Choose the appropriate description for the following pair of angles.

The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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Answer:

poopjdjdjdjdndiddnr ddjdididndndnddndndjx

Step-by-step explanation:

poop kdfkdkddkejdfjdidjs didneidndzusnxixdn

1 1/2 hours

Time spent by Antonio in driving = 3 1/4 = 13/4

Time spent in gardening = 1 3/4 = 7/4

In order to find how much he spend driving than gardening, we can subtract 13/4 and 7/4.

13/4 - 7/4

Te denominator is same. So, we can directly subtract the numerators.

13-7/4

=6/4

= 3/2 = 1 1/2

Therefore, Antonio spent 1 1/2 hours more in driving than gardening.

Answer: 336

Step-by-step explanation:

it is 336 because if it is 21 poundes it is large so it sums up to 336 ounces

Answer:

C

Step-by-step explanation:

using the sin ratio in the lower right triangle and the exact value

sin45° = \(\frac{1}{\sqrt{2} }\) , then

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{7}{y}\) = \(\frac{1}{\sqrt{2} }\) [ y represents the hypotenuse ]

cross-  multiplying gives

y = 7\(\sqrt{2}\)

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

using the sine ratio in the upper right triangle

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{y}{x}\) = \(\frac{7\sqrt{2} }{x}\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

x = 7\(\sqrt{2}\) × \(\sqrt{2}\) = 7 × 2 = 14

Answer:

The expression is \(n = (\frac{1.645*0.5}{0.03})^2\)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

The margin of error is of:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a p-value of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

What expression would give the smallest sample size that will result in a margin of error of no more than 3 percentage points?

We have to find n for which M = 0.03.

We have no prior estimate for the proportion, so we use \(\pi = 0.5\). So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}\)

\(0.03\sqrt{n} = 1.645*0.5\)

\(\sqrt{n} = \frac{1.645*0.5}{0.03}\)

\((\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2\)

\(n = (\frac{1.645*0.5}{0.03})^2\)

The expression is \(n = (\frac{1.645*0.5}{0.03})^2\)

Step-by-step explanation:

Given: To make smallest 3-digit number of 825.

To find: The smallest 3-digit number of 825.

Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...

Final answer: The smallest 3-digit number of 825 is 258.

hope it helps

Answer:

258

Step-by-step explanation:

We are given 3 numbers:

8 2 5

And we are asked to find the smallest 3 digit number using those 3 digits above.

To make the smallest number, place the numbers in value from least to greatest:

2 5 8

This is your 3 digit number: 258.

Hope this helps! :)

To subtract 47.96 from 320.041, you can align the decimal points and then subtract each digit from right to left.

First, write the numbers with the decimal points aligned:

320.041

- 47.960

Next, subtract the digits in the ones place, which is 1 minus 0, resulting in 1. Then, subtract the digits in the tenths place, which is 4 minus 6. Since 4 is less than 6, you need to borrow 1 from the digit to the left, making the 2 into a 1 and adding 10 to the 4, giving you 14. So, 14 minus 6 equals 8.

Continue subtracting each digit in the same way:

   320.041

-   47.960

= 272.081

Therefore, 320.041 minus 47.96 is equal to 272.081.

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Answer:

Option (A)

Option (D)

Step-by-step explanation:

From the graph attached,

Values of function have been plotted on y-axis for every input value of 'x' on x-axis.

Graph clearly states that the function is positive (positive y-values or y > 0) in the two intervals,

-5 < x < 0 and 3.5 < x < 5

Therefore, option (A) and Option (D) will be the correct options.

Answer:

x = y = 26 cm; z = 13 cm

Step-by-step explanation:

We can calculate the dimensions of the square base as

∛(2·8788) = 26 cm

the height of the box will be half of 26/2 which is 13 cm.

x = y = 26 cm; z = 13 cm

then the minimum area for the given volume can be calculated using what we call Lagrange multipliers, this makes it easier

area = xy +2(xz +yz)

But we were given the volume as 8788

Now we will make the partial derivatives of L to be in respect to the cordinates x, y, z, as well as λ to be equal to zero, then

L = xy +2(xz +yz) +λ(xyz -8788)

For x: we have

y+2z +λyz=0

For y we have

y: x +2z +λxz=0

For z we have 2x+2y +λxy=0............eqn(*)

For we have xyz -8788=0

If we simplify the partial derivative equation of y and x above then we have

λ = (y +2z)/(yz).

= 1/z +2/y............eqn(1)

λ = (x +2z)/(xz)

= 1/z +2/x.............eqn(2)

Set eqn(1 and 2) to equate we have

1/z +2/y = 1/z +2/x

x = y

From eqn(*) we can get z

λ = (2x +2y)/(xy) = 2/y +2/x

If we simplify we have

1/z +2y = 2/x +2/y

Then z = x/2

26/2 =13

Therefore,

x = y = 2z = ∛(2·8788)

X= 26

y = 26 cm

z = 13 cm

Answer:

5

Step-by-step explanation:

(n-2)180 = 108

          n

Distribute

180n-360=108n

-360=-72n

5=n

n=5

Answer:

5 sides

Step-by-step explanation:

Use the formula for the measure of an interior angle of a polygon

\(\frac{(n - 2)180}{n}\)

Solve for n (the number of sides):

108 = \(\frac{(n - 2)180}{n}\)

108n = (n - 2)180

108n = 180n - 360

-72n = -360

n = 5

So, the polygon has 5 sides.

