What is the equation of the line that is parallel to the given line and passes through the point (-3, 2)?

Answer:

The graph in the attached figure ( is the third option)

Step-by-step explanation:

we have the compound inequality

[tex]-18> -5x+2\geq -48[/tex]

Divide the compound inequality in two inequalities

[tex]-18> -5x+2[/tex] -----> inequality A

[tex]-5x+2\geq -48[/tex] -----> inequality B

Step 1

Solve inequality A

[tex]-18> -5x+2[/tex]

[tex]-18-2> -5x[/tex]

[tex]-20> -5x[/tex]

Multiply by -1 both sides

[tex]20<5x[/tex]

[tex]4<x[/tex]

Rewrite

[tex]x > 4[/tex]

The solution of the inequality A is the interval ------>(4,∞)

Step 2

Solve the inequality B

[tex]-5x+2\geq -48[/tex]

[tex]-5x\geq -48-2[/tex]

[tex]-5x\geq -50[/tex]

Multiply by -1 both sides

[tex]5x\leq 50[/tex]

[tex]x\leq 10[/tex]

The solution of the inequality B is the interval -----> (-∞,10]

therefore

The solution of the compound inequality is

(4,∞) ∩ (-∞,10]=(4,10]

All real numbers greater than 4 (open circle) an less than or equal to 10 (close circle)

The solution in the attached figure

The zeros of the function are 2 and -1.

The zeros of a function are the values of x when f(x) is equal to 0.

Given function is,  [tex]f(x)=\frac{(x-2)(x+1)}{x(x-3)(x+5)}[/tex]

Equate given function to zero.

          [tex]\frac{(x-2)(x+1)}{x(x-3)(x+5)} =0\\\\(x-2)(x+1)=0\\\\x=2,x=-1[/tex]

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Answer:

150 bags

Step-by-step explanation:

Given the total area:

The area will be:

=75*50

= 3750 square feet

As it is given that one bag covers 25 square feet. To find the total number of bags we have to find how many 25s will be in 3750 square feet.

So,

Total number of bags = 3750 / 25

= 150 bags

Hence, total number of bags that will be used are 150 ..

Answer:

The second layer of skin is the dermis, located under the epidermis. It contains connective tissue, nerve endings, and hair follicles.

The dermis layer of the skin contains hair follicles.

The layer of the skin that contains hair follicles is the dermis.

The dermis is the layer of skin directly under the epidermis, and it is made of tough connective tissue. It contains hair follicles, sweat glands, oil glands, and blood vessels.

For example, when you pluck a hair from your skin, you are pulling it out from the dermis.

Answer:

y= 125,000 (1.15x)

Step-by-step explanation:

Answer:

A. [tex]y=125,000\cdot (1.15)^x[/tex]

Step-by-step explanation:

We have been given that Jessa bought her home for $125,000 in 2010 Property values have increased 15% every year since she has owned the home.

We can see that increase in value of house is not constant, so the value of house in increasing exponentially.

We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,

a = Initial value,

b = For growth b is in form [tex](1+r)[/tex], where r represents growth rate in decimal form.

[tex]r=\frac{15}{100}=0.15[/tex]

[tex]y=125,000\cdot (1+0.15)^x[/tex]

[tex]y=125,000\cdot (1.15)^x[/tex]

Therefore, the equation [tex]y=125,000\cdot (1.15)^x[/tex] represents the price of the home x years after 2010.

Answer:

9x² + 28x - 32

Step-by-step explanation:

Given

(9x - 8)(x + 4)

Each term in the second factor is multiplied by each term in the first factor, that is

9x(x + 4) - 8(x + 4) ← distribute both parenthesis

= 9x² + 36x - 8x - 32 ← collect like terms

= 9x² + 28x - 32

Answer:

Option D

Step-by-step explanation:

Answer:

y - 1 = -2(x + 1).

Step-by-step explanation:

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

= -4 / 2

= -2.

In point slope form:

y - y1 = m(x - x1)

Using m = -2 and the point (-1, 1):

y - 1 = -2(x + 1).

