Given: AABC, mzC = 90°
m2A = 30°, BC = 16
Find: AB and AC
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Answer:

x=-1

Step-by-step explanation:

−2x+12=14

−2x=14−12

−2x=2

x=

−2

2

​

The answer for 20 is ( ∞ , 4) .

The answer for 22 is ( ∞ , 3) .

The answer for 24 is ( -∞ ,  -24/11) .

An inequality that consists of two or more parts is called a compound inequality. Either "or" or "and" may be used in these components. A number between 5 and 10 could be used as x in an inequality, for instance, if it states that "x is larger than 5 and less than 10". Any time one of the two inequalities is true when the two inequalities are united by the word or, the compound inequality is solved. The two separate solutions have been combined to form the final answer. Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and."(20)   2x - 5 > 3

x > 8/2

x > 4

Hence , ( ∞ , 4)

(22)   -x + 1  > -2

x > 3

Hence , ( ∞ , 3)

(20)   -5/8x + 2 + 3/4x > -1

11x > -24

x > -24/11

Hence , ( ∞ , -24/11)

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Among the options given in the question, the following are the properties of the linear correlation coefficient:

The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

If r=−​1, then a perfect negative linear relation exists between the two variables.

Properties of linear correlation coefficient:

Linear correlation coefficient is a value calculated from given data and used to measure the strength of linear relationship between two variables, for instant between x and y variables.

The sign of this coefficient (r) indicates the direction linear relationship will take between x and y. Below are some properties of the linear correlation coefficient:

Now, the properties of the linear correlation coefficient among the given ones in the question are:

b. The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

d. A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

f. If r=−​1, then a perfect negative linear relation exists between the two variables.

Hence, options b, d and f are correct.

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Probability of people liking comedy movies = 1/6

Hence,

If total number of people are 90, then the number of people liking comedy movies = 90/6 = 15

If total number of people are 180, then the number of people liking comedy movies = 180/6 = 30

If total number of people are 270, then the number of people liking comedy movies = 270/6 = 45

If total number of people are 360, then the number of people liking comedy movies = 360/6 = 60

Let the x-axis represent the total number of people and,

The y-axis represent the number of people liking comedy films.

The function will be :-

f(x) = x/6 , where x is the total number of people.

The graph is attached.

67 cubes of area 1.5 cm² can be fitted in the rectangular prism of volume 100 cm³.

So, first, we need to find the volume of the rectangular prism as follows:

The formula for the volume of the rectangular prism: V= whl

Substitute values as follows:

The volume of a rectangular prism is 100 cm³.

Now, the area of the cube:
The formula for the area of the cube: is 6a²

The area of the cube is 1.5 cm².

A number of cubes that can be fitted in the rectangular prism:

Therefore, 67 cubes of area 1.5 cm² can be fitted in the rectangular prism of volume 100 cm³.

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The correct question is given below:

A small cube has sides that are 1/2 cm. How many small cubes would fit inside a rectangular prism that has a length of 10, a width of 5, and a height of 2?

The change in score can be shown as:

On the number line we'll get:

And the points marked are:

The final score is:

The length of the triangular prism that has a volume of 225 cm³ and cross-sectional area of 15 cm² is calculated as: 15 cm.

A triangular prism looks like the shape shown in the image that is attached below. The shaded part is the cross-sectional area of the triangular prism.

The volume of a triangular prism = area of cross-section × length of the prism

The volume of a triangular prism = (1/2 × b × h) × l

Given the following:

Cross-sectional area of the triangular prism = 15 cm²

Length of the triangular prism = l

Volume of the triangular prism = 225 cm³

Substitute the values into the given formula for the volume of the prism:

225 = 15 × l

225 = 15l

Divide both sides by 15

225/15 = 15l/15

15 = l

l = 15 cm

Length of the prism is therefore 15 cm.

