Two angles of a triangle measures of 70° and 85° which is not the measure of an exterior angle of the triangle

Answer: So, the possible number of additional senators who must vote in favor of the treaty in order to radify it is given by

[tex]19\leq x\leq 52[/tex]

Step-by-step explanation:

Since we have given that

Number of states = 50

Number of senators from each of the 50 states = 2

Total number of senators would be

[tex]50\times 2\\\\=100[/tex]

Since [tex]\dfrac{2}{3}[/tex] of the senators present must approve the treaty.

[tex]\dfrac{2}{3}\times 100\\\\=66.67[/tex]

Number of senators have voted in favor of a treaty = 48

So, remaining senators would be

[tex]67-48\\\\=19[/tex]

Let x be the number of senators needed.

So, Inequality would be

[tex]x\geq 19[/tex]

Now, [tex]100-48=52[/tex]

[tex]x\leq 52[/tex]

So, the possible number of additional senators who must vote in favor of the treaty in order to radify it is given by

[tex]19\leq x\leq 52[/tex]

The equivalent equation is: -100k + 3 + 101k = -245 - 181k

Finding the Equivalent Equation

We need to find the equation equivalent to:

-k + 0.03 + 1.01k = -2.45 - 1.81k

To eliminate decimals, we can multiply the entire equation by 100:

100*(-k + 0.03 + 1.01k) = 100*(-2.45 - 1.81k)

This simplifies to: -100k + 3 + 101k = -245 - 181k

Therefore, the equivalent equation is: -100k + 3 + 101k = -245 - 181k

Complete question:

Which equation is equivalent to –k + 0.03 + 1.01k = –2.45 – 1.81k?

–100k + 3 + 101k = –245 – 181k

–100k + 300 + 101k = –245 – 181k

–k + 3 + 101k = –245 – 181k

–k + 300 + 101k = –245 – 181k

In mathematics, a line segment can grow from a) zero-dimensional points or b) one-dimensional line segments but cannot grow from a three-dimensional object due to differences in properties such as volume.

In the field of mathematics, a line segment can grow from a zero-dimensional point and a one-dimensional line segment. The process of a line segment growing from a point involves extending out in a certain direction from the zero-dimensional point. When we say a line segment can grow from a one-dimensional object, it means an existing line segment can be extended to become a longer line segment.

A line segment cannot 'grow' from a three-dimensional object because a line segment is a one-dimensional entity, and dimensional objects have 'volume,' a property which a line segment does not possess.

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The solution to the equation 3.2 - 4d = 2.3d + 3 is d = 0.0317.

The given equation is,

3.2 - 4d = 2.3d + 3

Combine like terms by adding 4d to both sides of the equation:

3.2 - 4d + 4d = 2.3d + 3 + 4d

3.2 = 6.3d + 3

Move the constant term (3) to the other side of the equation by subtracting 3 from both sides:

3.2 - 3 = 6.3d + 3 - 3

0.2 = 6.3d

Divide both sides of the equation by 6.3 to isolate the variable d:

0.2/6.3 = 6.3d/6.3  

d = 0.0317

So, the solution to the equation 3.2 - 4d = 2.3d + 3 is d = 0.0317.

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Answer: D) 25π

Step-by-step explanation:

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The area of a piece of wood with a length of  [tex]\( \frac{5}{12} \)[/tex]  foot and a width of  [tex]\( \frac{2}{3} \)[/tex]  foot is [tex]\( \frac{5}{18} \)[/tex] square feet.

To find the area of a rectangular piece of wood with a length of [tex]\( \frac{5}{12} \)[/tex] foot and a width of [tex]\( \frac{2}{3} \)[/tex] foot, we use the formula for the area of a rectangle

[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]

Given that the length is  [tex]\( \frac{5}{12} \)[/tex]  foot and the width is  [tex]\( \frac{2}{3} \)[/tex]  foot, we plug these values into the formula:

[tex]\[ \text{Area} = \frac{5}{12} \times \frac{2}{3} \][/tex]

To multiply fractions, we multiply the numerators together and the denominators together:

[tex]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[ \text{Area} = \frac{5 \times 2}{12 \times 3} \]\[ \text{Area} = \frac{10}{36} \][/tex]

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

[tex]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[ \text{Area} = \frac{10 \div 2}{36 \div 2} \]\[ \text{Area} = \frac{5}{18} \][/tex]

So, the area of a piece of wood with a length of  [tex]\( \frac{5}{12} \)[/tex]  foot and a width of  [tex]\( \frac{2}{3} \)[/tex]  foot is [tex]\( \frac{5}{18} \)[/tex] square feet.

