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8. Explain how you can show that KL congruent to HJ.

When drawing horizontal or vertical lines with a triangle, you need to use two triangles at the same time. You can draw lines at angles of 30, 45, 60, and 90 degrees by combining the two.

Additionally, the values of the side lengths of this triangle are always inversely proportional to one another. and x2 is the side length that is in opposition to the 90-degree angle. likewise, the side length that is in opposition to the 90-degree angle is 72. Additionally, the side length at the opposite end of the 45-degree angle is 2.

Tips for Remembering the 30-60-90 Triangle Rule Remembering the ratio 1 is all it takes to remember the 30-60-90 triangle rules: √3 : 2, and being aware that the longest side length is always in opposition to the largest angle (90 degrees) and the shortest side length is always in opposition to the shortest angle (30 degrees).

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The equation of the line passing through (-3, 6) is y = 6.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a horizontal line is passing through (-3, 6), we are asked to find its equation,

Since, the equation that represents a horizontal line is of form y = a i.e, it must pass through point (0,a) on the y-axis.

We are given, the line passes through (-3, 6), it must pass through point (0,6) on the y-axis.

Hence, the equation of the line passing through (-3, 6) is y = 6.

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The recursive formula in this case is;

Arithmetic, t0=15

and tn=2.8+tn−1

where n≥1

Option A

A recursive formula is a formula that defines a sequence of values in terms of its previous values. It provides a way of defining a sequence in a compact form, with each term of the sequence depending on one or more preceding terms.

In mathematics, recursive formulas are often used to define sequences. We can see that in this sequence, the first term is 15 and the common difference is obtained by simple subtraction .

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The division expression that represents the capacity of the container is 2/3 ÷ 1/6, the multiplication expression that represents the capacity of the container is 2 x 6 / 3, the capacity of the container is 4 pound.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Let us assume total capacity of the container = x pounds.

Container contains 1/6th coffee of total x pounds,  that is x/6 pounds.

We also given that 1/6th part is equal to 2/3 of a pound.

So, we could setup an equation now.

x/6 pounds equals 2/3 of a pound.

[tex]\frac{x}{6} = \frac{2}{3}[/tex]

Dividing both sides by 1/6, we get

[tex]\frac{x}{6}[/tex] ÷ [tex]\frac{1}{6}[/tex] = [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{6}[/tex]

Therefore, x =  [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{6}[/tex]

for multiplication expression,

x = [tex]\frac{2}{3}[/tex] × 6    { ∵ a ÷ b = a × [tex]\frac{1}{b}[/tex] }

the capacity of the container is,

x =  [tex]\frac{2}{3}[/tex] × 6

x = 4 pound.

Therefore, the division expression that represents the capacity of the container is 2/3 ÷ 1/6, the multiplication expression that represents the capacity of the container is 2 x 6 / 3, the capacity of the container is 4 pound.

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Answer: -5x+8

Step-by-step explanation:

add the like terms

Answer:

-5x+8

Step-by-step explanation:

You just have to isolate the 5x, and it has a "-" before it, so the 5x is a negative expression (-5x), then you do 7+1 that is 8.

Answer:

A. See attached graph

B. [tex]\boxed{y = 0.12x^2+ 12}[/tex]

C. [tex]\boxed{160\;square\;feet}[/tex]

Step-by-step explanation:

Consider the figure which shows the cross-sectional view of the parabolic tunnel as viewed from the entrance

A. See attached graph

B. The parabola is drawn with the y-axis as the axis of symmetry.

The x-intercepts are at (-10, 0) and (10, 0)

The vertex is at (0, 12)

The vertex form equation for a parabola is
y = a(x - h)² + k

where (h, k) is the vertex - the (x, y) coordinates of the vertex

Here h = 0, k = 12

So the parabola equation is:

y = a(x - 0)² + 12

y = ax² + 12

To find a, plug in one of the x-intercepts, say (10, 0)

We get

0 = a(10)² + 12

0 = 100a + 12

100a = -12

a = -12/100 = -0.12

Therefore the equation of the parabola is
[tex]\boxed{y = 0.12x^2+ 12}[/tex]

