The tangent of O in this triangle is Which equation must be true? (MGSE9-
12.G.SRT.8)
a®
19°
A. sin a = 2
B. tan a = 2
C. sina = 1/2
D. . tan a = 1/2

The required equation of the line in the slope-intercept form is given as x = -3.

Given that,
to determine the equation of the line passing through (-3,2 and perpendicular to the line y = -4,

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The slope of the given line y = -4 is,
m = 0
Slope of the required line = -1/ 0
Now,
Slope intercept form of the equation,
y - y₁ = m (x - x₁)
y - 2 = -1/0{x + 3}
x = -3

Thus, the required equation of the line in the slope-intercept form is given as x = -3.

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If the probability of a dancing lady accepting an invitation to dance is 0.18.The accepted number of ladies asked before is 7.14 .

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).

According to the above discussion:

P{x(bar) (0.18)} = 0.07142371

                       = 7.14%

Therefore, the expected number is 7.14%.

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Answer:

[tex]x^{1}[/tex]=[tex]\frac{-3-\sqrt{7} }{2}[/tex] [tex]x^{2}[/tex]=[tex]\frac{-3+\sqrt{7} }{2}[/tex]

Step-by-step explanation:

1) collect like terms and move everything to the left

2[tex]x^{2}[/tex]2+3x-3+3x+4=0

2[tex]x^{2}[/tex]2 +6x-3+4=0

2) find the coefficients so you can plug them into the quadratic formula

a=2, b=6, c=1

3) plug these into the quadratic formula

4) use a calculator to solve both the positive and negative equations

The required measurement of each interior angle of the animal pen

An  interior angle is a point inside a shape. The polygons are the shut shape that has sides and vertices. A standard polygon has generally its interior angle equivalent to one another. For instance, a square has generally its  interior angle equivalent to the right point or 90 degrees.

The question expects us to track down the inside point of a customary heptagon.

To do this initially compute the outside angle of that polygon.

The amount of outside angle is 360°. A heptagon has 7 sides.

Along these lines, one exterior angle = 360°/7 = 51.4°

inside angle+exterior angle=180°

Interior angle = 180-51.4 = 128.6°

Thus, required interior angle is 128.6°.

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The cost of each apple is equal to $0.23.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=8x+3. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=8 and b=3.

The question gives:

You should convert the data into an equation:

15A+2.75=6.20

15A=6.20-2.75

15A=3.45

A=3.45/15

A=0.23

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Answer:

18b-45

Step-by-step explanation:

9(2b-5)

9*2b-9*5

18b-9*5

18b-45

Answer:

9(2b - 5)

Distribute

9(2b - 5)

18b - 45

Solution

18b - 45

The function is linear when the highest degree the the function is 1 .

In the question ,

we have been asked about when a function is called as linear .

By the definition ;

the Linear function is the function that has the highest degree as 1 and

On the coordinate plane the linear function represents the straight line .

the general form of the linear function is f(x) = mx + d ,

the slope is "m" and the y intercept is "d" .

The Examples of Linear Function are

f(x) = 3x + 2 ,

f(x) = -6x + 7

f(x) = 8 .

Therefore , the characteristic for the function to be linear is explained above.

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The polynomial function is P(x) = x⁴ - 14x³ + 59x² - 50x - 74

A polynomial is a function in which the least power of the unknown is 2.

The root of a polynomial is the value of the unknown which makes the polynomial equal zero.

Since we have that the given polynomial has roots 1 - √3 and 6 - i.

We also know that their conjugates 1 + √3 and 6 + i are also roots of the polynomial.

So, the factors of the polynomial are

So, the required polynomial is P(x) = [(x - 1) + √3][(x - 1) - √3][(x - 6) + i][(x - 6) - i]

= [(x - 1)² - (√3)²][(x - 6)² - i²]    (Since a² - b² = (a - b)(a + b))

= [(x - 1)² - 3][(x - 6)² - (- 1)]

= [(x - 1)² - 3][(x - 6)² + 1]

Expanding the brackets, we have

= [x² - 2x + 1 - 3][(x² - 12x + 36 + 1]

= [x² - 2x - 2][(x² - 12x + 37]

= x⁴ - 12x³ + 37x² - 2x³ + 24x² - 74x - 2x² + 24x - 74

Collecting like terms, we have

= x⁴ - 14x³ + 59x² - 50x - 74

So, the polynomial is P(x) = x⁴ - 14x³ + 59x² - 50x - 74

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The marked price is $1518 and the rate of the discount is 8.9%.

