Write the solution set of the inequality graphed below as a com-
pound inequality using the variable g.

Given:

The table of values is:

x :     -7          -5         -3           -1

y :      5           9         13          17

To find:

Whether the given data is linear and then find the equation.

Solution:

The given data is linear if the slope and rate of change is constant.

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using the slope formula. we get

[tex]\dfrac{9-5}{-5-(-7)}=2[/tex]

[tex]\dfrac{13-9}{-3-(-5)}=2[/tex]

[tex]\dfrac{17-13}{-1-(-3)}=2[/tex]

Since the rate of change is constant, i.e., 2, therefore the given data is linear.

The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-5=2(x-(-7))[/tex]

[tex]y-5=2(x+7)[/tex]

[tex]y-5=2x+14[/tex]

Adding 5 on both sides, we get

[tex]y-5+5=2x+14+5[/tex]

[tex]y=2x+19[/tex]

Therefore, the equation for the given data is [tex]y=2x+19[/tex].

Answer:

[tex](dimond):13/52=1/4[/tex]

[tex](spade):13/52=1/4[/tex]

[tex](\frac{1}{4} )(\frac{1}{4} )=\frac{1}{16} \hookleftarrow[/tex]

OAmalOHopeO

Distance = time/ speed

Distance = 200 seconds / 20 m/s

Distance = 10 meters

Answer:

Distance:

[tex]{ \tt{distance = speed \times time}} \\ { \tt{ = 20 \times 200}} \\ { \tt{ = 4000 \: metres}}[/tex]

Answer:

125 % increase

Step-by-step explanation:

assume a cube of side 10

then each side surface area = 100 * 6 = 600 units

now consider sides 15 (+50%)

each side = 225   ....  225 * 6 = 1350

(1350 - 600)/600  = 1.25 =  125 % increase

Answer: No

Step-by-step explanation:

Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:

9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.

Answer:

2(x + 4) / 6(x² - 3x - 28)

Step-by-step explanation:

Area of a rectangle = length × width

Length = 2/(x² - 3x - 28)

Width = x² - 16/6x - 24

= (x + 4)(x - 4) / 6(x - 4)

= (x + 4) / 6

Area of a rectangle = length × width

= 2/(x² - 3x - 28) × (x + 4) / 6

= 2(x + 4) / (x² - 3x - 28)6

= 2(x + 4) / 6x² - 18x - 168

= 2(x + 4) / 6(x² - 3x - 28)

Area of a rectangle =

2(x + 4) / 6(x² - 3x - 28)

Answer:

a -2b

Step-by-step explanation:

2(a+2b)-a-2b

Distribute

2a+4b -a-2b

Combine like terms

a -2b

Answer:

[tex]\sqrt{40\\}[/tex], [tex]2\sqrt{10}[/tex], or 6.3 (rounded).

Step-by-step explanation:

Use the distance formula, [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \\x_1 is -8, y_1 is 6, x_2 is -6, y_2 is 0.[/tex]

Answer:

C

Step-by-step explanation:

x + 40 + 100 + x=360. (sum of angles at a point)

2x+140=360

2x=360-140

2x=220

x=220/2

x=110⁰

Answer:

A scatter plot can show a positive relationship, a negative relationship, or no relationship. If the points on the scatter plot seem to form a line that slants up from left to right, there is a positive relationship or positive correlation between the variables.

Answers:

=========================================

Explanation:

In this exercise we have to use the knowledge of angles, in this way we can say that:

A) Right angles

B) Substitution

C) Congruence

So punctuating some necessary definitions we have that:

A) This alternative is a right angle, that is, an angle that has 90 degrees.

B) The substitution property allows us to replace one thing for another, as long as the two things are equal.

C) IIn this alternative, we are dealing with congruent angles, that is, angles that have the same measure, normally less than 90 degrees.