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (1, - 3)

m = [tex]\frac{-3-1}{1+1}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

Using either of the 2 points as a point on the line, then

Using (- 1, 1)

y - 1 = - 2(x - (- 1)), that is

y - 1 = - 2(x + 1) ← in point- slope form

Answer:

(x-4)(x-6)(x+3) or in more compressed form x³-7x²-6x+72

Step-by-step explanation:

To find the L.C.M, w first factorize each of the expressions.

x²-10x+24

Two numbers that when added give -10 but when multiplied give 24

will be, -4 and -6

Thus the expression becomes:

x²-4x-6x+24

x(x-4)-6(x-4)

=(x-4)(x-6)

Let us factorize the second expression.

x²-x-12

Two numbers when added give -1 and when multiplied give -12

are 3 and -4

Thus the expression becomes: x²-4x+3x-12

x(x-4)+3(x-4)

(x-4)(x+3)

Therefore the LCM between  (x-4)(x-6) and (x-4)(x+3)

will be

(x-4)(x-6)(x+3)

We can multiply the expression as follows.

(x-4)(x-6)

x²-6x-4x+24 = x²-10x+24

(x+3)(x²-10x+24)

=x³-10x²+24x+3x²-30x+72

=x³-7x²+-6x+72

Answer:

(E) 1

Step-by-step explanation:

2r+ (2r+3 ) < 11

Combine like terms

4r+3 < 11

Subtract 3 from each side

4r +3-3 < 11-3

4r < 8

Divide each side by 4

4r/4 < 8/4

r <2

The only possible choice is 1

Answer:

(E) 1

Step-by-step explanation:

the sum of 2r and 2r+3  less than 11 means :

2r+2r+3<11

we simplify we get :

4r+3<11

we take the 3 to the left :

4r<11-3

means

4r<8

we divide both sides by 4 we get :

r<2

so among all those values only the 1 satisfies the condition 1<2

so the answer is E

[tex]\huge{\boxed{y-3=m(x-2)}}[/tex]

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a point on the line.

Substitute the values. [tex]\boxed{y-3=m(x-2)}[/tex]

Note: This is in point-slope form. Let me know if you need a different form. Also, if you have any more problems similar to this, I encourage you to try them on your own, and ask on here if you are having trouble.

Answer:

y-3 = 3(x-2)  point slope form

y = 3x-3  slope intercept form

Step-by-step explanation:

We can use the point slope form of the equation for a line

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is the point

y-3 = 3(x-2)  point slope form

If we want the line in slope intercept form

Distribute

y-3 = 3x-6

Add 3 to each side

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

y = 3x-3  slope intercept form

Answer:

Step-by-step explanation:

For this case we must graph the following function:

[tex]f (x) = 13x-1[/tex]

We found the cut points:

Cutting point with the y-axis:

We make [tex]x = 0,[/tex]

[tex]y = 13 (0) -1\\y = 0-1\\y = -1[/tex]

Cutting point with the x axis:

[tex]0 = 13x-1\\1 = 13x\\x = \frac {1} {13} = 0.078[/tex]

It is observed that the line has a positive slope, [tex]m = 13[/tex]

The graph is seen in the attached image.

Answer:

See attached image

Answer:

2, 3, 4, 5, 6, 7 or 8.

Step-by-step explanation:

We know that the sum of two sides on a triangle should ALWAYS be greater than the third side. Then we have:

5-4 < x < 5 + 4

1 < x < 9

Therefore, the lenght of the third side could be any number between 1 and 9. If the lenght of the third side is an integrer, then the lenght could be:

2, 3, 4, 5, 6, 7 or 8.

