when the center line is one solid yellow line and one broken yellow line,who may cross the line to pass

Answer: First option.

Step-by-step explanation:

Given the function f(x):

 [tex]f(x)=2x-7[/tex]

And the function g(x):

[tex]g(x)=-6x-3[/tex]

You need to add them to get [tex]f(x)+g(x)[/tex]. Then:

 [tex]f(x)+g(x)=(2x-7)+(-6x-3)[/tex]

Therefore, when you add the like terms you get that [tex]f(x)+g(x)[/tex] is:

[tex]f(x)+g(x)=2x-7-6x-3[/tex]

[tex]f(x)+g(x)=-4x-10[/tex]

Since it is a linear function, the Domain is: All real numbers.

You can observe that the result obtained matches witht the first option.

Answer:

Depending of the exact career but measurements are plentiful in the healthcare business.

First, you'll most likely deal with weight and height... since that's part of most health care consultations.

Then, if you deal with medication, you'll use grams, milligrams, milliliters, liters all the time. depending if the medication is in solid or liquid form.

Even as a nutritionist, you'll deal with grams and such for portion sizes.

There are countless of ways you'll use maths and measurements in the healthcare sector.  

Answer:

Measurement can be used in healthcare career also. Like - the doctors and nurses are well trained to give medicines accurately as per measurement of milligrams or nano-gram. High doses can prove fatal with some medicines, so the correct measurement is very necessary.

Similarly, measurement is used in syrups. Like a child can be given upto 5 mg of syrup twice daily.

Answer:

5, 144°

Step-by-step explanation:

A vector with magnitude v and angle θ can be split into x and y components as:

vx = v cos θ

vy = v sin θ

Here, we're given the components and asked to find the magnitude and direction.  By matching, we can see the magnitude is 5 and the angle is 144°.

So the answer is 5, 144°.

Answer:

A

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

You have to do the number of options in each category by itsself

The correct statement about the function represented by the table is:

  D.  It is a linear function because the y-value increase by an equal difference over equal intervals of x-values.

The table of values are given as follows:

            x                    y

            1                    26

            2                   44

            3                   62

            4                   80

            5                    98

Here with the x-value is increasing by each 1.

Hence, we will check whether the difference in y-value is equal or not.

( Since, the rate of change is the ratio of the change in y-value to the change in x-value)

Hence,

44-26=18

62-44=18

80-62=18

and 98-80=18

Hence, we get that the change in y-value is equal .

Hence, we get that the slope or rate of change of the function is constant.

Hence, the function is linear.

For this case we have the following expression:

(63 + 9) ÷ 3 (2)

To find the value of the expression we must first solve the terms associated with parentheses, that is:

[tex](63 + 9) = 72\\3 (2) = 6[/tex]

So:

72 ÷ 6 =

12

So, the correct option is 12.

Answer:

(63 + 9) ÷ 3 (2) = 12

Option B

First add the numbers inside the parentheses, then divide the result by 3, and finally multiply that result by 2. The final answer is 48, matching option C.

Therefore, the answer to (63 + 9) ÷ 3(2) is 48, which corresponds to option C.

Answer:

$3000 was invested at 11%.

Step-by-step explanation:

The total interest was $426.  This was comprised of interest earned at 8% (represented by e) and (separately) interest earned at 11% (represented by v).

Then e + v = $4200 total investment, and  

i = $426 = e(0.08)(1 year) + v(0.11)(1 year)

We eliminate the variable e as follows:  since e + v = $4200, e = $4200 - v.  Thus,

i = $426 = e(0.08)(1 year) + v(0.11)(1 year) becomes:

i = $426 = ($4200 - v)(0.08)(1 year) + v(0.11)(1 year)  

This is one equation in one unknown, the amount of $ invested at 11%.

Performing the indicated multiplications:

426 = 4200(0.08) - 0.08v + 0.11v.  Simplifying this further, we get:

426 = 336 + 0.03v.

Then 90 = 0.03v, and v = 90 / 0.03 = $3000.