C. The cross-sectional area is given by the formula:

D.  To find the area of the parabola between x = -10 and x = 10 which forms the base of the parabola, you can use the formula
[tex]A = \dfrac{2}{3}bh\\\\[/tex]

where b is the base length and h is the height

Using the values for b = 20 and h = 12 we get

[tex]A = \dfrac{2}{3}\cdot 20 \cdot 12 = 160 \textrm { square feet}[/tex]

Using the definite integral, let's find the area between x = -10 and x = 10

I am not going through every step but leading you to the final answer

[tex]\int _{-10}^{10}\left(\:-0.12x^{2\:}+\:12\right)dx\\\\\\\textrm{We have}\\\\0.12\cdot \int _{-10}^{10}x^2dx=0.12\left[\frac{x^3}{3}\right]_{-10}^{10}\\\\[/tex]

[tex]=0.04\left[x^3\right]_{-10}^{10}\\\\= 80\\\\[/tex]

Therefore
[tex]-0.12\cdot \int _{-10}^{10}x^2dx = -80[/tex]

[tex]\int _{-10}^{10}12dx = \left[12x\right]_{-10}^{10} = 240[/tex]

So total area = -80 + 240 = 160 square feet

Ans: Cross sectional area = [tex]\boxed{160\;square\;feet}[/tex]

A triangle is 180 degrees because the sum of the interior angles of any polygon is always equal to 180 degrees times the number of sides minus two.

A triangle is 180 degrees because the sum of the interior angles of any polygon (a closed shape with at least three straight sides) is always equal to 180 degrees times the number of sides minus two. This is known as the polygon angle sum theorem. In the case of a triangle, which has three sides, the sum of the interior angles is 180 degrees times one less than the number of sides, or 180 degrees times (3-2), which equals 180 degrees. Additionally, since a triangle is a three-sided polygon, and each angle in a triangle is connected by three straight lines, the sum of the three angles in a triangle must always add up to 180 degrees.

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If the graphs of both functions are symmetric with respect to the line y = x, then we say that the two functions are inverses of each other.

The inverse function is represented by f⁻¹ with regards to the original function f and the domain of the original function becomes the range of the inverse function.

The range of the given function becomes the domain of the inverse function the injective function is the reflection of the original function with reference to the line y = x and is obtained by swapping (x, y) with the (y, x).

There are a few steps to find an Inverse Function:

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The elimination method is used to solve a linear system using multiplication.

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The theoretical likelihood of receiving a 2 is 1/6, but the actual likelihood is 1/3.

They are divided by one-half.

The potential likelihood

The theoretical likelihood of receiving a 2 is 1/6, which is the ratio of the number of fortunate events to all possible outcomes.

The experimental likelihood

The experimental probability of an event occurring is the proportion of total times the experiment was conducted that an event occurred during the experiment.

in this case, is 6/12 or 1/2.

1/2 - 1/6 = 3/6 - 1/6 = 2/6 = 1/3

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The equivalent expression of (-7 + 2i) + 6i- (11-15)  is -3 + 8i.

Two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same. In other words, equivalent expression are usually the same.

We can know the equivalent expression of (-7 + 2i) + 6i- (11-15) by simplifying it.

Hence, let's simplify (-7 + 2i) + 6i - (11 - 15) as follows:

Therefore,

(-7 + 2i) + 6i - (11 - 15)  = -7 + 2i + 6i - 11 + 15

combine like terms

-7 + 2i + 6i - 11 + 15 = -7 + 15 - 11 + 2i + 6i

Hence,

-7 + 15 - 11 + 2i + 6i = -3 + 8i

Therefore,

(-7 + 2i) + 6i - (11 - 15) = -3 + 8i

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Answer:r=175 this is for IXL I hope this helps

Step-by-step explanation:

r/-25 =-7

Multiply both sides of the equation by -25

-25 times r/-25=-25 time (-7)

Multiplying two negatives equals a positive: (-) times (-) =(+)

25•r/25=-25•(-7)

then

Cancel out the greatest common factor 25

R=-25 times (-7)

Also Multiplying two negatives equals a positive: (-) times (-) =(+)

r=25 times 7

Multiply the numbers 25•7

Then you get

R=175

The 5 examples of solution are:

1. When we combine salt with water (often table salt), we create salt water. In this case, the solvent is water, and the solute is salt.

