Round 7.19 to the nearest tenth

Answer:

Step-by-step explanation:

In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph

The two statements that are both true are as follows: line

AC is perpendicular to line HB and line AC is parallel to FG. That is option A.

A perpendicular line is defined as the line that forms angle 90° where it meets with another line in a plane.

A line is said to be parallel to each other when they do not intercept as they are both on the same plane.

From the given diagram, line AC is perpendicular to line HB because they form angle 90° at the point of intersection.

Also, line AC is parallel to FG, because they can never intersect till infinity.

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Answer:

D. 50 square centimeters

Answer:

Step-by-step explanation:

34,05m my love

Answer:

The height of the tree is approximately 15.14 meters, rounded to the nearest hundredth of a meter.

Step-by-step explanation:

Let's call the height of the tree "h". We can use similar triangles to set up an equation involving Joseph's height, the length of his shadow, the height of the tree, and the length of the tree's shadow.

The two triangles we're interested in are:

Joseph's triangle: This triangle has a height of 1.75 meters (Joseph's height) and a base of x meters (the length of Joseph's shadow).

Tree's triangle: This triangle has a height of h meters (the height of the tree) and a base of 29.7 - x meters (the length of the tree's shadow).

Since the two triangles are similar, we can set up the following proportion:

h / (29.7 - x) = 1.75 / x

To solve for h, we can cross-multiply and simplify:

h * x = 1.75 * (29.7 - x)

h * x = 52.075 - 1.75x

h = (52.075 - 1.75x) / x

Now we need to find the value of x that makes the tips of the two shadows meet. From the problem statement, we know that x + 34.05 = 29.7, so:

x = 29.7 - 34.05

x = -4.35

This means that the tips of the shadows don't actually meet, but the problem is likely assuming that the tips of the shadows are very close together, so we can use the value x = -4.35 to approximate the height of the tree.

Substituting x = -4.35 into our equation for h, we get:

h = (52.075 - 1.75(-4.35)) / (-4.35)

h = 15.14

Answer:

To determine which statements are true, we can use the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Using this form, we can rewrite the given equation as:

(x - 1)^2 + y^2 = 3^2 + 1^2 = 10

Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.

To find the radius, we can rearrange the equation as follows:

x^2 - 2x + y^2 = 8

Completing the square for x, we get:

(x - 1)^2 + y^2 = 9

This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Therefore, the three true statements are:

1.The radius of the circle is 3 units.

2.The center of the circle lies on the x-axis.

3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:

hope its help <:

Answer:

The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.

In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:

The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.

The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.

The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.

Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).

Answer:

2n + 14 = 30

Step-by-step explanation:

Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.

This model represents the total on the top and the 2 parts on the bottom.

Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!

The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.

The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.

For the given question:

Triangle with degree angles - 45-45-90

It means two legs are of same length 5 units.

Then, hypotenuse H will be:

H² = 5² + 5²

H² = 25 + 25

H² = 50

H = 5√2

Thus, the correct third side of the triangle will be 5√2.

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Answer:

Yes, ∆PQR is a right triangle.

Step-by-step explanation:

A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.

Answer:

Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:

Step-by-step explanation:

Answer:

44 students

Step-by-step explanation:

1200 for the first year

a third of that is 400

400 for the second year

a third of that is 133.4

133.4 for the third year

a third of that is 44

Answer:

Step-by-step explanation:

f Trevor used 2 lb 6 oz of a 5-lb bag of potatoes, then the weight of the remaining potatoes is:

5 lb = 80 oz (since 1 lb = 16 oz)

Remaining potatoes = Total potatoes - Used potatoes

Remaining potatoes = 80 oz - 2 lb 6 oz

Remaining potatoes = 80 oz - (2 × 16 oz + 6 oz)

Remaining potatoes = 80 oz - 38 oz

Remaining potatoes = 42 oz

Therefore, the remaining potatoes weighed 2 lb 10 oz (or 42 oz).

The tοtal price οf the game including tax is $29.96.

Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.

Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:

0.07 x $28 = $1.96 in taxes

As a result, the purchase tax is $1.96.