To find the total amount Jeremy earned from mowing lawns, we set up the equation x - $17 = $75 where x is the total earnings. Solving the equation, we find that Jeremy earned a total of $92.

The amount of money Jeremy earned mowing lawns can be found by setting up a simple algebraic equation. We know that after paying $17 for gas, he had $75 leftover for camp. Therefore, we can write the equation as:

Total Earnings - Gas Cost = Money for Camp

Let x represent the total amount Jeremy earned. The equation will then be:

x - 17 = 75

Now, we solve for x:

x = 75 + 17

x = 92

Jeremy earned a total of $92 from mowing lawns.

Answer:

Option d is correct

[tex]Csc \ \theta =\frac{1}{y}[/tex]

Step-by-step explanation:

Here P(x,y) is the point on unit circle  ( unit circle has radius 1 and center (0,0))

Now in a diagram we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

[tex]Csc\ \theta =\frac{hypotenuse }{opposite \ side} \\Csc\ \theta =\frac{OP}{AP}[/tex]

[tex]Csc \ \theta =\frac{1}{y}[/tex] ( since OP =1 and AP =y)

Answer:

1/y

Step-by-step explanation:

apex

To factor the expression x³ - 2x² - 9x + 18, use the grouping method to factor out a common binomial factor.

To factor the expression x³ - 2x² - 9x + 18, we can first look for any common factors. Since there are no common factors among all the terms, we will use the grouping method to factor the expression.

Step 1: Group the terms in pairs.
(x³ - 2x²) - (9x - 18)
Step 2: Factor out the greatest common factor from each pair.
x²(x - 2) - 9(x - 2)
Step 3: Notice that we now have a common binomial factor of (x - 2).
(x² - 9)(x - 2)

Therefore, the factored form of the expression x³ - 2x² - 9x + 18 is (x² - 9)(x - 2).

The student is looking to factor the polynomial expression x^3 - 2x^2 - 9x + 18. This process typically involves finding whether factors like binomials divide the polynomial without a remainder, using methods like grouping, trial and error, or the Rational Root Theorem, followed by long or synthetic division.

The student has asked to factor the expression x^3 - 2x^2 - 9x + 18.

To factor this expression, we can follow a systematic approach, which often starts with looking for common factors or applying techniques such as grouping, trial and error, or the use of the Rational Root Theorem. In this case, we may not see an immediate common factor, so we might try to group terms or apply synthetic division or the Rational Root Theorem to identify potential roots of the polynomial.

A factor of a polynomial is a binomial (or another polynomial) that divides the original polynomial without leaving a remainder. If we find such a factor, we can then divide the original polynomial by this factor to simplify the expression further. For example, if we discover that (x - 3) is a factor, then we can divide the polynomial by (x - 3) to find the other factors.

Unfortunately, without performing the actual factoring process or having additional information, we cannot factor this specific expression purely based on the question provided. If we had one root or factor given, we could use long division or synthetic division to further factor the expression, and then possibly factorize it completely into the product of binomials or another polynomial.

To find 60% of 33, first write 60% as a decimal by moving the decimal point two places to the left to get .60.

Next, the word "of" means multiply, so we are are going to multiply.

(.60) (33) = 19.8

Therefore, 60% of 33 is 19.8.

Answer:

C)  

late spring.

Step-by-step explanation:

just did the test on usatestprep

The cost of 1 bicycle is $48 by using the system of equations.

Word problems are a mathematical interpretation by using variables, numbers, and arithmetic operations to solve real-life problems.

From the given information:

We have a system of equations, and we can solve for the cost of1 bicycle

Using the Elimination method:

4U + 3B = 268

-2U + 3B = 110

2U + 0    = 158

U = 158/2

U = 79

The cost of 1 bicycle = 4(U) - 268

= 4(79) - 268

= 316 - 268

= $48

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Answer:

$48

Step-by-step explanation:

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