2. When sugar and water are combined, sugar water is created.

3. Several substances are dissolved in water to create mouthwash.

4. You may make iodine tincture by combining iodine crystals with alcohol.

5. In water, soda comprises sugar, carbon dioxide, color, and other ingredients.

Solvent and solute are combined to generate solutions. A solution is therefore a homogeneous mixture. Numerous solutions are available in our homes. Here is a short list:

1. Sugar and color are present in Kool Aid's water.

2. We make vinegar by combining acetic acid and water.

3. A solution of hydrogen peroxide between 3 and 6 percent is known as hydrogen peroxide solution.

4. This is created by combining water and hydrogen peroxide.

5. You can make detergent solution by combining detergent and water.

6. Window cleaner is made up of many chemicals in water with aroma.

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Answer: -7/3

Step-by-step explanation:

y/3 - 8 = -15

y/3 = -7

y = -7/3

Answer:

he did 89.5 hours in total

Step-by-step explanation:

Using umitary mwthod we get

4. 1

358. x

soling it

4x=358

or,x=358÷4

or,x=89.5 hours

©Thank You

Answered By Solution 49

The answer is 89.5 because it's 358 divided by 4.

No, 39 is not a perfect square number because it can't be equal to square of any integer.

An integer that can be expressed as the square of another integer is called a perfect square. In other words, a perfect square is the square of an integer such as 1 = 1², 4 = 2², 9 = 3², 16= 4², , forward. Thus , perfect square formula is written as N = x², where x is any integer. I have the number 39 and I need to check if it is a perfect square. For this we can take the square root of this number. A number is a perfect square if its square root is an integer. So, √39 = √3×13

= 6.2449 ( using calculator)

Which is not an integer, so it is not a perfect square.

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Answer:

20 weeks

Step-by-step explanation:

Salma's savings can be represented by the equation S = 35 + 8t, where t is the number of weeks after the beginning of the year.

Henry's savings can be represented by the equation H = 95 + 5t

To determine the number of weeks after the beginning of the year until Salma and Henry have the same amount of money saved, we need to set the two equations equal to each other and solve for t:

35 + 8t = 95 + 5t

3t = 60

t = 20

So it would take Salma and Henry 20 weeks after the beginning of the year to have the same amount of money saved.

Answer:

(1) ... y1 = -2.5, y2 = 4

(2) ... y1 = -2, y2 = 3

(3) ... z1 = -10, z2 = 0

(4) ... x1 = 0, x2 = 3

Hope this helps <3

Step-by-step explanation:

Answer:

1. y= -5/2, 2

2. y= 3, -2

3. z= 0,-10

4. x= 0,3

Step-by-step explanation:

The scale factor which was used to reduce the picture include the following: B. 1/4.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric figures such as airplanes, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure):

Scale factor = Dimension of image/Dimension of pre-image

Scale factor = 4/16 = 5/20

Scale factor = 1/4.

Therefore, this photo was reduced by a scale factor of 1/4.

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Answer choices are:

4

1/4

12

1/12

The required radius of the cylinder that can be covered by the paint is 3.8 feet. Option D is correct.

Franco has enough paint to cover an area of approximately 226 square feet. He needs to paint a cylinder that is 5 feet, and the maximum possible radius of the cylinder that can be covered by the paint is to determined.

Recall that a  cylinder is defined as a 3D solid that keeps two identical bases joined by a curved surface, at a certain distance.

Here,

Franco has enough paint to cover an area of approximately 226 square feet.

Area of the cylinder = 226

πr²h = 226

h = 5 feet and π = 3.14

3.14 * 5 * r² = 226

r² = 226/15.70

r = √14.70

r = 3.80

Thus, the required radius of the cylinder that can be covered by the paint is 3.8 feet. Option A is correct.

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Answer: 9 hours

Step-by-step explanation: To find the answer, I did:

315 / 35 = ? * 1

=9 * 1

= 9

I divided the 315 by the 35 because that would give us how many hours she drives. (at a constant rate) So, given that, I got 9. I hope this helped!