The marked price or list price is the amount that appears on a product's label. This is the price that the product will be sold for. But this price might be discounted in some way, and the product's real selling price might be less than the advertised price. Typically, MP is used to indicate it.

This was the initial selling price, but $194 was deducted, making the final price $1394.

Use the following formula to determine percent markdown:

(Markdown amount/Selling price)×100 is the percent markdown.

To locate Markdown

Original Selling Price – Markdown Price

Connect what you have now.

Markdown=$1518-$1394

M=124

The Markdown, as we already know, is 124.

At this point, Percent Markdown equals (124/1394)×100 PM=0.088952654×100

PM=8.9 (rounded)

As a result, the growth rate is 8.9%.

And $1394+$124=$1518.

Hence, The marked price is $1518 and the rate of the discount is 8.9%.

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The value of x in the solution to this system of equations y + 2x = -1 and y=x+4 is 3.

The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients. To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

Given,

Equations:

y + 2x = -1

y = x + 4

y - x = 4

Using elimination method,

y + 2x = -1

y - x = 4

-------------

x = 3

The value of x in the solution to this system of equations y + 2x = -1 and y=x+4 is 3.

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The pole and the birdhouse both stand 18.75 feet tall.

Jack has two dogs and eight cats. Jill owns 4 dogs and 7 cats. In total, how many dogs are there? How many more cats does Jane have than I do if she has 23 and I have 2, and then Jane gives me 5 cats?

To answer a word issue with algebra:

Establish a variable.

Utilizing the variable, write an equation.

Make the equation work.

Use the variable to determine the answer if it is not the word problem's solution.

A person standing close by casts a shadow that is five feet long. The individual is 4 feet tall..

Assume that for the birdhouse and the pole are (x) ft tall.

The shadow is now 5 feet long for a person that is 4 feet tall.

Then, for one feet long person, the shadow would be (5/4) feet long.

Then, for 15 feet long -

[tex]\frac{x}{15}[/tex] = [tex]\frac{5}{4}[/tex]

x = (15 x 5)/4

x = 75/4

x = 18.75 feet tall

As a result, both the pole and the birdhouse are 18.75 feet tall.

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Answer: no

Step-by-step explanation: the slope stays the same because the image and pre- image are parallel which means their slope is equal

1. The fraction of full-time employees who work in the bank is 16/31.

2. The fraction of pieces that David need to fix to complete the puzzle is 9/27

3. The fraction of girls that wore red outfits is 1/2.

4. The fraction of books on the shelf that are in Spanish is 2/7.

1. Alocal community bank has 31 employees on it’s rolls. 15 employees work part-time at the bank. The fraction of full-time employees will be:

= (31 - 15) / 31

= 16/31

2. David was gifted a 28 piece puzzle by his aunt. He has fixed 19 pieces of the puzzle. The fraction of pieces that David need to fix will be:

= (28 - 19)/28

= 9/28

3. 20 girls were dressed in green outfits and 10 girls donned red outfits at a dance recital. The fraction of girls that wore red outfits will be:

= 10/20

= 1/2

4. A section of Tina’s bookshelf has 15 French books and 6 Spanish books. The fraction of books on the shelf that are in Spanish will be:

= Spanish books / Total books

= 6 / (15 + 6)

= 6/21

= 2/7

The above illustrate the fraction.

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Answer:

A and B

Step-by-step explanation:

The triangle is labeled that all three sides are equal and all three angles are equal; thus, it is an equilateral triangle and “B” is correct.

Acute triangles have all acute angles. Understanding that the triangle is equilateral, equilateral triangles have all equal angles, and the total of all three angles in a triangle is 180, we can determine that all three angles are acute and the triangle is acute, so “A” is right. (one angle = x; three angles are equal and add up to 180 —> 3x = 180; x = 60; all angles are acute).

