Classify the following expression by the number of terms. 3x

Answer:

x=60

Step-by-step explanation:

180 is the some of the angle of an triangle

in the left triangle the angle is = 180-70-75=35

in the right triangle the angle is=180-35-60=85

x=180-80-45=60

Answer:

Step-by-step explanation:

Remember: The three interior angles of a triangle will always add up to 180 degrees.

In order to solve for x, we need to solve for other missing angles

1) Solve for the missing angle on the triangle to the left.

180 - 75 -70 = 35 degrees.

2) Solve for the missing angle on the triangle to the right (not x).

180 - 60 - 35 = 85 degrees

3) Finally, solve for the x angle by subtracting 45 and 85 from 180. x = 50 degrees.

Answer:

216

HOPE THIS HELPS

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Answer:

about 30.9 feet

Step-by-step explanation:

Using the Pythagorean Theorem:

[tex] {l}^{2} + {10}^{2} = {32.5}^{2} [/tex]

[tex] {l}^{2} = 956.25[/tex]

[tex]l = 30.9[/tex]

Answer: The population three years ago was 156250.

Step-by-step explanation:

Let 3 years ago, the population of a city = P

Rate of growth (R) = 8% p.a.

Present population (P) = 1,96,830.

Therefore,

[tex]A=P(1+R100)n[/tex]

P = A÷(1 + 8/100)³

196830 ÷ (1+2/25)³

=156250.

3 years ago, the population of the city = 156250.

The equation of the ellipse is equal to (x - 6)² / 49 + (y + 6)² / 36 = 1.

In this problem we must derive the equation of an ellipse based on information about the center, a vertex and a co-vertex thereof. The vertex represents the end of the major semiaxis that lies on the curve and co-vertex is the end of the minor semiaxis that lies on the curve. The major semiaxis is parallel with x-axis and the minor semiaxis is parallel with y-axis.

The standard form of the ellipse is shown below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

Now we proceed to derive the equation of the ellipse:

Major semiaxis:

A = (13, - 6) - (6, - 6)

A = (7, 0)

a = 7

Minor semiaxis:

B = (6, 0) - (6, - 6)

B = (0, 6)

b = 6

Equation of the elipse:

(x - 6)² / 49 + (y + 6)² / 36 = 1

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Answer:

360 degrees

Step-by-step explanation:

I remember learning this in Math class. The rhombus angle sum will make 360 degrees.

91.6 grams of a 100 gram sample will remain radioactive after 2 hours. The solution has been obtained by using the concept of radioactive decay.

What is Radioactive decay?

Radioactive decay is the spontaneous destruction of an atomic nucleus in a radioactive substance that causes the emission of radiation from the nucleus. A parent nuclide in a radioactive process is one that decays, and a daughter nuclide is one that is created in the radioactive process.

We are given that a radioactive substance has a decay rate of 0.044 per hour.

Using the radioactive decay formula,

N(t) = N₀ [tex]e^{-kt}[/tex]

Initially, N = 100

k = 0.044

t = 2

So,

⇒N(t) = 100 * e⁽⁻⁰°⁰⁴⁴ ˣ ²⁾

⇒N(t) = 91.5761

⇒N(t) = 91.6

Hence, 91.6 grams of a 100 gram sample will remain radioactive after 2 hours.

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Secant can be defined as the reciprocal of cosine. Secant of angle A will be hypotenuse/adjacent.

There are three basic trigonometric ratios. Sin, Cos and Tan.

Sin = opposite side/ hypotenuse

Cos = adjacent side/ hypotenuse

Tan = opposite side/ adjacent side

Here in the give image, Sin(A) = a/c

                                        Cos(A) = b/c

                                        Tan(A) = a/b

There are reciprocals for each trigonometric functions

Cosecant is the reciprocal of sine. Cosec(A) = c/a

Secant is the reciprocal of  Cosine. Sec(A) = c/b

Cotangent is the reciprocal of Tangent . Cot(A) = b/a

So secant is one of inverse trigonometric functions.

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The height of 164.8 centimeter after conversion to feet is equivalent to  5.41 feet .

The various measurements units that are used in measuring the height of an object are , centimeter (cm) , meter (m) , feet , inches .

