Two linear functions are described below.

Function f(x) has the equation f(x)=3x−4.

Function g(x) has the table of values shown below.

x g(x)
0 4
3 5
6 6
9 7
Which statement is true regarding the functions f(x) and g(x)?
A
The slopes of the two functions are the same.

B
The slopes of the two functions are opposites.

C
The y-intercepts of the two functions are the same.

D
The y-intercepts of the two functions are opposites.

Given:

The piecewise rectangular figure.

To find:

The area of the piecewise rectangular figure.

Solution:

Draw a line and divide the given figure in two parts (a) and (b) as shown in the below figure.

Figure (a) is a rectangle of length 5 yd and width 3 yd. So, the area of the rectangle is:

[tex]Area=length\times width[/tex]

[tex]A_a=5\times 3[/tex]

[tex]A_a=15[/tex]

Figure (b) is a square of edge 2 yd. So, the area of the square is:

[tex]Area=(edge)^2[/tex]

[tex]A_b=(2)^2[/tex]

[tex]A_b=4[/tex]

The area of the given figure is:

[tex]A=A_a+A_b[/tex]

[tex]A=15+4[/tex]

[tex]A=19[/tex]

Therefore, the area of the given figure is 19 square yd.

Answer:

Step-by-step explanation:

GHLM is a rectangle

MG = LH

MG = 14

ΔMXG ~ ΔKXL

In similar triangles, corresponding side are in same ratio.

[tex]\frac{MG}{MX}=\frac{XL}{XK}\\\\\frac{14}{7}=\frac{x}{8}\\\\\frac{14}{7}*8=x\\\\x = 8*2\\\\x= 16[/tex]

Answer:

[tex]-7x+1-10x^2=0[/tex]

[tex]-10x^2-7x+1=0[/tex]

[tex]quadratic\:equation:-[/tex] [tex]ax^2+bx+c=0[/tex]

[tex]solutions:-\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]For \\A=-10\\B=-7\\C=1[/tex]

[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}}{2\left(-10\right)}[/tex]

[tex]\sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}=\sqrt{89}[/tex]

[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{89}}{2\left(-10\right)}[/tex]

[tex]x_1=\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)},\:x_2=\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}[/tex]

[tex]\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)}=-\frac{7+\sqrt{89}}{20}[/tex]

[tex]\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}=\frac{\sqrt{89}-7}{20}[/tex]

[tex]x=\frac{\sqrt{89}-7}{20}[/tex]

OAmalOHopeO

the answer for your question is A :>

Answer:

The 1 liter bottle is better value

Step-by-step explanation:

Cost of 750 ml = £1.90

Cost of 1 liter = £2.50

1000 ml = 1 liter

Cost per 250 ml

750 ml / 3 = £1.90 / 3

250 ml = £0.6333333333333

Approximately,

£ 0.633

Cost per 250 ml

1 liter / 4 = £2.50 / 4

250 ml = £0.625

The 750 ml bottle is not a better value

The 1 liter bottle is better value

Answer:

8 cm

Step-by-step explanation:

We can use the Pythagorean theorem to solve since we have a right triangle

a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse

a^2 +6^2 = 10^2

a^2 +36 = 100

a^2 = 100-36

a^2 = 64

Taking the square root of each side

sqrt(a^2) = sqrt(64)

a =8

Answer:

8 cm

Step-by-step explanation:

Use the Pythagorean theorem- [tex]a^{2} +b^{2} =c^{2}[/tex]

leg a: 6cm

leg b: unknown

hypotenuse: 10cm

Therefore [tex]6^{2} +x^{2} =10^{2} = 36+x^{2} =100[/tex]

Subtract 36 to 100 to isolate the [tex]x^{2}[/tex].    [tex]x^{2} =64[/tex]

Square root both sides and get your answer of 8cm

Answer:

[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ { \tt{ \sin(55 \degree) = \frac{x}{15} }} \\ x = 15 \sin(55 \degree) \\{ \boxed{ \bf{ x = 12.29 \: }}} \: feet[/tex]

Solution :

Given data :

The mean length of the steel rod = 29 centimeter (cm)

The standard deviation of a normally distributed lengths of rods = 0.07 centimeter (cm)

a). We are required to find the proportion of rod that have a length of less than 28.9 centimeter (cm).

Therefore, P(x < 28.9) = P(z < (28.9-29) / 0.07)

                                    = P(z < -1.42)

                                   = 0.0778

b). Any rods which is shorter than [tex]24.84[/tex] cm or longer than [tex]25.16[/tex] cm that re discarded.

Therefore,

P (x < 24.84 or 25.16 < x) = P( -59.42 < z or -54.85)

                                         = 1.052

Answer:

2y + y/x + 2

Step-by-step explanation:

is the answer.....

Answer:

2/3

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

 = (12-8)/(4 - -2)

  (12-8)/(4+2)

  4/6

   2/3

Answer:

Step-by-step explanation:

f(x) + g(x) = 2x -  7 - 6x - 3

f(x) + g(x) = -4x - 10

The domain is any real number.

I think you have mixed up the question. None of the choices are correct. They look like they belong to another choice.

It could be f(x)*g(x)

(2x - 7) (-6x - 3)

-12x^2 - 42x - 6x + 32

-12x^2 - 48x + 21

Well it could be either A or C since they are identical.

