Evaluate the expression 2.5x−20 for x=15

1. Triangle jkl is congruent to triangle uvw, 2. Side lk corresponds to side vw, 3. Angle jlk corresponds to angle uvw. When we say that δjkl ≅ δuvw, it means that triangle jkl is congruent to triangle uvw.

Congruent triangles have corresponding sides and angles that are equal in measure. Therefore, side lk in triangle jkl corresponds to side vw in triangle uvw.

Similarly, if δuvw ≅ δabc, it implies that triangle uvw is congruent to triangle abc. Consequently, the corresponding parts of these triangles are equal. Hence, angle jlk in triangle jkl corresponds to angle uvw in triangle uvw.

In summary, the given information allows us to conclude that triangle jkl is congruent to triangle uvw. Side lk in triangle jkl corresponds to side vw in triangle uvw, and angle jlk in triangle jkl corresponds to angle uvw in triangle uvw. These congruences and corresponding parts help establish the relationships between the triangles and provide a framework for further analysis or geometric proofs.

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QUESTION:

Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements.

Triangle JKL is congruent to triangle

Side LK corresponds to sides

Angle JLK corresponds to angles

Answer:

The expression is equivalent to\(A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}\) is  \(\frac{\sqrt[4]{3}}{2}}\times \frac{\sqrt{x}}{y}\).

Step-by-step explanation:

The expression provided is:

\(A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}\)

Simplify the expression A as follows:

\(A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}\)

   \(=\sqrt[4]{\frac{24}{128}\times x^{(6-4)}\times y^{(1-5)}}\\\\=\sqrt[4]{\frac{3}{16}\times x^{2}\times y^{-4}}\\\\=[\frac{3}{16}\times x^{2}\times y^{-4}]^{1/4}\\\\=[\frac{3}{16}]^{1/4}\times x^{(2\times (1/4))}\times y^{(-4\times (1/4))}\\\\=\frac{\sqrt[4]{3}}{2}}\times x^{1/2}\times y^{-1}\\\\=\frac{\sqrt[4]{3}}{2}}\times \frac{\sqrt{x}}{y}\)

Thus, the expression is equivalent to\(A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}\) is  \(\frac{\sqrt[4]{3}}{2}}\times \frac{\sqrt{x}}{y}\).

Equivalent expressions are expressions that have equal values

The equivalent expression of \(\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}\) is \(\frac 1{2y}\sqrt[4]{ 3x^2}}\)

The expression is given as:

\(\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}\)

Divide 24 and 128 by 8

\(\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \sqrt[4]{ \frac{3x^6y}{16x^4y^5}}\)

Take 4th root of 16

\(\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 12\sqrt[4]{ \frac{3x^6y}{x^4y^5}}\)

Apply law of indices, to simplify the fraction

\(\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 12\sqrt[4]{ 3x^{6-4}y^{1-5}}\)

Simplify

\(\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 12\sqrt[4]{ 3x^{2}y^{-4}}\)

Rewrite as:

\(\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 12\sqrt[4]{ \frac{3x^{2}}{y^4}}\)

Take 4th root of y^4

\(\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 1{2y}\sqrt[4]{ 3x^2}}\)

Hence, the equivalent expression of \(\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}\) is \(\frac 1{2y}\sqrt[4]{ 3x^2}}\)

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Answer:

16/3

Step-by-step explanation:

Every cup of apple juice goes along with 1.5 cups of ornage juice. So, if you divide 8 cups of ornage juice by the 1.5, you get 16/3 cups of apple juice.

Transformation involves changing the form of a function. The function that represents is C; \(g(x) =- \sqrt[3]{x+1}\)

The function is a type of relation, or rule, that maps one input to specific single output.

Function f(x) is given byy;

\(g(x) = \sqrt[3]{x}\)

f(x) is reflected across the x-axis.

The rule of this transformation (i.e. reflection) is:

(x, y) ⇒ (x, - y)

So,

\(f'(x) = -f(x)\)

This gives

\(f'(x) = - \sqrt[3]{x}\)

Now, f'(x) is translated 1 unit left

The rule of this transformation (i.e. translation) is:

(x, y) ⇒ (x+ 1, y)

So,

g(x) = f'(x+ 1)

This gives

\(g(x) = -\sqrt[3]{x+1}\)

Hence, the function that represents g(x) is (c)

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Answer:

Step-by-step explanation:

its B on Edge just did it

We then divide the difference in y-coordinates by the difference in x-coordinates to find the slope of the line. This can be expressed mathematically as follows: slope = (y₂ - y₁) / (x₂ - x₁).

This procedure calculates the slope of a line using the coordinates of two points. It takes four numeric parameters as input: the x coordinate of the first point, the y coordinate of the first point, the x coordinate of the second point, and the y coordinate of the second point. The slope of a line is a measure of its steepness and is defined as the change in y divided by the change in x between two points on the line.