See more about angles at brainly.com/question/15767203

Answer:

4/8 or 1/2

Step-by-step explanation:

Answer:

y = 4x -18

Step-by-step explanation:

y-2 = 4(x-5)

y = 4x -20+2

y = 4x -18

Answer:

y = 4x-18

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 4x+b

Substitute the point in the equation and solve for b

2 = 4(5)+b

2 = 20+b

2-20 = b

-18 =b

y = 4x-18

Answer:

(0,-9)

Step-by-step explanation:

To find the y-intercept, substitute x=0

y=(0)^2+4(0)-9

=-9

Here's a tip to help you find the y-intercept faster, it is usually the constant of the graph equation

Answer:

see explanation

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

The equation of the axis of symmetry which is also the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 4x - 9 ← is in standard form

with a = 1, b = 4 , then

x = - [tex]\frac{4}{2}[/tex] = - 2

x = - 2 is the equation of the axis of symmetry

Substitute x = - 2 into the equation for corresponding y- coordinate of vertex

y = (- 2)² + 4(- 2) - 9 = 4 - 8 - 9 = - 13

vertex = (- 2, - 13 )

To find the y- intercept let x = 0 and solve for y

y = 0² + 4(0) - 9 = 0 + 0 - 9 = - 9

y- intercept = (0, - 9)

From the standard form of the parabola

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Here a = 1 , that is > 0

vertex (- 2, - 13 ) is a minimum

Answer:

[tex]\text {The \ area \ of \ the \ shaded \ segment, A} = 3 \cdot \pi - \dfrac{9}{4} \cdot \sqrt{3}[/tex]

Step-by-step explanation:

The details of the circle that has the shaded segment, and the segment are;

The radius of the circle, r = 3

The angle of the arc of the segment, θ = 120°

The area of a segment, A, is given as follows;

[tex]A = \dfrac{\theta}{360^{\circ}} \times \pi \times r^2 - \dfrac{1}{2} \times r^2 \times sin(\theta)[/tex]

The area of the given segment is therefore;

[tex]A = \dfrac{120^{\circ}}{360^{\circ}} \times \pi \times 3^2 - \dfrac{1}{2} \times 3^2 \times sin(120^{\circ}) = \dfrac{12\cdot \pi-9\cdot \sqrt{3} }{4} = 3\cdot \pi - (9/4)\cdot \sqrt{3}[/tex]

Answer:

Step-by-step explanation:

4x = 6/5 * 3

4x = 18/5

x = 18/5*4 = 9 / 10 = 0.9 Ans.

Answer:

0.9 I hope it help you to do this question

Answer:

base area=16π in² height=6 in ⇒ base area= πr²

16π²=π(r)²

r=4 in

v=1/3 ×π (4)²×(6)

v=32π in²

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

v=1/3 π(12/2)²×5

v=1/3π(31)×5=

v=60π in³

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

v=1/3 π×(25×4)=

v=100π/3 in³

OAmalOHopeO

Answer:

2 miles

Step-by-step explanation:

Given that :

Total distance = 10 miles

Distance = speed * time

Let distance from TBLS to flat Tyre spot = d

Time = distance / speed

Since the distance to and distance fro took a total of 48 minutes;

Hence ;

d/15 + d/3 = 48 minutes

48 minutes = 48/60 = 0.8 hours

d/15 + d/3 = 0.8

(d + 5d) / 15 = 0.8

d + 5d = 15 * 0.8

6d = 12

d = 12 / 6

d = 2 miles

Distance from TBLS to point bicycle had flat tyre is 2 miles

Answer:

sin X = 21/ 29

Step-by-step explanation:

Since this is a right triangle

sin X = opp side/ hypotenuse

sin X = 21/ 29

Answer:

[tex]\boxed{\sf sinX =\frac{21}{29}}[/tex]

Step-by-step explanation:

We need to find out the value of sinX using the given triangle . Here we can see that the sides of the triangle are 21 , 29 and 20.

We know that the ratio of sine is perpendicular to hypontenuse .

[tex]\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}[/tex]

Here we can see that the side opposite to angle X is 21 , therefore the perpendicular of the triangle is 21. And the side opposite to 90° angle is 29 . So it's the hypontenuse . On using the ratio of sine ,

[tex]\sf\longrightarrow sinX =\dfrac{ p}{h}=\dfrac{ZY}{ZX}[/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow \boxed{\blue{\sf sin\ X =\dfrac{21}{29}}}[/tex]

Hence the required answer is 21/29 .