Answer:

The length of the third side could be all real numbers greater than 1 unit and less than 9 units

Step-by-step explanation:

we know that

The Triangle Inequality Theorem,   states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

Applying the triangle inequality theorem

Let

x ----> the length of the third side

1) 4+5 > x

9 > x

Rewrite

x < 9 units

2) 4+x > 5

x > 5-4

x > 1 units

therefore

The solution for the third side is the interval -----> (1,9)

All real numbers greater than 1 unit and less than 9 units

therefore

The length of the third side could be all real numbers greater than 1 unit and less than 9 units

Answer:

−5 + 5 = 0

-6+6=0

14+-14=0

70+-70=0

100+-100=0

Step-by-step explanation:

hope this helps

Answer:

Point A' will be located 10 units away from point A along ray PA

Step-by-step explanation:

we have

The scale factor is 3

step 1

Find out the distance PA'

we know that

The distance PA' is equal to multiply the distance PA by the scale factor

so

[tex]PA'=PA*3[/tex]

we have

[tex]PA=5\ units[/tex]

substitute the given values

[tex]PA'=(5)*3=15\ units[/tex]

step 2

Find out how many units away from point A along ray PA will A’ be located

we know that

[tex]PA'=PA+AA'[/tex]

we have

[tex]PA=5\ units[/tex]

[tex]PA'=15\ units[/tex]

substitute the given values and solve for AA'

[tex]15=5+AA'[/tex]

[tex]AA'=15-5=10\ units[/tex]

therefore

Point A' will be located 10 units away from point A along ray PA

Answer:

10 units

Step-by-step explanation:

Answer:

Step-by-step explanation:

A function is a process or a relation that associates each element x of a set X, to a single element y of another set Y.

We have:

{(3, -2), (1, 2), (-1, -4), (-1, 2)}

for x = -1 are two values of y = -4 and y = 2. Therefore this realtion is not a function.

Answer: No, it is not a function.

Step-by-step explanation:

The given relation:  {(3, −2), (1, 2), (−1, −4), (−1, 2)}

According to the above definition, the given relation is not a function because -1 corresponds to two different output values i.e. -4 and 2.

Hence, the given relation is not a function.

Answer:

Statement 2 (The ages of the Stars are the most dispersed from the team’s mean).

Step-by-step explanation:

Standard deviation is one way to measure the average of the data by determining the spread of the data. It actually explains how much the observation points are further away from the mean of the data. Higher the standard deviation, higher the spread of the data and higher is the uncertainty. This means that the team with the highest standard deviation will have the most dispersion. In this case, the standard deviation of 4.1 is the largest number, therefore, the statement "The ages of the Stars are the most dispersed from the team’s mean." is true i.e. the option 2!!!

Answer:

B.The ages of the Stars are the most dispersed from the team’s mean

Step-by-step explanation:

Answer:

[tex]5+\sqrt{x+4}[/tex]

Step-by-step explanation:

The conjugate of the radical expression [tex]a+\sqrt{b}[/tex] is  [tex]a-\sqrt{b}[/tex]

The conjugate of the radical expression [tex]a-\sqrt{b}[/tex] is  [tex]a+\sqrt{b}[/tex]

The sign of the radical becomes its additive inverse in the conjugate,

The given expression is

[tex]5-\sqrt{x+4}[/tex] where [tex]x>-4[/tex] (domain)

The conjugate of this expression is [tex]5+\sqrt{x+4}[/tex]

Answer:

The conjugate is 5+√x+4

Step-by-step explanation:

To find the conjugate of of expression 5-√x+4

when x>-4

First let us understand that in simple terms terms the conjugate of a radical simply involves the change in sign of the radical

in the problem the conjugate of

5-√x+4 is 5+√x+4

it is that simple Just alternate the sign and you are done!!!

Answer:

Two line segments are congruent if they have the same length. Two angles are congruent if they have the same measure.

Two angles are said to be congruent if they are equal. For example, if two triangles each have an angle of 42 degrees, then those angles are congruent.

Answer: The temperature change is 19 degrees Fahrenheit.

Step-by-step explanation: Put a circle at -9 and 10. You can count the numbers in between them to get 19. Or you can add the two numbers. 9 + 10 = 19.

Answer:

a = 20 cm

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for a

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

a² + 21² = 29²

a² + 441 = 841 ( subtract 441 from both sides )

a² = 400 ( take the square root of both sides )

a = [tex]\sqrt{400}[/tex] = 20

Answer:

Part A)

x=-3i

x=3i

Part B)

(x+3i)(x-3i)

Step-by-step explanation:

Given:

Part A)

x^2+9=0

x^2=-9

x= √-9

x=√-1 *√9

x=± i *3

x=±3i

Part B)

x^2+9=0

x^2 - (-9)=0

x2-(3i)^2=0

(x-3i)(x+3i)=0 !