To calculate the slope of a line using the coordinates of two points, we need to first find the difference between the y-coordinates of the two points and the difference between the x-coordinates of the two points.

We then divide the difference in y-coordinates by the difference in x-coordinates to find the slope of the line. This can be expressed mathematically as follows: slope = (y₂ - y₁) / (x₂ - x₁). The resulting slope value can be positive, negative, or zero depending on the direction and steepness of the line. A positive slope indicates that the line is increasing from left to right, while a negative slope indicates that the line is decreasing from left to right. A slope of zero indicates a horizontal line.

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Answer:

you can measure it in ruler

The correct answers are option 3 and option5 which are y = 3x -10, y = 2x -7 also y =5x - 16, y = x - 4.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

The given point is having coordinates of ( 3,-1 ). We will check the equations for the above point.

Option 3

y = 3x -10, → ( - 1 ) = (3 x 3) -10 = -1 satisfying

y = 2x -7   → ( -1 ) = ( 2x3 ) - 7 = -1 satisfying

Option 5

y =5x - 16, → ( -1 ) = ( 5 x 3 ) - 16 = -1 satisfying

y = x - 4.  → ( -1 ) = ( 3 - 4 ) = -1  satisfying

Therefore the correct answers are option 3 and option 5 which are y = 3x -10, y = 2x -7 also y =5x - 16, y = x - 4.

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Answer:10

Step-by-step explanation:

Answer:

\(x \le -4\)

Step-by-step explanation:

Given

\(\qquad16x - 7 \leq -71\)

Required

Solve

Start by adding 7 to both sides

\(\qquad16x - 7 + 7 \leq -71 + 7\)

\(\qquad16x - 7 + 7 \leq -64\)

\(\qquad16x \leq -64\)

Divide both sides by 16

\(\frac{16x}{16} \leq \frac{-64}{16}\)

\(\frac{16x}{16} \leq -\frac{64}{16}\)

\(x \leq -\frac{64}{16}\)

\(x \le -4\) --- The solution

Answer:

x < -4

I did this on khan academy

Answer:

x = - 2, y = - 8

Step-by-step explanation:

13x - 6y = 22 → (1)

x = y + 6 → (2)

substitute x = y + 6 into (1)

13(y + 6) - 6y = 22

13y + 78 - 6y = 22

7y + 78 = 22 ( subtract 78 from both sides )

7y = - 56 ( divide both sides by 7 )

y = - 8

substitute y = - 8 into (2)

x = y + 6 = - 8 + 6 = - 2

then x = - 2 and y = - 8

What is \(\sf{\displaystyle\frac{1}{4}}\) of 12?

In order to find it, we should divide 12 by 4:-

3

Now, solve our word problem:-

Matthew bought 12 roses. \(\sf{\displaystyle\frac{1}{4} }\) of these roses were white.

And we already know how to solve this problem :)

Hence,

\(\bigstar{\boxed{\pmb{3~of~the~roses~were~white}}}\)

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

x=-1

Step-by-step explanation:

5x=-5

\(x=\frac{-5}{5}=-1\)

Answer:

Step-by-step explanation:

Let the greater part = x

Smaller part = 105 - x

2*(greater part) = (3*smaller part) - 15

2*x = 3*(105 -x) - 15

Use distributive property

2x = 3*105 - 3*x - 15    

2x = 315 - 3x - 15

2x =  300 - 3x

Add 3x to both sides

2x +3x = 300

5x = 300

Divide both sides by 5

x = 300/5

x =60

Smaller part = 105 - 60  = 45

Greater part = Rs. 60

Smaller part = Rs. 45

Answer:

A

Step-by-step explanation:

\(2x + y = 16 \\\)

\(y = x - 4\)

as y is given, u just need to substitue y's value into 2x+y=16

then u can solve it

Answer:

3/5

Step-by-step explanation:

6 black marbles and 4 white marbles.= 10 marbles

P( black marble) = number of black marbles / total marbles

                            =6/10 = 3/5

Answer:

6/4 or 1 1/2

Step-by-step explanation:

because there is 6 black marbles and 4 white marbles

Answer:

C

A. X-intercept (6,0) and y-intercept (0,-8) wrong

B. x-intercept (-8,0) and y-intercept (0,6)wrong

C. x-intercept (4,0) and y-intercept (0,-3) correct

D. x-intercept (-3,0) and y-intercept (0,4) wrong

The association between parental divorce and worse outcomes is well-documented, it is important to consider these potential confounding factors and individual differences before making causal claims.

The association between children whose parents divorce when they are young and worse outcomes, on average, compared to children whose parents stay together may be correlational rather than causal for several reasons.