ASAP stands for "as soon as possible". It is often used when something needs to be done quickly or urgently. When someone says "ASAP someone please help", it means that they need help immediately and cannot wait any longer.

If you find yourself in this situation, the first step is to identify the problem and determine what needs to be done. Once you have a clear understanding of the situation, you can then reach out to someone who can help you. It's important to be specific when asking for help. Provide as much information as possible so that the person you are asking can understand the situation and offer the best possible assistance.

In summary, there is no shame in asking for help. It's better to reach out for assistance when you need it rather than struggle on your own. Don't hesitate to ask for help when you need it, and always be grateful to those who offer their assistance.

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Answer:

64 is the area!

- love bri <3

Answer:

a. \((x - 3)^2 + 16\)

b. \(8(x -7)^2\)

c. \((a^2 - 1)(7x - 6)\) or \((a+1)(a-1)(7x-6)\)

d. \((x^2-4)(x^2+3)\) or \((x-2)(x+2)(x^2+3)\)

e. \((a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})\)

Step-by-step explanation:

\(a.\ (x + 1)^2 - 8(x - 1) + 16\)

Expand

\((x + 1)(x + 1) - 8(x - 1) + 16\)

Open brackets

\(x^2 + x + x + 1 - 8x + 8 + 16\)

\(x^2 + 2x + 1 - 8x + 24\)

Collect Like Terms

\(x^2 + 2x - 8x+ 1 + 24\)

\(x^2 - 6x+ 25\)

Express 25 as 9 + 16

\(x^2 - 6x+ 9 + 16\)

Factorize:

\(x^2 - 3x - 3x + 9 + 16\)

\(x(x -3)-3(x - 3) + 16\)

\((x - 3)(x - 3) + 16\)

\((x - 3)^2 + 16\)

\(b.\ 8(x - 3)^2 - 64(x-3) + 128\)

Expand

\(8(x - 3)(x - 3) - 64(x-3) + 128\)

\(8(x^2 - 6x+ 9) - 64(x-3) + 128\)

Open Brackets

\(8x^2 - 48x+ 72 - 64x+192 + 128\)

Collect Like Terms

\(8x^2 - 48x - 64x+192 + 128+ 72\)

\(8x^2 -112x+392\)

Factorize

\(8(x^2 -14x+49)\)

Expand the expression in bracket

\(8(x^2 -7x-7x+49)\)

Factorize:

\(8(x(x -7)-7(x-7))\)

\(8((x -7)(x-7))\)

\(8(x -7)^2\)

\(c.\ 7a^2x - 6a^2 - 7x + 6\)

Factorize

\(a^2(7x - 6) -1( 7x - 6)\)

\((a^2 - 1)(7x - 6)\)

The answer can be in this form of further expanded as follows:

\((a^2 - 1^2)(7x - 6)\)

Apply difference of two squares

\((a+1)(a-1)(7x-6)\)

\(d.\ x^4 - x^2 - 12\)

Express \(x^4\) as \(x^2\)

\((x^2)^2 - x^2 - 12\)

Expand

\((x^2)^2 +3x^2- 4x^2 - 12\)

\(x^2(x^2+3) -4(x^2+3)\)

\((x^2-4)(x^2+3)\)

The answer can be in this form of further expanded as follows:

\((x^2-2^2)(x^2+3)\)

Apply difference of two squares

\((x-2)(x+2)(x^2+3)\)

\(e.\ a^{4n} -b^{4n}\)

Represent as squares

\((a^{2n})^2 -(b^{2n})^2\)

Apply difference of two squares

\((a^{2n} -b^{2n})(a^{2n} +b^{2n})\)

Represent as squares

\(((a^{n})^2 -(b^{n})^2)(a^{2n} +b^{2n})\)

Apply difference of two squares

\((a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})\)

Answer:

Recede

Step-by-step explanation:

Famished means extremely hungry

Recede means go or move back or further away from a previous position

Answer:

Recede

Step-by-step explanation:

So let's look at the meanings of these two words.

Recede: To go or move back backward; become more distant.

Famished: Severely suffering from hunger.

So now you can see that recede is the word that makes more sense in the blank.

Far away on the horizon, we saw the tiny figures of a lonely traveler and his mule Recede into the sunset.

Hope this Helps!

Answer:

A

Step-by-step explanation:

Answer:

The 12 represents area of base of cuboid.

The 5 represents height of cuboid.

Step-by-step explanation:

Given:

DeAndre calculated the volume of the cuboid in three ways:

V= 12.5

V= 15.4

V=20.3

To find: what the 12 and the 5 represent in the figure

Solution:

Volume of cuboid is equal to length × breadth × height

or Area of the base of cuboid × height

Length = 4 units

Breadth = 3 units

So, area of base of cuboid = length × breadth = 4 × 3 = 12 square units

Height of cuboid = 5 units

The 12 represents area of base of cuboid.