The answer is:

A.

[tex]h(x)=9x-13[/tex]

To solve the problem, we need to perform the shown operation.

We have the functions:

[tex]f(x)=2x-1\\g(x)=7x-12[/tex]

So, performing the following operation, we have:

[tex]f(x)+g(x)=h(x)[/tex]

[tex]h(x)=f(x)+g(x)=(2x-1)+(7x-12)=7x+2x-1-12=9x-13[/tex]

[tex]h(x)=9x-13[/tex]

Hence, we have that the correct option is:

A. [tex]h(x)=9x-13[/tex]

Have a nice day!

Answer: A

Step-by-step explanation:

Find the area of the rug by multiplying the length by the width:

7 x 5 = 35 square meters.

Now multiply the area of the rug by the cost:

35 square meters x 285 pesos per square meter = 9,975 total pesos.

Answer:

So we have [tex]\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}[/tex].

Step-by-step explanation:

Ok so we are in quadrant 2, that means sine is positive while cosine is negative.

We are given [tex]\cos(\theta)=\frac{-2}{3}(\frac{\text{adjacent}}{\text{hypotenuse}})[/tex].

So to find the opposite we will just use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

[tex](2)^2+b^2=(3)^2[/tex]

[tex]4+b^2=9[/tex]

[tex]b^2=5[/tex]

[tex]b=\sqrt{5}[/tex]  This is the opposite side.

Now to find [tex]\csc(\theta)[/tex] and [tex]\tan(\theta)[/tex].

[tex]\csc(\theta)=\frac{\text{hypotenuse}}{\text{opposite}}=\frac{3}{\sqrt{5}}[/tex].

Some teachers do not like the radical on bottom so we will rationalize the denominator by multiplying the numerator and denominator by sqrt(5).

So [tex]\csc(\theta)=\frac{3}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}=\frac{3 \sqrt{5}}{5}[/tex].

And now [tex]\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{\sqrt{5}}{-2}=\frac{-\sqrt{5}}{2}[/tex].

So we have [tex]\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}[/tex].

Answer:

[tex]tan\theta{3}=-\frac{\sqrt5}{2}[/tex]

[tex]cosec\theta=\frac{3}{\sqrt5}[/tex]

Step-by-step explanation:

We are given that [tex]\theta[/tex] be an  angle in quadrant II and [tex]cos\theta=-\frac{2}{3}[/tex]

We have to find the exact values of [tex]cosec\theta[/tex] and [tex]tan\theta[/tex].

[tex]sec\theta=\frac{1}{cos\theta}[/tex]

Then substitute the value of cos theta and we get

[tex]sec\theta=\frac{1}{-\frac{2}{3}}[/tex]

[tex]sec\theta=-\frac{3}{2}[/tex]

Now, [tex]1+tan^2\theta=sec^2\theta[/tex]

[tex]tan^2\theta=sec^2\theta-1[/tex]

Substitute the value of sec theta then we get

[tex]tan^2\theta= (-\frac{3}{2})^2-1[/tex]

[tex]tan^2\theta=\frac{9}{4}-1=\frac{9-4}{4}=\frac{5}{4}[/tex]

[tex]tan\theta=\sqrt{\frac{5}{4}}=-\frac{\sqrt5}{2}[/tex]

Because[tex] tan\theta [/tex] in quadrant II is negative.

[tex]sin^2\theta=1-cos^2\theta[/tex]

[tex]sin^2\theta=1-(\farc{-2}{3})^2[/tex]

[tex]sin^2\theta=1-\frac{4}{9}[/tex]

[tex]sin^2\theta=\frac{9-4}{9}=\frac{5}{9}[/tex]

[tex]sin\theta=\sqrt{\frac{5}{9}}[/tex]

[tex]sin\theta=\frac{\sqrt5}{3}[/tex]

Because in quadrant II [tex]sin\theta[/tex] is positive.

