evaluate without a calculator: sec 30°

Answer:

  the direction changes if the coefficient is negative

Step-by-step explanation:

You want an explanation of the way you know the direction of the inequality symbol without solving the inequality.

If you have an inequality of the form ...

  ax < ( )

where the contents of ( ) has no terms containing x, then you know the solution is obtained by dividing both sides by 'a'.

You know that if 'a' is negative, that division will mean the inequality symbol is reversed:

  x > ( )/a . . . . . . . . for a < 0

When making this assessment, you only need to consider the sign of 'a', the coefficient of x. The rest of the inequality is immaterial.

__

Additional comment

Just as the sign of the variable coefficient tells you where the number line shading is relative to the boundary value, so the variable sign(s) can tell you where the shading is for a two-variable inequality.

For example, the inequality ...

  x -3y > 2

has a positive coefficient for x, so the shading will be to the right of the line (where x-values are greater than those on the boundary.)

The coefficient of y is negative, so this can be rewritten as ...

  y < ( )

meaning that shading is below the boundary line (where y-values are less than boundary values).

This inequality will have a boundary line with positive slope such that "right of the line" is the same as "below the line."

The shaded set of numbers shown on the y-axis on the graph can be expressed in interval notation as interval notation as

{y∣-11≤y<∞} or [-11,∞). This set represents the function's range.

Endpoints that are part of an interval are indicated by square brackets. Endpoints that are not part of an interval are indicated by parentheses. When using or, parentheses are always used.

As a result, the set of shaded numerals displayed on the interval notation can be used to express the y-axis as {y∣-11≤y<∞} or [-11,∞)

This set displays the functional domain.

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Kareem has $22, Raina has $28, Eric has $88.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Raina, Kareem, and Eric have a total of $138 in their wallets.

let Kareem has x dollar.

Then Raina has (x+6) dollar

and, Eric has 4x dollar

So, x+ 4x + x + 6 = 138

6x + 6 = 138

6x = 132

x= 22

Thus, Kareem has $22.

Raina has = 22 +6 = $28

and, Eric has =4x = $88

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Answer: [tex]6 \text{ m}^2[/tex]

Step-by-step explanation:

[tex]A=\frac{1}{2}bh=\frac{1}{2}(7.5)(1.6)=6 \text{ m}^2[/tex]

The complete table:

The fence → cost

3  → $18

5 → $30

7  → $42

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Yolanda is building a fence around her garden.

For every 2 feet of fencing, the cost is 12.

The unit rate = 12/ 2 = $6 per feet

The complete table:

The fence → cost

3  → $18

5 → $30

7  → $42

Therefore, the complete table is given above.

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Answer: it's 39.

Step-by-step explanation: for this figure, you want to divide it into two parts:    The triangle and the rectangle.

The triangle has a base of 6, and a height of 3.

The formula for area of a triangle is 1/2 bh.

So the area of the triangle is 9!! 6 x 3 is 18.. divided by two is 9.

Then the rectangle, a= b(h)

the height is 6 while the base is 5.

When you multiply thsoe two you get 30.

Rounding to the nearest day, the answer is 37 days.

Interest is a fee charged by a lender to a borrower for the use of money. It is typically a percentage of the amount borrowed and is paid periodically, such as monthly or annually. Interest is calculated based on the principal amount, which is the original sum of money borrowed, and the interest rate, which is the percentage charged for borrowing the money. Interest is a way for lenders to earn income on their investments, and for borrowers to pay for the use of money they do not currently have. There are different types of interest, such as simple interest, which is calculated only on the original principal, and compound interest, which is calculated on both the principal and any accumulated interest.

To find out how long it will take for Don's investment to earn $205 in interest, you can use the formula:

time = (interest earned) / (annual interest rate * balance)

First, you need to convert the interest rate from a percentage to a decimal by dividing it by 100: 5.5% ÷ 100 = 0.055.

Next, you can plug in the values:

time = $205 / (0.055 * $5500)

time = 0.03727272727 years, or approximately 37.2727272727 days.

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For given triangles, The correct proportion will be 16/12=18/x.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

For given triangles ABC and DEF

as ABC ≅DEF

Then AB=DE, BC=EF AND AC=DF

given BC=16, EF=12 and DE=18 then AB=?

Let AB=x then

16/12=18/x as ABC ≅DEF

Hence,

          The correct proportion will be 16/12=18/x.

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The slope-intercept equation of the line that includes the points (0, 12) and (4, 36) is y = 6x + 12.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (0, 12) and (4, 36) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 12 = (36 - 12)/(4 - 0)(x - 0)

y - 12 = 6(x - 0)

y = 6x + 12

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Answer: if u don't know that this language is than ill tell u.

its just random words that someone typed in. I'm being honest this is not a language this is some random typed words. trust me pls I'm being honest fr.