$3000 was invested at 11%.

[tex]\bf x^3=216\implies x=\sqrt[3]{216}\implies x=6[/tex]

Divide 216 by 3 to get your x-value

Answer: 230ft

Step-by-step explanation:

The perimeter is just all 4 sides added together, so,

75+75+40+40=230

The total distance around the wall is 230ft.

Answer:

17.872, 8

Step-by-step explanation:

Chords that pass through the center are the diameter, and lines that are tangent to the circle are perpendicular to the diameter at that point.

Therefore, what we are looking at are right triangles, and we can find the distance using Pythagorean theorem.

c² = a² + b²

(19.5)² = (7.8)² + b²

b ≈ 17.872

c² = a² + b²

(10)² = (6)² + b²

b = 8

Answer:

AA similarity theorem

Step-by-step explanation:

we know that

AA (Angle-Angle) Similarity states that  In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar

In this problem we have that

∠BCA=∠ECD ----> by vertical angles

∠BAC=∠DEC ---> because AB is parallel to ED (alternate interior angles)

therefore

Triangles ABC and EDC are similar by AA similarity theorem

Answer:

c

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

0.26*16 + 12.25 = 16.41

16.41 < 16.50

Answer:

No, Vicky should not switch.

Step-by-step explanation:

Vicky's checking account charges a monthly service fee = $12.25

Account also charges per-check fee = $0.26

Vicky writes checks per month = 16

His total monthly charges = 12.25+( 16 ×0.26 )

                                           = 12.25 + 4.16

                                           = $16.41

Another account that charges a $16.50 monthly service fee and no per-check fee.

Comparison between account = 16.50 > 16.41

So Vicky should not switch to another account because it charges more than her current account.

Answer:

a) 1.

f)6.

d)5.

c)7.

g)3.

e)4.

b)2.

Step-by-step explanation:

putting the steps for rewriting the equation of a circle below in standard form completing the square in order:

Step 1)

a. where 36 is added on both sides of the equation

as it is square of half of 12.

x^2 +12x+36 +y^2 +30y=24+36               ..........(1)

Step 2)

f. where 225 is added on both sides of equation as it is square of half of 30

x^2 +12x+36 +y^2 +30y+225=24+36+225             ............(6)

Step3)

d. adding numbers on r.h.s

x^2 +12x+36 +y^2 +30y+225=285             ............(5)

Step4)

c) Factoring the x values into binomial factors

(x+6)(x+6) +36 +y^2 +30y+225=285         .............(7)

Step5)

g) re-writing x factors as squares

(x+6)^2 +36 +y^2 +30y+225=285         ...............(3)

Step6)

e)Factoring the y values into binomial factors

(x+6)^2 +36 +(y+15)(y+15)=285             ...............(4)

Step7)

b)re-writing x factors as squares

(x+6)^2 +36 +(y+15)^2=285               ...........(2)!

Answer:

x = 8

Step-by-step explanation:

Step 1: Create an equation

(2+4+x+6) ÷ 4 = 5

Step 2: Solve the equation

(12+x) ÷ 4 = 5

(12+x) = 20

x = 8

The value of the unknown number x is 8.

The given numbers include:

The sum of the given numbers is calculated as follows;

2 + 4 + x + 6 = 12 + x

The mean of the given 4 numbers is calculated as follows;

[tex]\frac{12 + x}{4} = 5\\\\12 + x = 20\\\\x = 20 -12\\\\x = 8[/tex]

Thus, the value of the unknown number x is 8.

Learn more about mean of numbers here: https://brainly.com/question/281308

Answer:

Step-by-step explanation:

We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.

(look at the picture).

We have 2a = 20. Therefore a = y = 20 : 2 = 10 and a√3 = x = 10√3

Answer:

given

Step-by-step explanation:

The vertically opposite angles, ∠4 and ∠2 are equals.

Vertical angles are angles opposite each other where two lines cross.

A linear pair can be defined as two adjacent angles that add up to 180° or two angles which when combined together form a line or a straight angle.

