Which set of numbers is included in the solution set of the compound inequalities?

Answer:

O D. (2,5)

Step-by-step explanation:

y > 2x - 3

Substitute the points into the inequality and see if it is true

(3,2)

2 > 2(3) - 3

2> 6-3

2>3  False

(9,12)

12 > 2(9) - 3

12> 18-3

12>15  False

(4,4)

4 > 2(4) - 3

4> 8-3

4>5  False

(2,5)

5 > 2(2) - 3

5> 4-3

5>1  True

Answer:D

Step-by-step explanation:

Answer:

Perpendicular

Step-by-step explanation:

Definition of perpendicular lines:

Lines that intersect forming a right angle are perpendicular lines.

Answer:

Perpendicular

Step-by-step explanation:

Answer:

B about $98,000

Step-by-step explanation:

The equation that models the sales of the product after an initial release is:

[tex]S = 16 \sqrt{3t} + 25[/tex]

where s represents the total sales (in thousands) and t represents

the time in weeks after release.

The table and graph is shown in the attachment.

From the graph we estimate the sales

7 weeks after release to be about 98 thousands dollars.

The correct choice is B.

Answer: 3/2 (simplified: 1.5)

Step-by-step explanation:

X=pi

X=3pi/2

Remove pi from both equations because pi will cancel out each other then you will be left with the equation 3/2. So therefore the rate of change would be 3/2 simplified would be 1.5

Answer:

Step-by-step explanation:

The polynomial y = (x + 4)(x - 2)(x + 7) has 3 roots.

y = 0 ⇒ (x + 4)(x - 2)(x + 7) = 0 ⇔ x + 4 = 0 ∨ x - 2 = 0 ∨ x + 7 = 0

x + 4 = 0   subtract 4 from both sides

x = -4

x - 2 = 0      add 2 to both sides

x = 2

x + 7 = 0      subtract 7 from both sides

x = -7

The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots: -4, 2, and -7.A. 3

The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots, which can be found by setting y to zero and solving for the values of x that make the function equal to zero. When you set y to zero, the equation becomes 0 = (x + 4)(x - 2)(x + 7), and the roots are x = -4, x = 2, and x = -7. Hence, the correct answer to the question of how many roots the polynomial function has is:

A. 3

Answer:

  x = 29° + n·120° . . . or . . . 261° +n·360° . . . . for any integer n

Step-by-step explanation:

Multiplying by the denominator, the equation becomes ...

  sin((x -3)°) = cos((2x+6)°)

The sine and cosine are equal when ...

  (x -3) + (2x +6) = 90 + n·360 . . . . . for any integer n

  3x +3 = 90 + n·360 . . . . . . . . . collect terms

  x +1 = 30 +n·120 . . . . . . . . . . . .divide by 3

  x = 29 + n·120 . . . . . . . . . . . . . . subtract 1

__

The sine and cosine are also equal when ...

  (x -3) -(2x +6) = 90 + n·360

  -x -9 = 90 +n·360

  x = -99 -n·360

Since n can be any integer, this can also be written as ...

  x = 261 + n·360

Possible values of x include {29, 149, 261, 269} +n·360 for any integer n.

_____

The graph shows solutions to sin(x-3)-cos(2x+6)=0, which has the same solutions as the given equation.

Answer:

Part 1) The library is located at point (3.25,-1.5)

Part 2) The library is 1.5 miles from Road X

Part 3) The library is 3.25 miles from Road Y

Step-by-step explanation:

step 1

Find the coordinates of the library

we know that

Observing the graph

The length of each square in the graph is 0.5 miles

so

The coordinates of point L are (3.25,-1.5)

therefore

The library is located at point (3.25,-1.5)

step 2

Find the distance of the library from road X

we know that

The distance of point L from road X is the perpendicular distance of point L to the Road X

The perpendicular distance is the absolute value of the y-coordinate of point L

therefore

The library is 1.5 miles from Road X

step 3

Find the distance of the library from road Y

we know that

The distance of point L from road Y is the perpendicular distance of point L to the Road Y

The perpendicular distance is the absolute value of the x-coordinate of point L

therefore

The library is 3.25 miles from Road Y

Answer:

The 4th day so 21 miles the girls would have to run

Step-by-step explanation:

Answer:

Each girl would have ran a total of 21 miles and boys would have ran a total of 20 miles by the end of the fourth day before the couch order new javelins.

