb and 175lb.

For x = 170 lb

z = 170 - 172/29/√81

z = 170 - 172/29/9

z = -0.62069

Probability value from Z-Table:

P(x = 170) = 0.2674

For x = 175 lb

z = 175 - 172/29/√36

z = 175- 172/29/6

z = 0.93103

Probability value from Z-Table:

P(x = 175) = 0.82408

The probability that they have a mean weight between 170lb and 175lb is calculated as:

P(x = 175) - P(x = 170)

0.82408 - 0.2674

= 0.55668

Lemon juice:

pH = 2.4

pH is defined as the concentration of hydrogen ions in chemical solutions. Mathematically, this can be written as:

pH = -Log₁₀ [aH]

Where aH is the activity of hydrogen ions. We can replace the lemon juice pH value in order to obtain aH:

2.4 = -Log₁₀ [aH]

-2.4 = Log₁₀ [aH]

We take the 10 exponential:

10^(-2.4) = aH

aH = 3.98*10⁻³

So, the hydrogen concentration in lemon juice is 3.98*10⁻³ M.

M is the molarity unit (moles/liter).

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Step-by-step explanation:

pretty much, both sides will equal to 125° because of alternate interior angles

125=5x+30

minus 30 off both sides

95=5x

divide 5 off both sides

x=19

Based on the information, it can be inferred that the required numbers are 1010 and 1313.

To find the required numbers we must find the HCF, that is, the highest number by which these two numbers can be divided (303 and 101). We have tried this procedure with different numbers as shown below:

Once we have these digits, we must find the numbers whose difference is 303; these numbers are 1010 and 1313.

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To solve, we will follow the steps below:

3x+y=11 --------------------------(1)



5x-y=21 ------------------------------(2)

since y have the same coefficient, we can eliminate it directly by adding equation (1) and (2)

adding equation (1) and (2) will result;

8x =32

divide both-side of the equation by 8

x = 4

We move on to eliminate x and then solve for y

To eliminate x, we have to make sure the coefficient of the two equations are the same.

We can achieve this by multiplying through equation (1) by 5 and equation (2) by 3

The result will be;

15x + 5y = 55 ----------------------------(3)

15x - 3y =63 --------------------------------(4)

subtract equation (4) from equation(3)

8y = -8

divide both-side of the equation by 8

y = -1

Answer:

A

Step-by-step explanation:

Since 16.4 is 45% of a number, these two numbers need to be on the same side of the proportions. In A, they are both in the numerator.

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

C. 3/8

Step-by-step explanation:

Let \(f'\) be defined as:

\(f'= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\)

Where:

\(f(x) = 3\cdot \sqrt{x}+5\) and \(f(x+h) =3\cdot \sqrt{x+h}+5\)

The definition is now expanded:

\(f' = \lim_{h \to 0} \frac{3\cdot \sqrt{x+h}-3\cdot \sqrt{x}}{h}\)

By rationalization:

\(f' = 3\cdot \lim_{h \to 0} \frac{( \sqrt{x+h}-\sqrt{x})\cdot (\sqrt{x+h}+\sqrt{x})}{h\cdot (\sqrt{x+h}+\sqrt{x})}\)

\(f' = 3\cdot \lim_{h \to 0} \frac{h}{h\cdot (\sqrt{x+h}+\sqrt{x})}\)

\(f' = 3\cdot \lim_{h \to 0} \frac{1}{\sqrt{x+h}+\sqrt{x}}\)

\(f' = 3\cdot \lim_{h \to 0} \frac{1}{(x+h)^{1/2}+x^{1/2}}\)

If \(h = 0\), then:

\(f' = \frac{3}{2\cdot x^{1/2}}\)

\(f' = \frac{3}{2\cdot \sqrt{x}}\)

Let evaluate \(f'\)when \(x = 16\):

\(f'(16) = \frac{3}{2\cdot \sqrt{16}}\)

\(f'(16) = \frac{3}{8}\)

Which corresponds to option C.