Question 8 of 10
1 Point
Given the inequalities y< 2x+2 and y> x-7 graphed on the same coordinate
grid, which of the following coordinates gives a true statement?
O A. (2-2)
O B. (4.0)
O C. (0.4)
O D. None of the above

Answer:

y - 8 = -2(x - 6)

Step-by-step explanation:

Given the slope and one point on the line, we should use the point-slope formula:

y - k = m(x - h), where (h, k) is the point and m is the slope.

Here, we have y - 8 = -2(x - 6)

Answer:

y = - 2x + 20

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2, so

y = - 2x + c ← is the partial equation

To find c substitute (6, 8) into the partial equation

8 = - 12 + c ⇒ c = 8 + 12 = 20

y = - 2x + 20 ← equation of line

Using the Pythagorean theorem, given a right triangle with one leg 20 m and the hypotenuse 25 m, the length of the other leg is approximately 15 m.

To find the length of the third side of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In other words, if the lengths of the two legs are a and b, and the hypotenuse is c, the theorem is expressed as a^2 + b^2 = c^2.

Since we know the length of the hypotenuse (25 m) and one leg (20 m), we need to find the length of the other leg. Let's denote it as b. Therefore, the equation will be 20^2 + b^2 = 25^2. Solve for b, we get b = sqrt(25^2 - 20^2), which equals approximately 15 m.

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Answer:

1) x = 5√(1-sin^2t)

2) y = = -2+3t

Step-by-step explanation:

1)

Given rectangular equation:

x^2/25 + y^2 =1

Parametric equations y=-sint and x=?

Find parametric equation for x

Substituting value of y =-sint in given rectangular equation, we get

x^2/25 + (-sint )^2 =1

x^2/25 + sin^2t =1

x^2 + 25sin^2t = 25

x^2 =25 - 25sin^2t

taking square root on both sides

x= √(25 - 25sin^2t)

  = √25(1-sin^2t)

   = 5√(1-sin^2t)

2)

Given rectangular equation:

y=-3x+4

Parametric equations x=2-t and y=?

Find parametric equation for y

Substituting value of x=2-t  in given rectangular equation, we get

y= -3(2-t) +4

 = -6+3t+4

 = -2+3t !

30 x 30=900 square meters

The area of the square helicopter landing pad is equal to 900 square meters.

In Mathematics and Euclidean Geometry, the area of a square can be calculated by using this formula;

A = [tex]s^2[/tex]

Where:

By substituting the given side lengths into the formula for the area of square, we have the following;

Area of square, A = 30 × 30

Area of square, A = 900 square meters.

In this context, we can logically deduce that the area of the square helicopter landing pad is equal to 900 square meters.

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Answer: median

Step-by-step explanation: Statistical Mathematics

7, 10, 16, 21, 26, 30, 40, 43

Here we have an even number of the data entries so we get two values in the mid.

Now take the average of those mid values:

Answer:

259 divided by 170,000 gives you the % 259 is out of 170,000 which is .0015. Move the decimal two spaces to the right to get the actual commission rate=.15%

Answer: 52.5 units squared

Step-by-step explanation:

The formula to find the area of a trapezoid is, (base1 + base2)/2 * height

So you find out which variable is which

Base 1 = 4

Base 2 = 3

Height = 15

Then plug it into the formula,

(4+3)/2 * 15

Then solve the order of operations

7/2 * 15

3.5 * 15

52.5 is the answer

Answer:

52.5

Step-by-step explanation:

Formula

Area = (1/2) (a + b)*h

Givens

a = 4

b = 3

h = 15

Solution

Area = (4 + 3)*15/2

Area = 7 * 15/2

Area = 105/2

Area = 52.5

-4x<-12

-4x<-12 | /(-4)

x>3

Answer:

 150 minutes, or 2 1/2 hours

Step-by-step explanation:

You want to know the time required to empty a pond with the given dimensions if the level drops 20 cm in the first 30 minutes of pumping.

The average depth of the pond is the average of the depth at the shallow end and the depth at the deep end:

  (0.6 m + 1.4 m)/2

  = 2.0 m/2 = 1.0 m = 100 cm

If the level drops at the rate of 20 cm in 30 minutes, the time required for dropping the level by 100 cm is ...

  t/(30 min) = (100 cm)/(20 cm)

  t = 5·30 min = 150 min

The time to empty the pond completely is 150 minutes, or 2 1/2 hours.

__

Additional comment

As you know from the formula for the area of a trapezoid —

  A = 1/2(b1 +b2)h

the area is equivalent to that of a rectangle with base equal to the average of the two base lengths.