According to the given question.

On line m, we have

∠4 + ∠1 = 180 degrees ...(i)    (by linear pair)

On line n, we have

∠1 + ∠2 = 180 degrees ...(ii)   (by linear pair)

from equation (i) and (ii)

∠4 + ∠1 = ∠1 + ∠2

⇒ ∠4 = ∠2

Hence, we proved that the vertically opposite angles ∠4 and ∠2 are equals.

Find out more information about vertically opposite angles here:

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Answer:

Final answer is 3.

Step-by-step explanation:

Given function is [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Now we need to find about what is the maximum number of relative extremes contained in the graph of the given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Degree of the given function = 4.

Because degree is the highest power of variable.

Then relative number of extremas = degree - 1 = 4 - 1 = 3

Hence final answer is 3.

The scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].

The scale factor between two similar triangles is the ratio of the corresponding side lengths. In this case, we can find the scale factor by comparing the corresponding sides of triangles FGH and MNO.

Let's denote the scale factor as [tex]\( k \)[/tex]:

[tex]\[ k = \frac{MN}{FG} \][/tex]

Given that NO = 15 units and FG = 6 units, and MN is denoted as [tex]\( x \)[/tex], we can substitute these values into the formula and solve for [tex]\( x \)[/tex]:

[tex]\[ k = \frac{x}{6} \][/tex]

Since [tex]\( k = \frac{NO}{FG} \)[/tex] we can set up the equation:

[tex]\[ \frac{x}{6} = \frac{15}{9} \][/tex]

Now, solve for [tex]\( x \)[/tex]:

[tex]\[ x = \frac{15}{9} \times 6 \][/tex]

[tex]\[ x = 10 \][/tex]

So, the scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].

The scale factor of the given figures is 5 : 3.

The value of x is 10

What is the scale factor?

Scale factor is calculated by finding the ratio of the dimensions of the new shape to the dimensions of the original shape.

15 : 9 = x : 6

15/9 = x/6

Cross product

15 × 6 = 9 × x

90 = 9x

Divide both sides by 9

x = 90/9

x = 10

Therefore, the scale factor 15 : 9

= 15/9

= 5/3

= 5 : 3

Answer:

basically you have to calculate the perimeter-

Step-by-step explanation:

4+4+0.8+0.8=8+1.6=9.6

First you need to find the parameter

P= (L x 2)+(W x 2)

P=(4km x 2)+(0.8km x 2)

P=8km+1.6km

P=9.6km

700-175=525. 525/35=15

Answer:

1/9

Step-by-step explanation:

Of the 36 possible sums, 4 of them are 9. The probability is 4/36 = 1/9.

_____

Comment on these dice

Interestingly, the probability of any given sum is the same as it is with "normal" dice.

Answer:

A) P(stars) = 1/3

B) P(odd)= 4/7

C)P(solid grays or stars or striped)= 1

D)P(1,4 or 7)= 3/7

E)P(not striped)= 2/3

Step-by-step explanation:

Given:

sample set contains 1-7 solid gray, 1-7 stars and 1-7 striped cards

Let solid gray be x

stars be y

striped be z

then sample set be

1x,2x,3x,4x,5x,6x,7x,

1y,2y,3y,4y,5y,6y,7y,

1z,2z,3z,4z,5z,6z,7z

total number of cards in sample set =21

Now

a)Finding probability of stars

Number of star cards in above sample set = 7

P(stars)= 7/21

     P(y)=1/3

b)Finding probability of odd

Number of odd cards in above sample set = 12

P(odd)= 12/21

          =4/7

c)Finding probability of solid grays or stars or striped

P(solid grays or stars or striped) = P(x or y or z)

                                                      =P(x U y U z)

As the events are mutually exclusive

P(x U y U z)= P(x)+P(y)+P(z)

now P(x)= 1/3

P(y)=1/3

P(z)=1/3

P(x U y U z) = 1/3 + 1/3 + 1/3

                   = 3/3

                   =1

d)Finding probability of 1,4 or 7

Number of 1,4 or 7 cards in above sample set = 9

P(1,4 or 7) = P(1 U 4 U 7)

As the events are mutually exclusive

P(1,4 or 7) = P(1) + P(4) + P(7)

P(1)= 3/21

     =1/7

P(4)= 3/21

     =1/7

P(7)= 3/21

     =1/7

P(1,4 or 7)= 1/7 + 1/7 + 1/7

               =3/7

e)Finding probability of not striped

Number of not striped cards in above sample set = 14

P(not striped)= 14/21

                      = 2/3 !