Answer:Explanation:

Step-by-step explanation:Explanation:

We have that

6

x

2

+

19

x

+

15

=

6

x

2

+

10

x

+

9

x

+

15

=

2

x

⋅

(

3

x

+

5

)

+

3

⋅

(

3

x

+

5

)

=

(

2

x

+

3

)

⋅

(

3

x

+

5

)

Answer:

Step-by-step explanation:

6x² + 19 x +15 can be factor as (x-root1 )( x-root2)* coefficient of x²

use quadratic equation to fid the roots, x = (-b±√b²-4ac)/2a

6x² + 19 x +15 =0

x= (-19 ±√19²-4*6*15) / 2*6

x= (-19 ± √1)/ 12

x= (-19+ 1)/12 = -18/12 = -3/2

and

x= (-19-1)/12 = -20/12 = -5/3

6x² + 19 x +15 = 6*(x+(3/2)) (x+(5/3))

the length and with of the rectangle could be any combination of the factors of 6 and the (x+(3/2)) (x+(5/3))

if we consider 6 =2*3 we have length and width 2x+3 and 3x+5

because 2*[x+(3/2)]*3[ x+(5/3)]

if we consider 6 = 3*2 we have length and width 3x+(9/2) and 2x+(10/3)

because 3*[x+(3/2)]*2[ x+(5/3)]

if we consider 6= 6*1 we have length and width 6x+9 and x+(5/3)

because 6*[x+(3/2)]*1[ x+(5/3)]

if we consider 6= 1*6 we have length and width x+(3/2) and 6x+10

because 1*[x+(3/2)]*6[ x+(5/3)]

Answer:

8x + 2 and 4x - 6

Step-by-step explanation:

(f + g)(x)

= f(x + g(x)

= 6x - 2 + 2x + 4 ← collect like terms

= 8x + 2

(b)

(f - g)(x)

= f(x) - g(x)

= 6x - 2 - (2x + 4) ← distribute parenthesis by - 1

= 6x - 2 - 2x - 4 ← collect like terms

= 4x - 6

Answer:

I think the sum of the measures of the interior angles of an octagon =(8−2)180° . The sum of the measures of the interior angles of an octagon is 1080° .

I hope this help!:)

Answer:

[tex]135^{\circ}[/tex]

Step-by-step explanation:

The sum of the interior angles of a polygon with [tex]n[/tex] sides is equal to [tex](n-2)180[/tex]. Since an octagon has 8 sides, the sum of its interior angles is equal to:

[tex](8-2)180=6\cdot 180=1,080^{\circ}[/tex]

By definition, a regular polygon is a polygon with equal sides and angles. An octagon has 8 sides and 8 angles. Therefore, a each interior angle of a regular octagon must be equal to:

[tex]\frac{1,080}{8}=\boxed{135^{\circ}}[/tex]

Answer:

A: n/100 = 15/30 is the correct option

Answer:

The y intercept is (0,-1)

Step-by-step explanation:

To find the y intercept, let x = 0

y = -x^2 -6x-1

y = -0^2-6(0) -1

y = -1

The y intercept is (0,-1)

Answer:

32 cars

Step-by-step explanation:

we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32

Math step-by-step:

30-14=16

16×2=32

Answer:

[tex]2x + 3 = 13 \\ 2 \times 5 + 3 = 15 \\ 10 + 13 = 15 \\ 23 = 15 \\ 23 - 15 = 8 \\ \\ 3x + 2 = 13 \\ 3 \times 5 + 2 = 13 \\ 15 + 2 = 13 \\ 17 - 13 \\ = 4 \\ \\ x - 5 = 0 \\ 5 - 5 = 0 \\ 0 = 0 \\ \\ 4x - 9 = 21 \\ 4 \times 5 - 9 = 21 \\ 20 - 9 = 21 \\ 21 - 11 \\ = 10[/tex]

Answer:

Step-by-step explanation:

I answered this in your question from yesterday. See #24317186