The area of the triangle will increase at a rate of 3.81 m² per second

Given,

The length of the sides of the triangle are base, 12 m and hypotenuse 15 m

Area of the triangle = 1/2 bh

We have to find h;

That is,

Sin ∅ = opposite side /hypotenuse = h/15

h = 15Sin ∅

d∅/dt = 0.06rad/s

Now,

A = bh/2 = 12 × 15sin∅/2

A = 90sin∅,

By differentiating this equation with respect to A, we have

d(A)/dt = 90cos∅d∅/dt

d(A)/dt = 90cos∅(0.06)

∅ = π/4, cosπ/4 = 0.7071

90×0.7071×0.06

= 3.81m²/s

That is,

The area of the triangle will increase at a rate of 3.81 m² per second

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Answer:

The answer to the problem is:

(i) The speed of the car at B is -4 ms$^{-1}$.

(ii) The distance AB is 32 meters.

(iii) The time taken for the car to travel from B to C is 10 seconds.

Step-by-step explanation:

To find the speed of the car at B, we can use the formula $v = v_0 + at$, where $v$ is the final speed, $v_0$ is the initial speed, $a$ is the acceleration, and $t$ is the time. In this case, $v_0 = 20$ ms$^{-1}$, $a = -6$ ms$^{-2}$, and $t = 4$ s. Plugging these values into the formula gives us:

$v = 20 + (-6)(4) = 20 - 24 = -4$ ms$^{-1}$

Thus, the speed of the car at B is -4 ms$^{-1}$.

To find the distance AB, we can use the formula $d = v_0t + \frac{1}{2}at^2$, where $d$ is the distance, $v_0$ is the initial speed, $a$ is the acceleration, and $t$ is the time. In this case, $v_0 = 20$ ms$^{-1}$, $a = -6$ ms$^{-2}$, and $t = 4$ s. Plugging these values into the formula gives us:

$d = (20)(4) + \frac{1}{2}(-6)(4^2) = 80 - 48 = 32$ meters

Thus, the distance AB is 32 meters.

To find the time taken for the car to travel from B to C, we can use the formula $v^2 = v_0^2 + 2ad$, where $v$ is the final speed, $v_0$ is the initial speed, $a$ is the acceleration, and $d$ is the distance. In this case, $v_0 = -4$ ms$^{-1}$, $v = 20$ ms$^{-1}$, $a = 2$ ms$^{-2}$, and $d$ is the distance from B to C. We can find this distance by using the formula for distance and setting $t = 0$, since we're looking for the time it takes the car to travel from B to C, not from A to B:

$d = (20)(0) + \frac{1}{2}(-6)(0^2) = 0 - 0 = 0$ meters

Thus, the distance from B to C is 0 meters. Plugging these values into the formula gives us:

$20^2 = (-4)^2 + 2(2)(0) = 16 + 0 = 16$

We can solve this equation for $t$ to find the time it takes the car to travel from B to C:

$t = \sqrt{\frac{v^2 - v_0^2}{2a}} = \sqrt{\frac{20^2 - (-4)^2}{2(2)}} = \sqrt{\frac{400}{4}} = \sqrt{100} = 10$ seconds

Thus, the time taken for the car to travel from B to C is 10 seconds.

The velocity-time graph for the journey from A to C would have a positive slope from A to B, a negative slope from B to C, and a positive slope from C to the end of the journey.

In general, linear equations have one solution. However, they can have infinitely many solutions in some cases.

A linear equation in mathematics is an equation that can be written in the form

ax + b = 0

The values of x that make this equation true are the solutions to the equation. Generally speaking, linear equations have one solution, which means that there is only one value of x that will make the equation true. However, in some cases, linear equations can have infinitely many solutions. For example, if a = 0 and b = 0, then any value of x will make the equation true.

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The quotient of given polynomials division is x+2. So, the correct answer is option A.

A quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Given that, (x²+3x+2)÷(x+ 1)

x²+3x+2 can be written as

x²+1x+2x+2 (Splitting of middle term)

= x(x+1)+2(x+1)

= (x+1)(x+2)

Now, (x+1)(x+2)÷(x+1)

= [(x+1)(x+2)]/(x+1)

= (x+2)

Therefore, option A is the correct answer.

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What is the quotient of the following division problem (x²+3x+2)÷(x+ 1).

a. x+ 2

b. x +1

c. x²+3x +2

d. 0

Answer:

-17/8

Step-by-step explanation:

-10-7         -17

----------  = -------

4-(-4)          8

The  difference between addition and subtraction of polynomials is that addition involves like terms  and subtraction  involves taking one polynomial away from another.

A polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as addition, subtraction, multiplication, and division (No division operation by a variable).In addition to polynomials, the like terms are included whereas, in subtraction, the like terms are subtracted. The addition of polynomials involves combining like terms to form a single expression, while subtraction involves taking one polynomial away from another. In addition, when subtracting polynomials, the sign of each term in the second polynomial needs to be changed (from positive to negative, or from negative to positive).

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Answer:

B

Step-by-step explanation:

The median is the mid point value. Basically the median is whatever number is in the middle.

The amount of a good that is demanded will decrease as its price rises

According to the Law of Demand, there is an indirect correlation between a good or service's price and the amount of that good or service that customers are willing and able to purchase .In other words, if an item's price increases, people are less able and willing to buy it, and vice versa.

According to the law of demand, the demand curve demonstrates the inverse relationship between the amount of items sought and price.

The amount of a good that is demanded will decrease as its price rises. The demand curve will therefore have a negative slope if the law of demand and its underlying assumptions are true.

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When we dilate the area , it is multiplied by the square of dilation factor .

In the question ,

it is given that ,

the area of the figure ,

we have to explain what will happen to the area when we dilate the figure .

let the figure be a square ;

let the unit square's length be x ,

and let the dilation factor be "k" ;and

So ,the comparison square's length be kx .

the area of the original square is = x² and

the area of the new square is = (kx)²

So , the ratio of the areas will be = (kx)²/x²

simplifying further ,

we get ,

= k² .

Therefore , the area gets multiplied by k² .

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Multiplying 3/8 by the whole part and the fractional part is 21/32.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the whole and fractional part can be 1 3/4.

Therefore, the multiplication by 3/8 will be:

= 3/8 × 1 3/4.

= 3/8 × 7/4

= 21 / 32.

The fraction is 21/32.

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Complete question

Multiply 3/8 by 1 3/4 which depicts the whole part and the fractional part.

The class mean and standard deviation of the distribution used should be of most concern.

What is mean and standard deviation?

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Answer: 282

Step-by-step explanation:

The balance of Marissa’s retirement account after 15 years if She makes an initial deposit of $1,000. Her contributions are $500 a month for the next 15 years is $8500.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given data:

Initial deposit = $1000

Her contributions are $500 a month for the next 15 years

Amount after 15 years = Initial deposit  + 15 × 500

Amount after 15 years = $1000 + 7500

Amount after 15 years = $8500

Therefore, the balance of Marissa’s retirement account after 15 years if She makes an initial deposit of $1,000. Her contributions are $500 a month for the next 15 years is $8500.

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Answer:

= 5√7 - 3√77: 63 or 5√7 - 3√77/63

It will take 27 minutes 30 seconds to complete eleven questions.

When two values are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage, direct proportionality is represented by a straight line and it equation is of the form -

y = kx

k = y/x

where [k] is the constant

Given is that the number of questions [y] completed and time [x] it takes to complete them are proportional to each other.

The number of questions [y] completed is proportional to the time [x] it takes to complete them.

That means,

y ∝ x

y = kx, where k is constant.

k = y/x

So, we can write;

y₁/x₁ = y₂/x₂

According to the question:

Let  y₁= 6, x₁= 15, y₂= 11.

Substituting the values,

6/15 = 11/x₂

x₂ = 11 x 15 / 6

x₂ = 11 x 5 / 2

x₂ = 55 /2

x₂ = 27. 5

x₂ = 27 minute and 30 seconds.

Therefore, it will take 27 minutes 30 seconds to complete 11 questions.

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