Step-by-step explanation: what I did was going a a type of book that has all the language on it so u get to know the language.

The center of the circle is (13, 2)

The radius of the circle is 9

To find the center and radius of the circle described by the equation:

(x + 13)² + (y + 2)² = 81

We can compare with the standard form of the equation of the circle which is

(x - h)² + (y - k)² = r²

it can be deduced that

-h = 13, h = -13

-k = 2, k = -2

r² = 81, r = 9

This is the equation for a circle with center at (13, 2) and radius 9. So the center of the circle is (13, 2) and the radius is 9.

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Answer:

Center = (-13,-2)
Radius = 9

Answer:

15.25 - 5.75 h

this my be it but i'm not shore

The standard form of the given quadratic equation is;

x² - x - 6

The standard form of a quadratic equation can be written in the form;

ax² + bx + c =0 (In terms of variable x), where a ≠ 0.

The equation is expressed in the question as;

(x + 2)(x - 3)

To convert to standard form, we will just multiply out the bracket to get;

x² + 2x - 3x - 6

= x² - x - 6

Thus,  that final expression is the standard form of the given quadratic expression

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Answer:

It is 35 degrees that is the answer

Answer:

A

Step-by-step explanation:

We need to know that angles in a rhombus add up to 360!

To find m∠JKM we have to divide m∠JML by 2.

This is because opposite angles in a rhombus must be equal meaning that the line going from one end of the rhombus to the other end must be exactly in half!

We are told that m∠JML = 70°...

Have a lovely day :)

Answer: 882

Hope this helps :)

Step-by-step explanation:

Since there is only one other term in the parenthesis, there will only be one step.

Distribute the 9 to 98.

9 * 98 = 882

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{9(98)}\\\mathsf{= 98(9)}\\\mathsf{= 98 + 98 + 98 + 98 + 98 + 98 + 98 + 98 + 98}\\\mathsf{= 196 + 196 + 196 + 196 + 98}\\\mathsf{= 392 + 392 + 98}\\\mathsf{= 784 + 98}\\\mathsf{= 882}\\\\\\\\\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathsf{882}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The relationship is proportional, when, there is no added constant, which shows a proportional relationship represented by the equation y = 1/2x.

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol "::" or "=".

here, we have,

y = 1/2x

If the relationship is proportional, there is no added constant. The relation that is proportional is ...

y = 1/2x

Hence, The relationship is proportional, when, there is no added constant.

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The percent of people that preferred vanilla ice cream is equal to 25%.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the number of people that prefer vanilla ice cream, we would develop an expression to multiply the fraction of the number of people by 100 as follows;

Number of people who prefer vanilla ice cream = 9/36 × 100

Number of people who prefer vanilla ice cream = 0.25 × 100

Number of people who prefer vanilla ice cream = 25%.

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The equation of the line passing through point (-8, 7) and parallel to a line -9x+8y = -24, is y = 9x/8 + 16

The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

Given that, a line is passing through point (-8, 7) and parallel to a line -9x+8y = -24,

We need to find the equation of the line,

Converting the parallel line equation into slope-intercept form,

-9x + 8y = -24

8y = 9x - 24

y = 9x/8 - 3

Here, slope = 9/8

We know that, two lines which are parallel have equal slopes,

Therefore, the slope for the asked line is 9/8

Now, the equation of line is =

y = 9x/8 + c

To find c, put x = -8 and y = 7 in the equation,

7 = -9 + c

c = 16

Therefore, the equation =

y = 9x/8 + 16

Hence, the equation of the line passing through point (-8, 7) and parallel to a line -9x+8y = -24, is y = 9x/8 + 16

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The value of p and q are set to be equal ( option B)

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The sum of angles In a triangle is 180.

Therefore to find p

p+80+20 = 180

p = 180-(100)

p = 80

To find angle q

q+45+55 = 180

q = 180-(45+55)

q = 180-100

q = 80

q = 80= p

therefore the values of p and q are equal

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Answer:

x = 27

Step-by-step explanation:

[tex]\displaystyle 4x^{\frac{2}{3}}-5=31\\4x^\frac{2}{3}=36\\x^{\frac{2}{3}}=9\\x=9^\frac{3}{2}\\x=27[/tex]

Answer:

f(x) = {

C(x) = 6, 0 < x ≤ 50

C(x) = 8, 50 < x ≤ 100

C(x) = 10, 100 < x ≤ 200

}

Step-by-step explanation:

The probability that the mean of a sample of 36 people is less than 13 is approximately 0.744.