Answer:

Polynomial Expression.

Step-by-step explanation:

Answer:

3 units

Step-by-step explanation:

The period of a wave is the time taken to complete a cycle of motion of the wave

In the given figure, the graduations of the x-axis, which is the usually time axis = 1 unit

At the origin, (0, 0), the vertical displacement of the wave = 0

The maximum value of the wave function is between x = 0 and x = 1

The minimum value of the wave function is between x = 2 and x = 3

At the point (3, 0) the value of the wave function is again 0, and a cycle of the wave is completed

Therefore, the period of the wave = 3 units of the x-variable

Answer:

you are correct'v'

Step-by-step explanation:

in the first column it adds the next odd number, 1, 3, 5,7

and in the 2nd it mutiplies by 2 so it would be faster by a whole lot

Answer:

A

Step-by-step explanation:

the -1 represents the graph going down by 1

Answer:

A.]A chord of a circle of diameter 40 cm subtends an angle of 70° at the centre of the circle.

Solution given;

diameter [d]=40cm

centre angle [C]=70°

(a) Find the perpendicular distance be tween the chord and the centre of the circle.

Answer:

we have

the perpendicular distance be tween the chord and the centre of the circle=[P]let

we have

P=d Sin (C/2)

=40*sin (70/2)

=22.9cm

the perpendicular distance be tween the chord and the centre of the circle is 22.9cm.

(b) Using = 3.142, find the length of the minor arc.

Solution given;

minor arc=[tex]\frac{70}{360}*πd=\frac{7}{36}*3.142*40[/tex]

=24.44cm

the length of the minor arc. is 24.44cm.

B.]In the diagram, XZ is a diameter of the cir cle XYZW, with centre O and radius 15/2 cm.

If XY = 12 cm, find the area of triangle XYZ.

Solution given:

XY=12cm

XO=15/2cm

XZ=2*15/2=15cm

Now

In right angled triangle XOY [inscribed angle on a diameter is 90°]

By using Pythagoras law

h²=p²+b²

XZ²=XY²+YZ²

15²=12²+YZ²

YZ²=15²-12²

YZ=[tex]\sqrt{81}=9cm[/tex]

:.

base=9cm

perpendicular=12cm

Now

Area of triangle XYZ=½*perpendicular*base

=½*12*9=54cm²

the area of triangle XYZ is 54cm².

Answer:

a)

d = 40 cm ⇒ r = 20 cm

Let the perpendicular distance is x.

Connecting the center with  the chord we obtain a right triangle with hypotenuse of r and leg x with adjacent angle of 70/2 = 35°.

From the given we get:

b)

The minor arc is 70° and r = 20

The length of the arc is:

Since XZ is diameter, the opposite angle is the right angle, so the triangle XYZ is a right triangle.

Find the missing side, using Pythagorean:

The area of the triangle:

Answer:

2

Step-by-step explanation:

Divide 9/37 and you get repeating decimal of 0.243

Divide 2005 by 3 because the decimal repeats 3 numbers

You will get reminder of 1 from dividing 2005 by 3

Move 1 place from the decimal point and you get 2

Answer:

i think i know the answer sorry if im wrong but i would say B

Step-by-step explanation:

Answer:

All functions have a dependent variable.

All functions have an independent variable.

A horizontal line is an example of a functional relationship.

Step-by-step explanation:

Answer:

0.00111111 hrs

Step-by-step explanation:

Have a nice day

Answer:

4/3600 = .001111 hr

Step-by-step explanation:

4 seconds * 1 hour            *    1 minute            =    4/3600 = .001111 hr

                    60 minutes          60 seconds

Considering that the quadratic equation has no solutions, the discriminant is classified as:

C. Negative.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The discriminant is:

[tex]\Delta = b^2 - 4ac[/tex]

The solutions are as follows:

Looking at the graph, the equation has no solutions, hence [tex]\Delta < 0[/tex] and option C is correct.

More can be learned about the discriminant of a quadratic equation at https://brainly.com/question/19776811

#SPJ1

Answer:

6/50 = .12 m/min

.12 * 35 =4.2 miles

Step-by-step explanation:

The solution couldn't fit but I can explain

You basically solve the sum in the brackets first

multiply the sign in the brackets after the sum

Answer:

308 m^3

Step-by-step explanation:

The volume is given by

V = l*w*h  where l is the length , w is the width and h is the height

V = 7*4*11

V = 308 m^3

Answer:

hii

Step-by-step explanation:

Given question is incorrect; here is the complete question.

"Which of the following is a correct tangent ratio for the figure attached"

A) tan(76°) = [tex]\frac{24}{8}[/tex]

B) tan (76°) = [tex]\frac{8}{24}[/tex]

C) tan (24°) = [tex]\frac{76}{8}[/tex]

D) tan (8°) = [tex]\frac{24}{76}[/tex]

Option A will be the correct option.

   From the figure attached,

By applying tangent ratio of angle having measure 76°.

tan(76°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

             = [tex]\frac{24}{8}[/tex]

    Therefore, Option (A) is the correct option.

Learn more,

https://brainly.com/question/14169279

Answer:

1.1x

Step-by-step explanation:

that is the procedure above