We have to convert the height of 164.8 cm to feet ;

we know that , 1 centimeter is = 0.0328 feet ;

So , we multiply the units given in centimeter by 0.0328 ,

On multiplying 164.8 cm by 0.0328 ;

We get ;

⇒ 164.8 centimeter = 164.8 × 0.0328 ;

⇒ 164.8 centimeter = 5.40544 feet ≈ 5.41 feet ;

Therefore , 164.8 cm is approximately equal to 5.41 feet .

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Minimum and Maximum Calculator is an online widget that helps you find the max and min values ​​of a function.

The maximum value is the point at which the function has the highest value of all other values, while the minimum value is the lowest value in the entire function.

The calculator returns the global maximum and minimum of the function along with a graph on the Cartesian plane as the solution. A min-max calculator is an online calculator that can be used to find the maximum and minimum values ​​of a mathematical function.

Finding the extreme values ​​of a function is also known as optimization. Feature optimization is a central concept in engineering, business, and machine learning.

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Answer:

blank=9

Step-by-step explanation:

The politician should obtain a sample of at least 602 voters to estimate the proportion of voters supporting her position on forced busing with a 90% level of confidence and a 4% margin of error.

What is the proportion?

A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.

To determine the sample size needed to estimate the proportion of voters supporting a certain position within a certain margin of error and level of confidence, we can use the following formula:

n = (Z² * p * (1 - p)) / E²

where:

n is the sample size

Z is the z-score corresponding to the desired level of confidence (in this case, 90%, which corresponds to a z-score of 1.645)

p is the estimated proportion of voters supporting the politician's position (we don't have an estimate, so we'll use 0.5, which maximizes the sample size and provides the most conservative estimate)

E is the desired margin of error (in this case, 4%, which is equivalent to 0.04)

Substituting the values given, we get:

n = (1.645² * 0.5 * (1 - 0.5)) / 0.04²

n = 601.5625

We need to round up to the nearest whole number since we can't have a fractional sample size, so the minimum sample size needed is 602 voters.

Therefore, the politician should obtain a sample of at least 602 voters to estimate the proportion of voters supporting her position on forced busing with a 90% level of confidence and a 4% margin of error.

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Answer:

1.5

Step-by-step explanation:

Answer: 1.5

Step-by-step explanation:

Answer:

155.744

Step-by-step explanation:

To complete a ratio table, we need to find the missing values that would make the ratios equivalent. 82   19    4:1     164  38    4:1  57   13.5  4:1

328  76    4:1   410  95    4:1

To complete the given ratio table, we need to find the missing values that would make the ratios equivalent. Ratios are used to compare two or more quantities and are expressed in the form of a fraction, with the numerator representing one quantity and the denominator representing another.

Starting with the first row of the table, we can see that the ratio of the first two values is 82:19. To find the missing value in this row, we need to determine what value multiplied by 19 would give us 82. Using basic algebra, we can set up the equation

19x = 82

And solve for x, which gives us

x = 82/19.

= 4.32

This value is approximately 4.32. Therefore, the missing value in the first row is 82:19:4.32.

Moving on to the second row, we can see that the ratio of the first two values is 164:38. Similar to the first row, we can find the missing value by determining what value multiplied by 38 would give us 164.

Solving the equation

38x = 164

x = 164/38,

= 4.32.

Therefore, the missing value in the second row is 164:38:4.32.

In the third row, only one value is given, which means we need to determine the other value that would make the ratio equivalent to the previous rows.

Since the missing value in the first two rows is 4.32, we can set up the equation

57: x = 82/19

And solve for x.

This gives us x = 57 * (82/19), which is approximately 244.42. Therefore, the ratio in the third row is 57:244.42.

In the fourth row, we can use the same approach as the previous rows to find the missing value. Setting up the equation

76x = 328

x = 328/76,

which is approximately 4.32. Therefore, the missing value in the fourth row is 328:76:4.32.

Finally, in the last row, we are asked to explain the process of completing a ratio table. To complete a ratio table, we need to determine the missing values that would make the ratios equivalent. This involves setting up equations based on the given ratios and solving for the missing values. Once we have found the missing values, we can add them to the table and ensure that the ratios are equivalent across all rows

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If A be a matrix with linearly independent columns, then the statement that must be true is (A) The equation Az=b always has a solution for all b.