The difference between the smallest 6-digit number with five different digits and the greatest 5-digit number with four different digits is 358.

The aim is to find the largest 5-digit number with four different digits and the smallest 6-digit number with five different digits, and then we need to find how many numbers are between these two values.

Let's start by finding the smallest 6-digit number with five different digits.

We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit, 1; therefore, it can be used in the highest place value.

Thus, we can create the required 6-digit smallest number with 0 and 1.

Hence, the smallest 6-digit number is 100234.

Now, we will discover the largest 5-digit number.

As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 5-digit number with the digit 9.

Thus, the largest 5-digit number is 99876.

Now, calculate the difference between these two numbers.

So, we can determine the difference between the smallest 6-digit number and the largest 5-digit number by subtracting the smallest from the largest.

Thus, we get,

⇒100234 - 99876

⇒358

Hence, 358 is the difference between the smallest 6-digit with five different digits and the largest 5-digit number with four different digits.

--The given question is incomplete; the complete question is

"What is the difference between the smallest 6-digit number with five different digits and the greatest 5-digit number with four different digits?"--

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Answer:

5/9

Step-by-step explanation:

Exponential functions and logarithmic functions are related but inverse of each other.

Exponential functions are used to model growth and decay, while logarithmic functions are used to model inverse growth and decay.

An exponential function is a function in the form of f(x) = b^x, where b is a positive constant called the base. The variable x is the exponent, and the value of the function is the result of raising the base to the power of x. For example, f(x) = 2^x is an exponential function. The graph of an exponential function is always increasing and never touches or crosses the x-axis, as long as b>1.

On the other hand, a logarithmic function is a function in the form of f(x) = log_b(x) or f(x) = ln(x), where b is a positive constant called the base (or e for natural logarithm) and x is the argument of the logarithm. The value of the function is the exponent to which the base must be raised to produce x. For example, f(x) = log2(x) is a logarithmic function. The graph of a logarithmic function is always decreasing and asymptotic to the x-axis.

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Answer:

x = 100

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. In this case, you will add 10 to both sides of the equation, to isolate x:

x - 10 = 90

x - 10 (+10) = 90 (+10)

x = 90 + 10

x = 100

x = 100 is your answer to the equation.

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Answer:

m = 24

Step-by-step explanation:

To solve the equation m/3-7 =1, we can start by isolating m on one side of the equation. To do this, we will add 7 to both sides of the equation:

m/3 - 7 + 7 = 1 + 7

m/3 = 8

The next step is to multiply both sides of the equation by 3 to get rid of the fraction:

m/3 * 3 = 8*3

m = 24

So the solution to the equation is m=24

The value of √N is 3.16159

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: A quadrilateral WXYZ with ∠Z=75 and ∠X=105

Let P be a point on ZW such that ZP=x and WP=4-x, then we form a right-angled triangle ΔZPY with tan 15°=x/PY

∴ PY=x/tan 15

       =3.732x

Now using Pythagoras' theorem we get ZY as

 [tex]\sqrt{13.927x^2+x^2} \\=\sqrt{14.92x^2}\\ =3.862641x[/tex]

Now let's connect the diagonal ZX we get the right triangle ZWX

Thus using Pythagoras' theorem we get

ZX=[tex]\sqrt{4^2+4^2}[/tex]

    =4√2

Again let Q be an extension such that YQ=4-x & ∠YXQ=75°

Thus Sin 75=4-x/√N

            √N=4-x/0.965923

squaring both sides we get N=(4-x)²/0.9330127........(1

Now using the Pythagoras theorem in ΔZYX we get

√N=

[tex]\sqrt{ZX^2-ZY^2} \\=\sqrt{32-14.92x^2} \\[/tex]

⇒N=32-14.92x²..,.......2)

Thus equation two values of N we get

(4-x)²/0.9330127=32-14.92x²

16-8x+x²=29.8564-13.920549x²

14.921x²-8x-13.856=0

Thus using the quadratic formula we get the value of x as

x= 8±29.85 /29.84

x=1.2684  (∵ Distance cannot be negative)

∴ Value of N=32-14.92×1.2684

                    N=13.075

                   √N=3.6159

Hence, The value of √N is 3.16159

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