Step-by-step explanation:

Girls track team

First day of practice=3 miles

Days afterwards= 6 miles

Boys track team

Everyday= 5 miles

coach will order new javelins at the end of the day that each girl's total mileage surpasses each boy's.

First day

Each girl total mileage= 3 miles

Each boy total mileage= 5 miles

Second day

Each girl total mileage= 3miles+6miles=9 miles

Each boy total mileage=5 miles+5 miles= 10 miles

Third day

Each girl total mileage= 3+6+6=15 miles

Each boy total mileage=5+5+5=15 miles

Fourth day

Each girl today mileage= 3+6+6+6=21 miles

Each boy total mileage=5+5+5+5= 20 miles

Difference=girls-boys

=21-20= 1 mile

The fourth day is the day each girl's total mileage(21 miles) surpasses each boy's total mileage(20 miles) with a total of 1 mile

Answer:

yes

Step-by-step explanation:

6 times 6 = 36

Answer: Yes

Step-by-step explanation: Yes, it is a perfect square of 6. 6 x 6 = 36.

Answer:

1/2 hr.

Step-by-step explanation:

Make a whole number of the wall. In this case, multiply by 2:

1/2 x 2 = 2

Because you multiplied 2 to the wall, you must also multiply 2 to the hours:

1/4 x 2 = 2/4

Remember to simplify:

(2/4)/(2/2) = 1/2

It will take you 1/2 hr to paint one wall.

~

30 minutes

A quarter of an hour is 15 minutes, because 60÷4=15.

So, this means that half of a wall equals to 15 minutes.

If you painted half of a wall, you have another half remaining.

Therefore, 2×15=30

30 minutes is the answere

Final answer:

The volume of the oblique rectangular prism is calculated using the length, width, and height. The formula V = l  times w  times h gives a volume of 504 cubic centimeters.

Explanation:

To find the volume of an oblique rectangular prism, we use the same formula as for a right rectangular prism because the volume is not affected by the obliquity of the sides. The formula for the volume (V) is the product of the length (l), width (w), and height (h). So, using the provided dimensions:

V =l  times w  times h = 8 cm  times 7 cm times 9 c

Now, let's calculate:

V = 8  times 7  times 9 = 504 cm

Therefore, the volume of the oblique rectangular prism is 504 cubic centimeters.

Answer:

-7/5 if your function really is f(x)=-5x-7

Step-by-step explanation:

The zeros of an expression are the numbers you can plug into that expression that will make that expression 0.

So what value of x will make the expression

-5x-7=0.

You don't have to this by observation. We can just solve it and see.

-5x-7=0

Add 7 on both sides:

-5x. =7

Divide both sides by -5:

x. =7/-5

x. =-7/5

So -7/5 will make the expression equal to 0.

Let's test this:

-5x-7 when x=-7/5

-5(-7/5)-7

7-7

0

So it does indeed.

Answer:

16 N

Step-by-step explanation:

If the 7 N force is at 0°, and the 11 N force is at 60°, then the components of the resultant force are:

Fₓ = 7 cos 0° + 11 cos 60° = 12.5

Fᵧ = 7 sin 0° + 11 sin 60° ≈ 9.53

The magnitude of the resultant force is:

F = √(Fₓ² + Fᵧ²)

F ≈ 15.7

Rounded to the nearest whole number, the magnitude is 16 N.

Answer:

y = 2x - 5

Step-by-step explanation:

We are to find the equation of line the line which passes through the points (4, 3) and (2, -1).

Finding the slope:

Slope = [tex]\frac{3-(-1)}{4-2} =2[/tex]

Substituting the coordinates of one of the given points and slope in the standard form of an equation to find the y intercept.