Tο calculate the tοtal price, add the purchase price and the tax:

Purchase price + Tax = Tοtal Price

Tοtal cοst: $28 + $1.96 = $29.96

As a result, the tοtal cοst οf the game, including tax, is $29.96.

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Answer:

8.449 square centimeters

Step-by-step explanation:

Area of the figure = area of square + area of triangle

[tex] {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5[/tex]

[tex].142 \times 59.5 = 8.449[/tex]

So 8.449 square centimeters of this figure is green.

Answer:

To find all values of x for which f(x) = 26, we can set up the equation:

8x + 15/x = 26

Multiplying both sides by x, we get:

8x^2 + 15 = 26x

Bringing all the terms to one side, we get:

8x^2 - 26x + 15 = 0

We can factor this quadratic equation using the factoring method or by using the quadratic formula. Here, we will use the factoring method:

8x^2 - 26x + 15 = 0

(4x - 3)(2x - 5) = 0

Setting each factor equal to zero and solving for x, we get:

4x - 3 = 0 OR 2x - 5 = 0

4x = 3 OR 2x = 5

x = 3/4 OR x = 5/2

Therefore, the values of x for which f(x) = 26 are x = 3/4 or x = 5/2.

The solutions for x are x= +[tex]\sqrt{12.5[/tex] and -[tex]\sqrt{12.5[/tex] which has been obtained by solving the equations given in the question.

Define Equation?

An equation can be defined in numerous ways. An equation is a claim that demonstrates the equivalence of two mathematical expressions, according to algebra.

In the initial equation, we get: by substituting y=x:

[tex]x^2[/tex] +[tex]y^2[/tex]= 25

[tex]x^2[/tex] +[tex]x^2[/tex] = 25 (since y = x)

2[tex]x^2[/tex] = 25

[tex]x^2[/tex] = 12.5

When the two sides are square, we get:

x = ±[tex]\sqrt{12.5[/tex]

Therefore, the solutions for x are x = +[tex]\sqrt{12.5[/tex] and x = -[tex]\sqrt{12.5[/tex]

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Answer:

the answer is supposably 75900000

The wrestler's weight before he went on his diet was 78.0 kilograms.

What is y-intercept?

In the context of a graph of a function, the y-intercept is the point where the graph intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero. Geometrically, the y-intercept is the value of the function at the point where it crosses the y-axis.

To determine the wrestler's weight before he went on his diet, we need to find the y-intercept of the linear function that represents his weight gain over time. This is because the y-intercept corresponds to the initial weight of the wrestler, i.e., his weight before he started his diet.

We can use the two data points where the time is 0 (i.e., at the start of the diet) to find the slope of the linear function:

(1.5, 85.8) and (3.0, 93.6)

The change in weight over the time interval of 1.5 to 3.0 months is:

93.6 - 85.8 = 7.8

The change in time over that interval is:

3.0 - 1.5 = 1.5

So the slope of the linear function is:

7.8 / 1.5 = 5.2

Now we can use the point-slope form of a linear function to write an equation for the wrestler's weight gain over time:

y - 85.8 = 5.2(x - 1.5)

where y represents the wrestler's weight and x represents the time in months.

To find the wrestler's weight before he went on his diet, we need to evaluate this equation at x = 0:

y - 85.8 = 5.2(0 - 1.5)

y - 85.8 = -7.8

y = 78.0

Therefore, the wrestler's weight before he went on his diet was 78.0 kilograms.

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Answer:

The percent decrease in population can be calculated by dividing the difference between the two populations by the original population and then multiplying by 100. In this case, the percent decrease is ((137000-117820)/137000)*100 = 14%.

Step-by-step explanation:

Answer:

The answer is 96

Step-by-step explanation:

2*(26+22)

2*48

96

Answer: The building is approximately 16.6 feet tall.

Step-by-step explanation:

Use Pythagorean theorem (a²+b²=c²) to solve this.

We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.

Your equation would be: 20²+x²=26²

subtract 20² from 26² --> 276=x²

then take the square root --> 16.6=x

Guitar tabs are generally considered easier to read than regular musical notation because they are written in a language that most guitarists are familiar with.