Cumulative probability refers to the sum of probabilities of all possible outcomes that are less than or equal to a specific value. It is used to calculate the probability of observing a value less than or equal to a given value. For example, if we have a cumulative probability distribution function (CDF), we can use it to find the probability that a random variable is less than or equal to a particular value. The cumulative probability is the area under the probability density function (PDF) to the left of the specified value. It provides a complete picture of the distribution of a random variable, and it can also be used to calculate probabilities for ranges of values.

To find the probability that the mean of a sample of 36 people is less than 13, we need to calculate the z-score associated with the value of 13, and then look up the corresponding cumulative probability in a standard normal table.

The z-score is given by:

z = (13 - 12) / (3.2 / √(36)) = 0.625

Using a standard normal table, we can find that the cumulative probability associated with a z-score of 0.625 is approximately 0.744.

So, the probability that the mean of a sample of 36 people is less than 13 is approximately 0.744.

For the second part of the question, the probability that the mean of a sample of 36 people is greater than 13 can be calculated as 1 minus the cumulative probability associated with a z-score of 0.625, which is approximately 1 - 0.744 = 0.256.

For the last part of the question, the probability that the mean of a sample of 36 people is between 11 and 12 can be calculated by subtracting the cumulative probabilities associated with the z-scores corresponding to 11 and 12 from a standard normal table.

z1 = (11 - 12) / (3.2 / √(36)) = -0.938

z2 = (12 - 12) / (3.2 / √(36)) = 0

Using a standard normal table, we find that the cumulative probability associated with z1 = -0.938 is approximately 0.172, and the cumulative probability associated with z2 = 0 is 0.5.

So, the probability that the mean of a sample of 36 people is between 11 and 12 is approximately 0.5 - 0.172 = 0.328.

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The equation connecting a and d where a is the first term and d is the common difference​ is; a + d = 0

The formula for the nth term of an arithmetic sequence is expressed as;

aₙ = a + (n - 1)d

where;

a is first term

d is common difference

n is position of term

Thus;

a₈ = a + 7d

a₄ = a + 3d

The 8th term of an A.P is three times the 4th term. Thus;

a + 7d = 3(a + 3d)

a + 7d = 3a + 9d

3a - a = 7d - 9d

2a = -2d

a = -d

a + d = 0

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Answer: x = -4

Step-by-step explanation: Multiply both sides of the top equation by 2 so you can cancel the y's.

4x + 3x = -28.

7x = -28

x = -4

Answer:

The expression (6 × 10^7) × 0.007 simplified is 4.2 x 10^5.

Step-by-step explanation:

The factored form of the trinomial x² - 2x - 35 is ( x - 7 )( x + 5 ).

Given the trinomial in the question;

x² - 2x - 35

To simplified in a factored form,

Consider the trinomial in its standard form; ax² + bx + c.

Now, find a pair of integers whose product is c and whose sum is b.

In this case, we use -7 and 5

The product of -7 and 5 = -35

The sum of -7 and 5 = -2

Next, we write the factored form using the integers -7 and 5

( x - 7 )( x + 5 )

Therefore, the factored form is ( x - 7 )( x + 5 ).

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The equation of the line that is parallel to  2x - y = 7 and passes through the point (10, 0) is  y = 2x - 20.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

To find an Equation that is parallel to 2x - y = 7 and passes through the point (10, 0)

Since, Both equations are parallel thus, the slope of the given equation will be the Same.

equation of the first line in slope intercept form: y = 2x - 7

Thus, Slope = 2

From the general formula of the linear equation in slope-intercept form:

y=mx+b,

where m is the slope

b is the y-intercept

in our case,

Slope = 2

So Line,

y = 2x + b

Since line passes through (10, 0)

b= -20

Thus,

Equation of line  y = 2x - 20

Therefore, The equation of the line that is parallel to  2x - y = 7 and passes through the point (10, 0) is  y = 2x - 20.

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If 24,783 is invested, part at 15% and the rest 9%. If the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 9% by $894.09: 51,960 is invested at 15%, and 22,823 is invested at 9%.

Let's x represent the amount invested at 15%

Let the  amount invested at 9% = 24,783 - x.

Interest earned at 15% is 0.15 * x

Interest earned at 9% is 0.09 * (24,783 - x)

We can set up the equation: 0.15x = 0.09 * 24,783 - 0.09x + 894.09

Solving for x:

0.06x = 24,783 * 0.09 + 894.09

0.06x = 2223.47 + 894.09

0.06x = 3117.56

x = 51,960

So,

(24,783 - x)

24,783 - 51,960

= 22,823

Therefore 51,960 is invested at 15%, and 22,823 is invested at 9%.

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Answer:

vjjvwplast

Step-by-step explanation:

past I 1 days its just is right