[tex]cosec\theta=\frac{1}{sin\theta}=\frac{1}{\frac{\sqrt5}{3}}[/tex]

[tex]cosec\theta=\frac{3}{\sqrt5}[/tex]

[tex]cosec\theta[/tex] is positive in II quadrant.

Answer:

The correct answer is option a.  400

Step-by-step explanation:

Points to remember

Area of square = a²

Where 'a' is the side length of square

To find the area of square

It is given that, the side length of square is 20 inches.

Here a = 20 inches

Area = a²  

 = 20²

 = 400

Therefore the correct answer is option a.  400

Answer:

[tex]\large\boxed{-2(10r+4)+10(7r+2)=50r+12}[/tex]

Step-by-step explanation:

[tex]-2(10r+4)+10(7r+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(-2)(10r)+(-2)(4)+(10)(7r)+(10)(2)\\\\=-20r-8+70r+20\qquad\text{combine like terms}\\\\=(-20r+70r)+(-8+20)\\\\=50r+12[/tex]

Answer:

[tex]x = 11[/tex]

Step-by-step explanation:

The bases of a trapezoid are parallel

The angles,

[tex](9x) \degree[/tex]

and

[tex](7x + 4) \degree[/tex]

are same side interior angles. These two angles are supplementary.

[tex](7x + 4) + 9x = 180 \degree[/tex]

[tex]7x + 9x = 180 - 4[/tex]

[tex]16x = 176[/tex]

Divide both sides by 16.

[tex]x = \frac{176}{16} [/tex]

[tex]x = 11[/tex]

Answer:

[tex]x=11[/tex]

Step-by-step explanation:

We have been given that a carpenter cuts the corners of a rectangle to make the  trapezoid. We are asked to find the value of x.

Since trapezoid is made of rectangle, so both bases will be parallel to each other.

We know that two consecutive interior angle of parallel lines are supplementary. We can set an equation to solve for x as:

[tex]9x+7x+4=180[/tex]

[tex]16x+4=180[/tex]

[tex]16x+4-4=180-4[/tex]

[tex]16x=176[/tex]

[tex]\frac{16x}{16}=\frac{176}{16}[/tex]

[tex]x=11[/tex]

Therefore, the value of x is 11.

C

By the law of sines, [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex] where A, B, C are the angles and a, b, c are the lengths of the sides opposite their respective angles. In this case, [tex]110^{\circ}[/tex] is opposite 4.6 and A is opposite 3.2, so [tex]\frac{sinA}{3.2}=\frac{sin(110^{\circ})}{4.6}[/tex], giving the answer.

Answer:

it’s c

Step-by-step explanation:

Answer:

(k ∘ p)(x)=2x^2-12x+13

Step-by-step explanation:

(k ∘ p)(x)=k(p(x))

(k ∘ p)(x)=k(x-3)

(k ∘ p)(x)=2(x-3)^2-5

(k ∘ p)(x)=2(x-3)(x-3)-5

Use foil on (x-3)(x-3) or use this as a formula:

(x+a)^2=x^2+2ax+a^2.

(k ∘ p)(x)=k(p(x))

(k ∘ p)(x)=k(x-3)

(k ∘ p)(x)=2(x-3)^2-5

(k ∘ p)(x)=2(x-3)(x-3)-5

(k ∘ p)(x)=2(x^2-6x+9)-5

Distribute: multiply terms inside ( ) by 2:

(k ∘ p)(x)=2x^2-12x+18-5

(k ∘ p)(x)=2x^2-12x+13

The composite function is [tex]k(p(x))=2x^{2} -12x+13[/tex]

Option b is correct.

Given function are,

               [tex]k(x)=2x^{2} -5,p(x)=(x-3)[/tex]

We have to find composite function [tex]k(p(x))[/tex].

                  [tex]k(p(x))=k(x-3)\\\\k(p(x))=2(x-3)^{2}-5\\ \\k(p(x))=2(x^{2} +9-6x)-5\\\\k(p(x))=2x^{2} +18-12x-5\\\\k(p(x))=2x^{2} -12x+13[/tex]

Thus, the composite function is [tex]k(p(x))=2x^{2} -12x+13[/tex]

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