The 5 represents height of cuboid.

The coordinates of point H' include the following: H' (0, -1).

In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

By translating the pre-image of this trapezoid vertically downward by 2 units and horizontally right by 3 units, the coordinates of the image include the following:

(x, y)                               →                  (x + 3, y - 2)

E(-1, 4)                        →                  (-1 + 3, 4 - 2) = E' (2, 2).

H (-3, 1)                        →                  (-3 + 3, 1 - 2) = H' (0, -1).

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The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

From the question, we have the following parameters that can be used in our computation:

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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The difference between the boards’ total lengths is  86 inches.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The difference between the total lengths of the boards is the positive value when we subtract one from another.

The total length of the red cedar board is = (8×10.25) = 82 inches.

The total length of the tiger maple board is = (16×10.5) = 168 inches.

∴ The difference is (168 - 82) = 86 inches.

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Answer:

B similar

Step-by-step explanation:

Both of these triangles have the same proportions and angles even though they are different sizes, making them similar.

Have a most wonderous day!

Answer:

it should be similar

Step-by-step explanation:

I hope this helps

Answer:

0.54

Step-by-step explanation:

A =  "she's up all night 'til the sun"

B = "she's up all night for good fun"

P(A) = 0.29

P(B) = 0.27

P(A or B) = 0.02

The following relationship is known:

\(P(A\ or\ B) = P(A)+P(B) - P(A\ and\ B)\)

Therefore, applying the given data:

\(P(A\ and\ B) = P(A)+P(B)-P(A\ or\ B)\\P(A\ and\ B) = 0.29+0.27-0.02\\P(A\ and\ B) = 0.54\)

The probability that "she's up all night 'til the sun" AND "she's up all night for good fun" is 0.54.

Answer:

False.

Step-by-step explanation:

The equation f(x) = \(-x^4\) + 3 has a maximum interval of (0, 3).

First simplify the equation:

f(x) = \(-4x^3\)

Then find the intervals:

Increasing -∞<x<0, Decreasing 0>x>∞

Plug x = 0 into \(-x^4\)+3: 3

Therefore the maximum interval of \(f(x) = -x^4 + 3\) is (0, 3)

Penjelasan langkah demi langkah:

1)

\(= 243^{\frac{2}{3} }\\= (\sqrt[3]{243})^2\\= 7^2\\= 49\)

2) √32 +3√18-2√50

= √16*2 +3√9*2-2√25*2

= 4√2 + 3(3√2)-2(5√2)

= 4√2 + 9√2-10√2

= 13√2-10√2

= 3√2

3) 1000 ⅔×64⅙

 \(= (\sqrt[3]{1000}) ^2 \times (2^6)^{1/6} \\= 10^2 \times 2\\= 100 \times 2\\= 200\)

4) 3/4+√2

\(3/4+\sqrt{2} \\= \frac{3+4\sqrt{2} }{4 }\)

5) 2√3×√18

= 2√3×√9*2

= 2√3×3√2

= (2*3)(√3*√2)

= 6√6

6) 12/3+√3

= 4+√3

7) √1000—2√40

= 10 -2 (√4*10)

= 10-2(2√10)

= 10 - 4√10

8) 2- ¹+3-¹

\(= \frac{1}{2} + \frac{1}{3}\\ = \frac{3+2}{6}\\ = \frac{5}{6}\)

9)

\(\frac{5}{\sqrt{5} }\\ merasionalisasikan\\= \frac{5}{\sqrt{5} }\times \frac{\sqrt{5} }{\sqrt{5} }\\= \frac{5\sqrt{5} }{\sqrt{25} }\\= \frac{5\sqrt{5} }{5}\\ = \frac{\sqrt{5} }{1}\)

Jika pernyataannya opsional, penyebutnya adalah 1

10) 2√3×√18

= 2√3×√9*2

= 2√3×3√2

= (2*3)(√3*√2)

= 6√6

The answer would be B.

Answer:

Answer is -4

Step-by-step explanation:

To solve this, you want to substitute the values of x and y. So, 2(-3)^2-5(-3)(-2)-(-2)^3 which will give you -4.

Answer:

B. 1788

Step-by-step explanation:

The volume of solid shaped is expressed in cubic yards. The sides of the shape are multiplied or powered as 3 for the volume determination. Volume is the total space covered by the object. It includes height, length, width. The three dimensional objects volume is found by

length * height * width

The volume for current object is :

12 * 28 * 5

= 1788 cubic yards.

Answer: 1778

Step-by-step explanation:

because Ik I had the question

Answer:

D.It is less than 0 because the addends have opposite signs and the positive addend is farther from zero.

Step-by-step explanation:

The given expression is :

When we subtract a larger number from a smaller number, we get a negative answer as mathematically we cannot subtract a larger number from smaller, so we subtract the numbers in standard format and out a negative sign in front of the answer.

Like this given expression will become : -519.70

Now, any negative number is smaller than zero.

Therefore, the correct answer is option D.