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(2x+3)(4x-7)

To convert this quadratic formula on the general expression, we need to multiply both parenthesis as follows:

8x^2 - 14x + 12x - 21 =

8x^2 -2x - 21

where a, b and c correspond to the coefficients of the equation:

a = 8

b = -2

c = -21

Answer:

x = 4

Step-by-step explanation:

Answer:36

Step-by-step explanation:

Usando propiedades de triangulos rectangulos veremos que el angulo de elevación es 38.65°

El ángulo de elevación del sol sera el angulo que esta en el vertice derecho del triangulo rectangulo en la imagen.

Sabemos que:

tan(a) = (cateto opuesto)/(cateto adjacente).

En este caso:

cateto opuesto = 24m

cateto adjacente = 30m

Entonces:

tan(a) = 24m/30m = 0.8

Aplicando la funcion inversa, obtenemos:

a = Atan(0.8) = 38.65°

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The statement "if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s" is false.

A vector set's linear independence is an important attribute. If no vector in a set can be written as a linear combination of the other vectors in the set, the set is said to be linearly independent. The set is said to be linearly dependent if any of the vectors can be represented as a linear combination of the others.

If S is a linearly dependent set, then each vector in S is a linear combination of the others.

This is false.

For example, v₁ = (1,0), v₂ = (2,0), and v₃ = (1,1). Then v₂ = 2v₁ but v₃ is not a linear combination of v₁ and v₂, since it is not a multiple of v₁. But 2v₁ - 1v₂ + 0 v₃ = 0.

If an indexed set of vector S is linear dependent, then it is only necessary that one of the vectors is in the set.

Hence, the correct answer would be option (B).

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Answer:

57,600 square feet

57600 square feet of sod are needed to cover a football field.

The area of Rectangle is length times of width.

Given,

A football field measures 360ft by 160ft

We need to find square feet of sod are needed to cover a football field

Which means we need to find the area of  football field

let the length of  football field is 360 ft

Three hundred sixty feet

Width of  football field is One hundred sixty feet 160ft.

Area=Length×Width

=360×160

=57600 square feet

Hence, 57600 square feet of sod are needed to cover a football field.

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Answer:

-72q - 48

Step-by-step explanation:

Answer:

-75q - 45

Step-by-step explanation:

Given expression,

→ -3q - 9(5 + 8q)

Simplifying the expression,

→ -3q - 9(5 + 8q)

→ -3q + (-9 × 5) + (-9 × 8q)

→ -3q - 45 - 72q

→ -75q - 45

Hence, answer is -75q - 45.

For Sally to reach the cabin fastest the distance from point P to the distance cabin at point C must be 25 ft

Let Sally be at point S and the cabin diagonal-opposite to her at point C. We need to find the distance between P and C such that Sally reaches the cabin the quickest. We know SX = 100ft

By Pythagoras' theorem

SX² + XP² = SP²

⇒100² + x² = SP²

⇒SP = √(100²+x²)       (1)

speed = distance/ time

⇒ time = distance / speed

We need to minimize the time taken by sally

time taken to reach cabin t = (SP/3) + (PC/5)

⇒t = (SP/3) +(PC/5)

⇒t = (√(100²+x²) /3) + (PC/5)

⇒t = (√(100²+x²) /3) + (100-x/5)

⇒dt/dx = x/ (3*√(100²+x²)) -(1/5) = 0     (to minimize)

⇒5x = 3√(100²+x²)

⇒25x² = 9(100² + x²)

⇒16x² = 90000

⇒x²= 5625

⇒x = √5625

⇒x= 75 ft

Thus the distance from point P to cabin C = PC = 100 - x = 100-75=25 ft

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Answer:

5/8

Total = 5 cup of strawberry + 3 cup of blueberries

=8

1 cup of fruits=8 cup of mix fruits(5 cup of strawberry + 3 cup of blueberries)

=8-3

=5/8

The greatest number of bags that she can fill is 9.

The number of boxes of oatmeal that will be in each bag is 3

The number of boxes of raisins that will be in each bag is 2

In order to determine the greatest number of bags that she can fill, we needed to determine the highest common factor of 18 and 27. The highest common factor of a number is the greatest number that perfectly divides two or more numbers.

Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 27 = 1, 3, 9, 27

Highest common factor = 9

The greatest number of bags that she can fill is 9.

Number of boxes of oatmeal that will be in each bag: 27 / 9 = 3

Number of boxes of raisins that will be in each bag: 18 / 9 = 2

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Answer:The single transformation that maps triangle A onto triangle B is the reflection about the x-axis

Step-by-step explanation:

Answer: 27 students

Step-by-step explanation:

The value of 360 whole -5/6 in fraction upon calculation is found to be 2156/6 or 359.33

360 - 5/6 solving in fraction

This can be written as

360/1 - 5/6

taking the LCM of 1 and 6, the LCM is 6

Multiplying 6 with the numerator and denomenator of the term having 1 as its denominator and multiplying 1 with the numerator and denomenator of the term having 6 as its denominator,

360 x 6)/ 1 x 6 - (5 x 1)/ 6 x 1

= [tex]\frac{360*6}{1*6} - \frac{5*1}{6*1}[/tex]

=[tex]\frac{2160 - 5}{6}[/tex]

= 2156/6

= 359.333

Therefore the value of 360 whole -5/6 in fraction upon calculation is found to be 2156/6 or 359.33

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The value of x can be determined as 130 as is found out by solving the linear equation this formed from the provided data in the question.

An equation is said to be linear if the maximum power of the variable is consistently 1. It is also known to be as the one-degree equation.

There are numerous ways to express linear equations, but they often contain constants (such as "2" or "c") and call for straightforward variables (like "x" or "y").

The coefficients present in a linear equation, can be any expressions as long as they don't contain any of the variables, can be thought of as the equation's parameters.

Most of the times, a linear equation is written to represent a straight line.

Here it is provided that the equation is

x + 50 = 180

⇒ x = 130

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

STEP 2: Simplify the expression

For the quotient to be defined, the numerator and the denominator must be greater than zero, this means that:

For the numerator,

Merging both interval, we have:

Hence, the answer is given as:

Answer:

x ≥ -4

or [-4, ∞)

Step-by-step explanation:

What is value of x in the equation below?

33 ≥ -6x + 9

subtract 9 from both sides:

33 - 9 ≥ -6x + 9 - 9

24 ≥ -6x

divide both sides by -6 and remember to flip sign direction:

24/-6 ≥ -6x/-6

-4 ≤ x

or: x ≥ -4

in set builder notation: [-4, ∞)

Answer:

Below in bold

Step-by-step explanation:

33 ≥ -6x + 9

-6x ≤ 33 - 9

-6x ≤ 24

x ≥ -4

- note that the inequality is flipped as we are dividing by a negative.

Answer:

y=x+1

Step-by-step explanation:

first use the equation in point - slope form:

y+2=1(x+3)

then rearrange them to make it in slope intercept form - y=mx+b

y= 1x + 1 or y=x+1

(x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15 as there is no remaider.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given a polynomial function f(x) = x³ - x² - 17x -15.

If (x - 5) is it's factor then f(5) = 0.

∴ f(x) = x³ - x² - 17x -15.

f(5) = 5³ - 5² - 17(5) - 15.

f(5) = 125 - 25 - 85 - 15.

f(5) = 0.

So, the remainder is zero hence (x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15.

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Answer:

m = -3

Step-by-step explanation:

Distribute 8 to both sides

Add 40 to both sides

Add the numbers

Which you'll get 48

-16 divided by 48 = -3

The number that makes the ratio equivalent to 1:9 include 2 and 18.

The numbers that number that makes the ratio equivalent to 1: 9: 4 include 2, 18, and 8.

It should be noted that ratio is used to show the comparison between the numbers illustrated.

It should be noted that based on the information, 1:9 is equivalent to 2 and 18. This can be illustrated as:

= 2/18 = 1/9.

Also, 1:9:4 equals 2, 18 and 8. In their case, the ratio is multiplied by 2 to get the numbers.

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