For this case we have the following equations:

[tex]f (x) = \frac {1} {x}\\g (x) = x ^ 2-3x[/tex]

We must find [tex](f_ {o} g) (x):[/tex]

By definition of composition of functions we have to:

[tex](f_ {o} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {o} g) (x) = \frac {1} {x ^ 2-3x}[/tex]

We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.

[tex]x ^ 2-3x = 0\\x (x-3) = 0[/tex]

So, the roots are:

[tex]x_ {1} = 0\\x_ {2} = 3[/tex]

The domain is given by all real numbers except 0 and 3.

Answer:

x other than 0 and 3

ANSWER

0 and 3

EXPLANATION

The given functions are

[tex]f(x) = \frac{1}{x} [/tex]

and

[tex]g(x) = {x}^{2} - 3x[/tex]

[tex]( f \circ g)(x) = f(g(x))[/tex]

[tex]( f \circ g)(x) = f( {x}^{2} -x )[/tex]

[tex]( f \circ g)(x) = \frac{1}{ {x}^{2} - 3x} [/tex]

Factor the numerator:

[tex]( f \circ g)(x) = \frac{1}{ x(x - 3)} [/tex]

The function will be undefined if the denominator is zero.

[tex]x(x - 3) \ne0[/tex]

[tex]x \ne0 \: and \: x \ne3[/tex]

Therefore 0 and not in the domain of the composed function.

A 9

B 10

C 6

Hope this helps;$

Answer:

a. 3:24 = 9:72.

b.  10:18 = 5:9.

c. 6:6 = 36:36.

Step-by-step explanation:

a.  72 / 24 = 3 so we multiply 3 by 3 to give 9.

b.  18/9 = 2  so we multiply 5 by 2 = 10.

c.  The answer is 6.

Answer:

t x 2.5 =m

Step-by-step explanation:

Answer:

66°

Step-by-step explanation:

Since segments MN and MP are tangent to the circle, then

[tex]\angle MPO=\angle MNO=90^{\circ}[/tex]

The sum of the measures of all interior angles of the quadrilateral is equal to 360°, so

[tex]\angle NOP+\angle MPO+\angle MNO+\angle NMP=360^{\circ}\\ \\114^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}\\ \\x^{\circ}=360^{\circ}-114^{\circ}-90^{\circ}-90^{\circ}\\ \\x^{\circ}=66^{\circ}[/tex]

Answer:

The value of x = 66°

Step-by-step explanation:

From the figure we can see that,

PM and MN are the tangent from the point M to the circle with center O

m<PON = 114°

To find the value of x

From the figure we can write,

m<PON + m<PMN = 180°

114 + x = 180

x = 180 - 114 = 66°

Therefore the value of x = 66°

Answer:

its 0.4

Step-by-step explanation:

Answer:

The answer is C) 0.4

Answer:

The missing angle has a measure of 2 degrees.

Step-by-step explanation:

Every triangle's inner angles can be added and will always equal 180. Therefore, use subtraction to find any missing angle. In this case,

180 - 91 = 89

89 - 87 = 2

So, your answer is 2.

If the two angles of the triangle are 91° and 87°. Then the measure of the third angle of the triangle will be 2°.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The two angles of the triangle are 91° and 87°.

Then the measure of the third angle of the triangle will be

Let x be the third angle. Then we have

91° + 87° + x = 180

                 x = 180° - 87° - 91°

                 x = 2°

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