[tex]y=mx+c[/tex]

[tex] -1 = 2 (2) + c \\\\ c = - 5 [/tex]

So the equation of the line would be [tex]y=2x-5[/tex]

Answer: first option.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

To find "m", we need to substitute the coordinates of the points  (4, 3) and (2, -1) into this formula:

 [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We can identify that:

[tex]y_2=-1\\y_1=3\\x_2=2\\x_1=4[/tex]

Then:

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

To find "b" we must substitute the slope and one of the given points into [tex]y=mx+b[/tex] and solve for "b". Then, this is:

[tex]3=2(4)+b\\\\3-8=b\\\\b=-5[/tex]

Therefore, the equation of this line is:

[tex]y=2x-5[/tex]

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers

Step-by-step explanation:

Final answer:

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Prime numbers have many interesting properties and applications in mathematics.

Explanation:

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, it is a number that is only divisible by 1 and itself.

For example, the numbers 2, 3, 5, and 7 are prime numbers because they have no divisors other than 1 and themselves. On the other hand, the number 4 is not prime because it is divisible by 1, 2, and 4.

Prime numbers have many interesting properties and applications in mathematics, including their role in number theory and cryptography.

Answer:

Im pretty sure its C

Step-by-step explanation:

because when u line up the the right angles u see the hypotenuse and leg of another triangle is the same

The given triangles are not congruent since the hypotenuse of one triangle is equal to the length of leg of another triangle.

So the corresponding sides of the triangles are not equal.

So the triangles are not congruent.

So, option C is correct.

Find more about "Congruency" here:  brainly.com/question/2938476

#SPJ2

Answer:

3/6 or 50%

Step-by-step explanation:

The probability of rolling an odd number from the dice numbered,  {1,2,3,4,5,6} is 3/6.

6 numbers in all.

3 odd numbers.

3 even numbers.

Therefore, 3/6 or 50%.

Answer:

constant of variation = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

The constant of variation is 1/2.

Step-by-step explanation:

y = kx where k is the constant of variation.

So k = y/x = 2/4 = 1/2.

Answer:

[tex]x_1=x_2=-\dfrac{2}{3}[/tex]

Step-by-step explanation:

For the quadratic equation [tex]ax^2+bx+c=0[/tex] the discriminant is defined as

[tex]D=b^2-4ac[/tex]

and the quadratic formula for the roots gives us two roots:

[tex]x_1=\dfrac{-b-\sqrt{D}}{2a}[/tex]

and

[tex]x_2=\dfrac{-b+\sqrt{D}}{2a}[/tex]

For the equation [tex]9x^2 +12x+4=0[/tex] use quadratic formula to find roots:

[tex]D=12^2-4\cdot 9\cdot 4=144-144=0[/tex]

So,

[tex]x_1=x_2=\dfrac{-12\pm \sqrt{0}}{2\cdot 9}=-\dfrac{12}{18}=-\dfrac{2}{3}[/tex]

Answer:

Option C. The system of the equations has no solution; the two lines are parallel.

Step-by-step explanation:

we have

-3x+4y=12 -----> equation A

(1/4)x-(1/3)y=1 ----> equation B

Multiply equation B by -12 both sides

-12*[(1/4)x-(1/3)y]=1*(-12)

-3x+4y=-12 ----> equation C

Compare equation A and equation C

The lines are parallel , but the y-intercepts are different

therefore

The system has no solution

Answer: C: 3rd degree polynomial wit 3 terms.

Step-by-step explanation: The polynomial has 3 terms and the highest degree is 3.

C. Third degree polynomial with three terms.

Terms are, by definition, the number of nonzero coefficients for powers of x. In this case, there are 3 nonzero coefficients (3 terms) because [tex]-1=-1x^0[/tex]. For example, [tex]2x^3[/tex] has one term, but [tex]0[/tex] has 0 terms.

The degree of a polynomial is the highest power involved in the expression. In this case, it's [tex]4x^3[/tex], so the degree is 3.

Answer:

C.WXYZ equal to PNLM

Step-by-step explanation:

Look at the given statement, WZYX is equal to PMLN.

WZYX is equal to PMLN.   W corresponds to P.