Here, the volume of the pond is the product of the area of the trapezoidal face and the pond width (1 m). That trapezoidal face has an area equivalent to that of a rectangle 1 m high and 2 m wide. The 1 m height is the depth we used in the above calculation.

Answer:

y = x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x is in this form

with slope m = 1 and c = 0

• Parallel lines have equal slopes, thus

y = x + c ← is the partial equation of the parallel line

To find c substitute (2, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = x + 2 ← equation of parallel line

The equation of the line parallel to y = x and passing through the point (2, 4) is y = x + 2.

In mathematics, two lines are said to be parallel if they have the same slope. The given line is y = x, and because its slope is 1 (the coefficient of x), the line we're looking for, which is parallel to this, will also have a slope of 1.

To find the equation of a line with a given slope that passes through a certain point, we use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the point. Substituting 1 for m, and the given point (2, 4) into this equation gives us y - 4 = 1(x - 2), which simplifies to y = x + 2, the equation of the line we were seeking.

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The transformed image will be located in Quadrant III.

To solve this problem, we can think about what happens to the hour hand when it is rotated 90 degrees counterclockwise around the origin, and then reflected across the x-axis.

Rotation: When the hour hand is rotated 90 degrees counterclockwise around the origin, it moves to the position of the 3 o'clock hour. This means that the x and y coordinates of the tip of the hour hand are swapped. For example, if the tip of the hour hand was originally at (3, 4), after the rotation it would be at (4, 3).

Reflection: When the hour hand is reflected across the x-axis, its y-coordinate is multiplied by -1. This means that if the tip of the hour hand was at (4, 3) after the rotation, after the reflection it would be at (4, -3).

Now, let's look at the quadrants:

Quadrant I: x > 0, y > 0

Quadrant II: x < 0, y > 0

Quadrant III: x < 0, y < 0

Quadrant IV: x > 0, y < 0

Before the rotation, the tip of the hour hand is in Quadrant I, because both its x and y coordinates are positive.

After the rotation and reflection, the tip of the hour hand is in Quadrant IV, because its x-coordinate is still positive and its y-coordinate is now negative.

Therefore, the image will be in Quadrant III.

Answer:

One year has 365 days

Step-by-step explanation:

The question in English is

How many days does the year have?

we know that

[tex]1\ year=12\ months[/tex]

[tex]1\ year=52\ weeks[/tex]

[tex]1\ year=365\ days[/tex]

therefore

One year has 365 days

Answer:

365

Step-by-step explanation:

[tex]\bf \textit{Half-Angle Identities} \\\\ sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 75\cdot 2\implies 150\qquad \qquad \qquad \cfrac{150}{2}\implies 75 \\\\[-0.35em] ~\dotfill\\\\ sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{1-cos(150^o)}{2}}\implies sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{1-\left( -\frac{\sqrt{3}}{2} \right)}{2}}[/tex]

[tex]\bf sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{1+\frac{\sqrt{3}}{2}}{2}}\implies sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{\frac{2+\sqrt{3}}{2}}{2}} \\\\\\ sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{2+\sqrt{3}}{4}}\implies sin\left( \cfrac{150^o}{2} \right)=\pm\cfrac{\sqrt{2+\sqrt{3}}}{\sqrt{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill sin\left( \cfrac{150^o}{2} \right)=\pm\cfrac{\sqrt{2+\sqrt{3}}}{2}~\hfill[/tex]

The value of sin75 by using half angle identity is [tex]sin\dfrac{[150^0]}{[22]}=\pm\dfrac{\sqrt{2+\sqrt{3}}}{2}[/tex]

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

Value of sin75 by using half angle identity is calculated as:-

Half angle identity for is,

[tex]sin\dfrac{\theta}{2}=\pm\sqrt{\dfrac{1-cos\theta}{2}[/tex]

[tex]\dfrac{\theta}{2}=\dfrac{150}{2}[/tex]

[tex]sin\dfrac{150}{2}=\pm\sqrt{\dfrac{1-cos150}{2}[/tex]

[tex]sin \dfrac{150}{2}=\pm\sqrt{\dfrac{{1+\dfrac{\sqrt{3}}{2}}}{2}[/tex]

[tex]sin \dfrac{150}{2}=\pm\sqrt{\dfrac{2+\sqrt{3}}{4}[/tex]

[tex]sin\dfrac{[150^0]}{[22]}=\pm\dfrac{\sqrt{2+\sqrt{3}}}{2}[/tex]

Hence, the value of sin75 is [tex]sin\dfrac{[150^0]}{[22]}=\pm\dfrac{\sqrt{2+\sqrt{3}}}{2}[/tex].