Guitar is a stringed musical instrument played with the fingers or a pick. It is one of the most popular instruments in the world and is widely used in genres such as rock, jazz, blues, country, folk, and classical.

Unlike traditional notation, guitar tabs do not require any knowledge of music theory to understand. Instead, they are laid out in a straightforward format that conveys the pitch of a note and the timing of when it should be played. This makes it easier for most guitarists to quickly learn a new piece of music without having to spend time studying the complexities of traditional notation. Additionally, guitar tabs also offer an easy way to determine the fingering of certain chords or techniques.
While guitar tabs are easier to read than traditional notation, they do have some drawbacks. For one, guitar tabs cannot convey the same level of detail about a piece of music as traditional notation can. Additionally, it can be difficult for some to distinguish between rhythm and lead parts when reading guitar tabs. Finally, guitar tabs do not easily convey the dynamics or expression of a piece of music, which are important to consider when playing music.

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Answer:

Step-by-step explanation:

adjacent:   [tex]\angle BOC, \angle EOD[/tex]   (both are adjacent)

complementary:  [tex]\angle BOC[/tex]

supplementary:   [tex]\angle EOD[/tex]

vertical angles:   [tex]\angle AOE[/tex]

The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac

The distributive property is a mathematical property that applies to multiplication and addition or subtraction.

It states that when you multiply a number (or variable) by a  sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.

This is represented by the following formula:

a(b + c) = ab + ac

This is represented by Option (B)

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The correct option is 1 and 4  of the given inequality  –3(2x – 5) < 5(2 – x)

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x

x < 5

Therefore, options 1 and 4 are correct. The other options do not correctly represent the inequality.

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Using trigonometric functions, we can find that the value of the angle N is 3°.

The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.

Here, using the cosine theorem:

CosM = n² + l² - m²/2nl

⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70

⇒ -0.981 = 729 + 4900 - m²/3780

⇒ 5629 - m² = -3708

⇒ m² = 9337.

Now Cos N = m² + l² - n²/2ml

= (9337 + 4900 - 729) / (2 × √9337 × 70)

= 0.9985

Cos N = 0.9985

Putting [tex]Cos^{-1}[/tex] on both sides:

[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985

⇒ N ≈ 3°

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The complete question is:

In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.

In response to the stated question, we may state that Therefore, the cylinder volume of the tank is approximately 301 cubic feet.

A cylinder is a three-dimensional polyhedron made up of two congruent parallel circular bases but a curving surface linking the two bases. The bases of a cylinder are all equal to its axis, which is an artificial straight line across the centre of both bases. The volume of a cylinder is the composite of its base area and length. The volume of a cylinder is computed as V = r2h, where "V" represents the volumes, "r" represents the circle of the base, and "h" is the height of the cylinder. The formula to find the volume of a cylinder is:

[tex]V = \pir^2h[/tex]

Where V is the volume, r is the radius, h is the height, and π is a constant value that approximates to 3.14.

[tex]V = 3.14 * 4^2 * 6\\V = 3.14 * 16 * 6\\V = 301.44\\V = 301 ft^3[/tex]

Therefore, the volume of the tank is approximately 301 cubic feet.

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Answer:

-2

Step-by-step explanation:

Hence, x has a value of 36 as the sum of the supplementary angles 3x and 2x must equal 180 degrees .

Angles in mathematics are used to quantify how much two intersecting surfaces or lines rotate relative to one another. Angles can be measured in degrees, radians, or various ways. Degrees, which divide a whole rotation into 360 equal parts, are the most popular unit of measurement for angles. Angles are a fundamental idea in geometry and trigonometry and have practical uses in a number of industries, including physics, engineering, and navigation.

given

The sum of the supplementary angles 3x and 2x must equal 180 degrees. Which is:

3x + 2x = 180

Putting similar phrases together on the left side, we get:

5x = 180

When we multiply both sides by 5, we get:

x = 36

Hence, x has a value of 36 as the sum of the complementary angles 3x and 2x must equal 180 degrees .

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