Since the columns of A are linearly independent, the matrix A has full column rank, i.e., its column space is the entire space R^n. Here are the implications of this fact for each statement:

A. The equation Az=b always has a solution for all b.

This is true, because for any b in R^n, we can write it as a linear combination of the columns of A, say b=c_1a_1+c_2a_2+...+c_na_n. Then, the solution to Az=b is simply z=[c_1,c_2,...,c_n]^T.

B. The equation Ab has a solution for all b precisely when it has more rows than columns.

This statement is false. The equation Ab=b is always solvable, regardless of the dimensions of A and b. The solution is simply b expressed in the basis of the column space of A.

C. There is no easy way to tell if Ax-b has a solution for all b.

This statement is also false. Since the columns of A are linearly independent, the equation Ax=b has at most one solution for each b. Therefore, Ax=b has a solution for all b if and only if the columns of A span the entire space R^n. This can be checked by computing the rank of A.

D. The equation Az-b has a solution for all b precisely when it has more columns than rows.

This statement is false. The equation Az=b is always solvable, regardless of the dimensions of A and b, as we have seen in (A).

E. The equation Ax-b never has a solution for all b.

This statement is false. The equation Ax=b has at most one solution for each b, and it is solvable for all b if and only if the columns of A span the entire space R^n, as we have seen in (C).

F. The equation Az-b has a solution for all b precisely when it is a square matrix.

This statement is false. The equation Az=b is always solvable, regardless of whether A is square or not, as we have seen in (A).

Therefore, the only true statement among the given options is (A) The equation Az=b always has a solution for all b.

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The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

What is an angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

There is an angle of elevation from point R to S. Thus point R is lie above S.

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

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The length of the guy wire, to the nearest foot is 23 feet.

Based on the information provided, we can logically deduce that triangle ABE (ΔABE) is similar to triangle (ΔCDE) and the following parameters about the geometric figures;

Additionally, the corresponding sides of similar triangles are equal;

AB/CD = BE/DE

AB/6 = (9 + 4)/4

AB/6 = 13/4

AB = 19.5 feet.

By applying Pythagorean' theorem, side AE is given by:

AE = √(AB² + BE²)

AE = √(19.5² + 13²)

AE = 23.44 ≈ 23 feet.

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AC=3x-4 AB=62 BC=x-2, x = 17. This can be solved by using the concept of simplification.

A line is an endlessly long object without breadth, depth, or curvature in geometry. So, despite the fact that they can exist in two, three, or more dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its endpoints in daily life.

The most clear and simple way to calculate depreciation is along a straight line. It is most beneficial when an asset's value declines slowly over time at a pace that is close to constant.

Given that,

AC=3x-4

AB=62

BC=x-2

As we can clearly see in line AB:

AC+BC= AB

=>(3x-4)+(x-2)= 62

=>4x -6 = 62

=>4x = 62+6

=>4x = 68

=>x = 68/4

=>x= 17

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The complete question is as follows:

The length of the sides x and y of the right-angled triangle are both equal to 9m using the trigonometric ratio of sine and cosine of angle 45°

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle, we shall calculate for the length x and y by application of the trigonometric ratio of sine and cosine for the angle 45°.

sin 45° = y/9√2 {opposite/hypotenuse}

by cross multiplication

y = 9√2 × sin 45°

recall that sin 45° = √2/2

y = 9√2 × √2/2

y = 9m

cos 45° = x/9√2 {adjacent/hypotenuse}

by cross multiplication

x = 9√2 × cos 45°

recall that cos 45° = √2/2

x = 9√2 × √2/2

x = 9m

Therefore, the length of the sides x and y of the right-angled triangle are both equal to 9m using the trigonometric ratio of sine and cosine of angle 45°.

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A multiplying polynomials calculator is a tool used to multiply two or more polynomials together.

A multiplying polynomials calculator is a tool used to multiply two or more polynomials together. It can be helpful for simplifying algebraic expressions, solving equations, and performing various calculations in mathematics and engineering.