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Answer:

The entry terrace has an area of

48

square feet. The total area of the tree house including the entrance, porch, and side deck is

350

square feet.

Step-by-step explanation:

I just took a test with this question and this was the right answer

~Please mark me as brainliest : )

Answer:

Option B is correct

Step-by-step explanation:

Given:

f(x) = -20x^2 +14x +12 and

g(x) = 5x - 6

We need to find f/g and state its domain.

f/g = -20x^2 +14x +12/5x - 6

Taking -2 common from numerator:

f/g = -2(10x^2 - 7x - 6) / 5x -6

Factorize 10x^2 - 7x - 6= 10x^2 - 12x +5x -6

Putting in the above equation

f/g = -2(10x^2 - 12x +5x -6)/ 5x -6

f/g = -2(2x(5x-6) + 1 (5x-6)) / 5x-6

f/g = -2 ( (2x+1)(5x-6))/5x-6

cancelling 5x-6 from numerator and denominator

f/g = -2(2x+1)

f/g = -4x -2

The domain of the function is set of all values for which the function is defined and real.

So, our function g(x) = 5x -6 and domain will be all real numbers except x = 6/5 as denominator will be zero if x=5/6 and the function will be undefined.

So, Option B is correct.

ANSWER

-4x-2; all real numbers except x=6/5

Option B is correct.

EXPLANATION

The given functions are:

[tex]f(x) = - 20 {x}^{2} + 14x + 12[/tex]

We factor to get,

[tex]f(x) = - 2(10 {x}^{2} - 7x - 6)[/tex]

Split the middle term:

[tex]f(x) = - 2(10 {x}^{2} + 5x - 12x - 6)[/tex]

[tex]f(x) = - 2(5x(2{x} + 1)- 6(2x + 1))[/tex]

[tex]f(x) = - 2(2{x} + 1)(5x - 6)[/tex]

and

[tex]g(x) = 5x - 6[/tex]

[tex]( \frac{f}{g} ) = \frac{f(x)}{g(x)}[/tex]

[tex]( \frac{f}{g} ) = \frac{ - 20x + 14x + 12}{5x - 6}[/tex]

where 5x-6≠0

x≠6/5

[tex]( \frac{f}{g} ) = \frac{- 2(2{x} + 1)(5x - 6)}{5x - 6}[/tex]

Cancel the common factors to get,

[tex]( \frac{f}{g} ) = - 2(2{x} + 1)[/tex]

[tex]( \frac{f}{g} ) = - 4{x} - 2[/tex]

Answer:

52 IN. FOR SURE

Step-by-step explanation:

Formula: A=2(wl+hl+hw)

Fill the formula and you'll understand I promise or search formula for surface area of a rectangular prism fill the numbers and your all set!!!

PLZZZ MARK BRAINLIST!!! PLZZ

She is 3 years older than her brother and has (x+3) in the equation means that x is being used as her brothers age. (She is adding 3 to her brothers age)

The answer is Amy's brother's age.

Answer:

B

Step-by-step explanation:

Answer:  $277.91

Step-by-step explanation:

The average of the 2 highest salaried quarters is:

[tex]\dfrac{\$13,500+\$12,775}{2}=\dfrac{\$26,275}{2}=\$3,137.50[/tex]

Divide that by 26 (weeks) to find out her average weekly salary:

[tex]\dfrac{\$3,137.50}{26}=\$505.29[/tex]

Multiply that by 55% (0.55) to calculate her weekly unemployment benefit:

[tex]\$505.29(0.55)=\$277.908[/tex]

Round to the nearest penny --> $277.91

Answer:

x = e^2 = 7.39

Step-by-step explanation:

We have been given the logarithmic equation;

6+In x=8

The first step is to subtract 6 on both sides of the equation;

6 + ln x - 6 = 8 - 6

ln x = 2

We then introduce the exponential function, since the exponential function and the natural log function are inverses of each other;

[tex]e^{lnx}=e^{2}\\\\x=e^{2}=7.38906[/tex]

Answer:

Step-by-step explanation:

6 + ln(x)  = 8

ln(x) = 8 - 6

ln(x) = 2

x = [tex]e^{2}[/tex]

x = 7.38905609893

x = 7

Answer:

r > - 12

Step-by-step explanation:

4r – 5 < 5r+7

4r - 5r < 7 + 5

-r <12

r > - 12 (when you multiply or divide a negative number, the sign will be flipped)

Answer:D

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Triangles consists of 180 degrees. 132 + 13 = 145      180 - 145 = 35, therefore the smallest measurement of the triangle is 13 since 132 and 35 are larger numbers.