Firstly, there could be other factors, such as parental conflict or financial difficulties, that are associated with both divorce and worse outcomes for children. These confounding variables could be responsible for the observed correlation.

Secondly, it is also possible that the effects of divorce on children's outcomes vary based on individual and contextual factors.

For example, children from divorced families may experience different levels of social support or have different coping mechanisms, which could influence their outcomes.

Therefore, while the association between parental divorce and worse outcomes is well-documented, it is important to consider these potential confounding factors and individual differences before making causal claims.

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Answer: 7

Step-by-step explanation:

As \(\angle T \cong \angle T\) by the reflexive property, we know that \(\triangle RST \sim \triangle UVT\) by AA.

Since corresponding sides of similar triangles are proportional,

\(\frac{UT}{5}=\frac{13.2+5}{13}\\UT=(5)\left(\frac{13.2+5}{13} \right)=\boxed{7}\)

Answer:

Step-by-step explanation:

(1) Yes

Answer:

(8, 15, 17) (20, 21, 29) (30, 40, 50)

Step-by-step explanation:

I got it correct on my assignment

Answer:

>

Step-by-step explanation:

Let the amount of payouts in March be M.

From the problem, we know that the payouts in March increased by 8.5%, which means:

M = 12,400 + 0.085(12,400)

M = 12,400 + 1,054

M = 13,454

Next, we know that the payouts in April dropped by 5%, which means:

A = M - 0.05M

A = 0.95M

A = 0.95(13,454)

A = 12,781.3

Therefore, the amount of the payouts in April was $12,781.3.

Answer:

a. 3:45 a.m. = 3:345

b. 9:16 a.m. = 9:16

c. 12 ( midnight ) = 00:00

d. 12 ( noon ) = 12:00

Answer:

D

Step-by-step explanation:

Answer:  D. No, it asks only the girls in the shop

Erica's survey leaves out the boys which means the boys are completely under-represented while the girls are over-represented. The population consists of boys and girls. This means the sample needs to have the same proportional mix of those genders (ie around 50% for each) if you want the sample to be representative of the population.

Answer:

Step-by-step explanation:

Let the number be 'x'

\(\dfrac{x}{6}-10=2\\\\\\Add \ 10 \ to \ both \ sides\\\\\\\dfrac{x}{6}=2+10\\\\\\\dfrac{x}{6}=12\\\\Multiply \ both \ side \ by 6\\\\\\x=12*6\\\\x=72\)

2)

\(\dfrac{1}{7}+x=\dfrac{2}{3}x\\\\\\x - \dfrac{2}{3}x=\dfrac{-1}{7}\\\\\\\dfrac{3}{3}x-\dfrac{2}{3}x=\dfrac{-1}{7}\\\\\\\dfrac{1}{3}x=\dfrac{-1}{7}\\\\\\\x=\dfrac{-1}{7}*3\\\\\\x=\dfrac{-3}{7}\)

3)-3(v + 25) = 111

Use distributive property

-3v + (-3)*25 = 111

-3v - 75 = 111

Add 75 to both sides

-3v = 111+ 75

-3v = 186

Divide both sides by (-3)

v = 186/(-3)

v = -62

Answer:

3/0

Step-by-step explanation:

to find the slope use rise over run or y-y/x-x, in this case, 2-(-1)/-6-(-6)the negative and the subtraction sign cancel out resulting in something like this: 2+1/-6+6 equaling 3/0

I hope this helps have a nice day

The number of residuals outside the 95% prediction bands depends on the specific data and regression model. The explanation below provides general insights.

The number of residuals lying outside the 95% prediction bands can vary depending on the data and the estimated regression model. In a simple linear regression, the prediction bands represent the range within which future observations are expected to fall with 95% confidence.

Ideally, if the model assumptions are met and the regression is a good fit, we would expect only about 5% of the residuals to fall outside the prediction bands by chance. However, if the assumptions are violated or the model is not appropriate, more residuals may deviate beyond the bands.

The distribution of residuals above or below the estimated regression line depends on the symmetry of the errors. If the errors are normally distributed and the model is unbiased, roughly half of the residuals lying outside the prediction bands should be above the line, and the other half should be below the line.



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Answer:

Step-by-step explanation:

Given:

Solution

As per midpoint formula;

Answer:

Perimeter = 4s

Step-by-step explanation:

The perimeter of a square = 4*length

Given that length = s

Perimeter = 4s

-Chetan K

The cosine for 60 degrees is ( 1 / 2 ) and the tangent will be √3.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

The trigonometric identities for the given image will be calculated as below:-

Cosine value:-

cos60 = Base / Hypotenuse

cos60 = 4 / 8 = 1 /  2

Tangent value:-

tan60 = perpendicular / Base

tan60= 4√3 / 4

tan60 = √3

Therefore, the cosine for 60 degrees is ( 1 / 2 ) and the tangent will be √3.

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