The calculator takes the coefficients of each polynomial as input and uses the distributive property to multiply the terms of each polynomial together. It then combines like terms and arranges the result in descending order of degrees. Multiplying polynomials can be a tedious and error-prone process, especially for large polynomials, so using a calculator can save time and reduce the chances of errors. The multiplying polynomials calculator is commonly used by students, teachers, engineers, and anyone working with algebraic expressions.

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Answer: x=15

Step-by-step explanation:

3x+5=50

3+5=50

Subtract the numbers

3x+5-5=50-5

3x/3=45/5

x=15

The area of the triangular prism is 240 mm²

A triangular prism is a prism with three rectangular faces connecting its two congruent triangular faces. It consists of 5 faces, 6 edges, and vertices.

The sum of the areas of all the triangle's faces is the surface area. By using the net of a prim we can determine the area of the prism as given below. Here we calculate the individual parts of the net to get the total area.

Here we have

A right triangular prism and its net  

The area of the prism can be calculated by calculating the area of the 2 triangles and the areas of 3 rectangles in the given net

As we know Area of rectangle = Length × Width

Area of rectangle parts = [ 3 × 8 ] + [ 3 × 15 ] + [ 17 × 3 ]

= 24 mm² + 45 mm² + 51 mm²

= 120 mm²  

Area of triangle parts = 2 [ 1/2 (15 × 8) ]

= 120 mm²  

Total area of prism = 120 mm² + 120 mm² = 240 mm²

Therefore,

The area of the triangular prism is 240 mm²

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Answer:

C

...................

Answer:

B) 5

Step-by-step explanation:

   AB = 4 units

  BC = 3 units

Use Pythagorean theorem to find the length of AC,

                AC² = AB² + BC²

                      = 4² + 3²

                       = 16 + 9

                       = 25

                  [tex]AC = \sqrt{25}\\\\[/tex]

                 AC = 5 units

answer:

answer:1/8

answer:1/8explanation :

answer:1/8explanation :0.125 as a fraction in simplest form is 1/8

answer:1/8explanation :0.125 as a fraction in simplest form is 1/8Step 2: Find the HCF or the highest common factor of 125 and 1000.

answer:1/8explanation :0.125 as a fraction in simplest form is 1/8Step 2: Find the HCF or the highest common factor of 125 and 1000.hope this helped.

The measure of ∠S is 75 degrees

The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:

cos(S) = (q² + r² - s²)/2qr  

where q, r and s are the lengths and Q, R and S are the angles

Using the formula:

cos(S) = (q² + r² - s²)/2qr

cos(S) = (99² + 17² - 96²)/(2*99*17)

cos(S) = 0.2597

S = cos⁻¹(0.2597)

S = 75 degrees

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High temp ≥ Low temp + difference

High temp ≥ -8°F + 35°F

High temp ≥ 27°F

An inequality is a relationship between two different quantities or expressions.

An inequality may be expressed by a mathematical sentence that uses the following symbols:

< is less than

> is greater than

≤ is less than or equal to

≥ is greater than or equal to

≠ is not equal to

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Answer: 152

Step-by-step explanation:

Length: f(x) = x+5

Width: g(x) = 7x-2

Area: A= f(x) *g(x)

A= (x+5)(7x-2)

= 7x^2 -2x + 35x -10

= 7x^2 +33x -10 // Substitute 3 in for x

=7(3)^2 +33(3) -10

=7(9) +99 -10

=63+99-10

=152

Answer:

152

Step-by-step explanation:

took the test xx

The corresponding parts are as follows;

Angle ATS = Angle ABC

side AS = side AC

Angle SAT = Angle CAB

Angle AST = Angle ACB

Side AT = Side AB

ΔABC ~  ΔDEF  only if ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal and the angle included in both sides are congruent.

Suppose the two sides of ΔABC are AB and BC, and that of DEF be DE and EF.

For two similar figures, the pair by pair similar angles of those two similar figures are called corresponding angles. They are of same measurement.

We are given the similar triangles as;

ΔACB =  ΔAST

Angle ATS = Angle ABC

side AS = side AC

Angle SAT = Angle CAB

Angle AST = Angle ACB

Side AT = Side AB

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