WZYX is equal to PMLN.   Z corresponds to M.

WZYX is equal to PMLN.   Y corresponds to L.

WZYX is equal to PMLN.   X corresponds to N

Now look in the choices. The letters must correspond like they do above.

W must correspond to P.

WXYZ equal to P...

X must correspond to N.

WXYZ equal to PN...

Y must correspond to L.

WXYZ equal to PNL...

Z must correspond to M.

WXYZ equal to PNLM

Answer: C.WXYZ equal to PNLM

Answer: C.WXYZ equal to PNLM

Answer:

172°

Step-by-step explanation:

Connect the center of the circle with two endpoints of the chord. You'll get the isosceles triangle with the angles adjacent to the base of

[tex]94^{\circ}-90^{\circ}=4^{\circ}[/tex]

Then the angle between two congruent sided (two radii of the circle) is

[tex]180^{\circ}-2\cdot 4^{\circ}=172^{\circ}[/tex]

This angle is central angle subtended on the arc z, so the measure of z is 172°.

Answer: OPTION B.

Step-by-step explanation:

It is important to remember that:

[tex]Tangent\ chord\ angle=\frac{1}{2}(Intercepted\ arc)[/tex]

We can identify in the figure that 94° is the measure of a tangent chord angle. Then, we can find "x":

[tex]94\°=\frac{1}{2}x\\\\(2)(94\°)=x\\\\x=188\°[/tex]

Since there are 360° in a circle, we can subtract 360° and the value of "x" to find the value of "z". Then we get:

[tex]z=360\°-x\\\\z=360\°-188\°\\\\z=172\°[/tex]

Step-by-step explanation:

solve the equation:

5x-10=4x+20

Answer:

The correct answer is option B. 140

Step-by-step explanation:

From the figure we can see that,

AB ║ CD

To find the value of x

From the figure we can see that,

<CFE = <BEF      [Alternate interior angles are equal]

4x + 20 = 5x - 10

5x - 4x = 20 + 10

x = 30

To find the measure of <BEF

m<BEF = 5x - 10

 = (5*30) - 10

 = 150 - 10

 = 140°

Therefore the correct answer is option B. 140

Answer:

[tex]5\sqrt{5}[/tex]

Step-by-step explanation:

We start by factoring 125 and look for a perfect square:

125= 5*5*5=[tex]5^{2} *5[/tex].

This allow us to simplify the radical:

[tex]\sqrt{125} = \sqrt{5^{2} *5}[/tex]

So we have:

[tex]\sqrt{5^{2} *5} =5\sqrt{5}[/tex]

[tex]\huge\boxed{1 \frac{4}{5}\ \text{ft}}[/tex]

Change [tex]\frac{1}{5}[/tex] so that is has a common denominator.  [tex]\frac{1*2}{5*2}=\frac{2}{10}[/tex]

Make an equation.  [tex]\frac{7+7+2+2}{10}[/tex]

Add.  [tex]\frac{14+4}{10}[/tex]

Add.  [tex]\frac{18}{10}[/tex]

Divide both sides by 2.  [tex]\frac{9}{5}[/tex]

Convert to a mixed number.  [tex]1 \frac{4}{5}[/tex]

Answer:

1 4/5 ft.

Step-by-step explanation:

Change 7/10 into 70

Change 1/5 into 20

( It will be easier to find perimeter this way )

Formula: P=2(l+w)

P=2(l+w)=2·(70+20)=180

Then, you change the 180 back into a fraction to get 1 4/5.

Answer:

[tex]\frac{60c}{m}[/tex]

Step-by-step explanation:

We can use the unity rule to solve this problem.

Number of toys made in m minutes = c

Number of toys made in 1 minute = [tex]\frac{c}{m}[/tex]

Number of toys made in 60 minutes = [tex]\frac{c}{m} \times 60 = \frac{60c}{m}[/tex]

Since 60 minutes = 1 hours, we can write:

Number of toys made in 1 hour = [tex]\frac{60c}{m}[/tex]

Therefore, we can say that Kevin makes [tex]\frac{60c}{m}[/tex] toys per an hour.