Answer: All values make a true statement.

Step-by-step explanation: Since f(x) and g(x)=x, f(x)=g(x) can also be written as x=x. That is a true statement so all values of x works.

Hope this helps!

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

we know that

To find the fraction of the store's books that are fiction mysteries, multiply 1/2 by 3/5

so

[tex](\frac{1}{2})(\frac{3}{5})=\frac{3}{10}[/tex]

Answer:

v = -3

Step-by-step explanation:

Step 1: Use the Distributive Property

6v + 3= -75v - 240

Step 2: Isolate v

81v = -243

Step 3: Simplify

v = -3

The value of v in the equation 3(2v + 1)=-15(5v + 16)​ is -3 after rearranging and solving.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a linear equation in one variable:

3(2v + 1)=-15(5v + 16)​

6v + 3 = -75v -240

6v + 75v = -240 - 3

81v = -243

v = -3

Thus, the value of v in the equation 3(2v + 1)=-15(5v + 16)​ is -3 after rearranging and solving.

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the missing exponent would be 2

[tex]\bf (5^?)^{3}=5^1\implies 5^{?\cdot 3}=5^1\implies \stackrel{\textit{same base, the exponents must also be the same}}{?3=1\implies ?=\cfrac{1}{3}}[/tex]

Answer:

y = 3x-9

Step-by-step explanation:

y = -1/3 x +2

The slope is -1/3

We want a line perpendicular to it

Perpendicular lines have negative reciprocal slopes

The new slope is -(-3/1) = 3

We have a slope  m=3 and a point (5,6)

We will use point slope form to find the line

y-y-1 = m(x-x1)

y-6 = 3(x-5)

In slope intercept form

Distribute

y-6 = 3x-15

Add 6 to each side

y-6+6 = 3x-15+6

y = 3x-9

Answer:

x = 20

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

let's take a peek, we have two fractions, let's get the LCD of all fractions, in this case the LCD of 2 and 5, hmmmm that'd be 10.

now, let's multiply both sides by the LCD of 10 to do away with the denominators and proceed.

[tex]\bf \cfrac{x}{2}+\cfrac{2x}{5}=18\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{x}{2}+\cfrac{2x}{5} \right)=10(18)}\implies 5x+4x=180 \\\\\\ 9x=180\implies x=\cfrac{180}{9}\implies x=20[/tex]

Answer: 5 • (2x2 - 17x - 2)

 ———————————————————

        x - 8      

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

Step  2  :

           10x2 - 85x - 10

Simplify   ———————————————

                x - 8      

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  10x2 - 85x - 10  =   5 • (2x2 - 17x - 2)  

Trying to factor by splitting the middle term

3.2     Factoring  2x2 - 17x - 2  

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -17x  its coefficient is  -17 .

The last term, "the constant", is  -2  

Step-1 : Multiply the coefficient of the first term by the constant   2 • -2 = -4  

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   -17 .

     -4    +    1    =    -3  

     -2    +    2    =    0  

     -1    +    4    =    3  

Observation : No two such factors can be found !!  

Conclusion : Trinomial can not be factored

Answer:

C

Step-by-step explanation:

ln 1 = 0, so f(1) = 0 + 2 = 2.  So we need to find a graph that passes through (1, 2).  Only graph C fits.

The graph of the function f(x) = In x + 2 is the graph b

The parent function for the natural log function is f(x) = ln(x).

To transform the graph of f(x) = ln(x) to the graph of f(x) = ln(x) + 2, we perform the following transformation:

Vertical Shift:

The graph is shifted two units upward.

This is because adding 2 to the output of the function has the same effect as shifting the graph two units upward.

So, the graph of f(x) = In x + 2 is b

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Answer:

r

0.15r

1.15r

Step-by-step explanation:

The problem states that r cm of rain fell on the garden on Thursday, so the first answer is:

The centimeters of rain on Thursday    r

On Saturday, 15% more rain fell than on Thursday. The extra amount of rain on Saturday, as compared to Thursday is 15% of r. 15% of r is the same as 15% times r. 15% can be written as a decimal as 0.15, so 15% of r is the same as 0.15r. This is the answer to the second line.

How many more centimeters of rain fell on Saturday than on Thursday   0.15r

The amount of rain on Saturday is the amount of rain on Thursday plus the additional 15%. We already know that the additional 15% of rain is 0.15r. The total amount of rain on Saturday is r + 0.15r = 1r + 0.15r = 1.15r. That answers the third question.

The centimeters of rain on Saturday     1.15r