Two cars started from a point and traveled in opposite directions; each
car has traveled some miles as shown on the number line. Find the
distance between the two cars.

Answer:

2nd option

{(-8, -2), (-4, 1), (0, -2), (2, 3), (4, -4)}

Step-by-step explanation:

For a function to exist, every value of input must have exactly one value of output.

The rest of the relations(1, 3, and 4) have 2 outputs for 1 input so they dont make a function.

Answer:

(B)

Step-by-step explanation:

If you noticed, all the other input values have one input value that has two output values. This doesn't represent a function. Only (B) has one output for each input.

Hope that helps (●'◡'●)

Answer:it’s C

Step-by-step explanation:

The system of inequalities can be used to determine, if The selling price of model A was less than $8,000, The selling price of model B was at most $10,000, are x < 8000 × 0.88, and y < 1000 × 0.85.

The selling price of a good or service is the final cost to the seller, or what the buyer actually pays. A commodity or service in a specific amount, weight, or measurement can be exchanged.

It is one of the most crucial things for a business to decide. It is significant since it determines whether it will survive. Sales of a product are directly impacted by its price.

Given:

The selling price of model A was less than $8,000,

The selling price of model B was at most $10,000,

The price of model A is decreasing at a rate of 12% each year,

The price of model B is decreasing at a rate of 15% each year,

Write the inequality as shown below,

Assume the selling price of A is x,

x < 8000

Assume the selling price of B is y,

y < 1000

The decreased selling price of A,

x < 8000 × (1 - 0.12) = x < 8000 × 0.88

The decreased selling price of B,

y < 1000 × (1 - 0.15) = y < 1000 × 0.85

To know more about the selling price:

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Answer:

s for length of either equal side

b for the unequal side

b=-2+2*(s+s) and 2s+b=40

b=2*2s-2

b=4s-2

2s+4s-2=40

6s-2=40

6s=42

s=7

b=4*7-2

b=28-2

b=26

Answer:

x=2

Step-by-step explanation:

We have

y = 2x-1

y= 4x-5

Therefore, as 2x-1=y=4x-5, we can say that

2x-1=4x-5

add 1 to both sides to make one side have only x components

2x = 4x-4

subtract 4x from both sides to separate the x components

-2x = -4

divide both sides by -2 to separate the x

x = 2

Answer:

32

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

.......

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Explanation:

Let's start with what the hint gives us. So the first sub-goal is to prove triangle ABE is similar to triangle DCE.

Since points A and D are points of tangency, this means the radii of each of those circles is perpendicular to the common internal tangent. So angles EAB and EDC are 90 degrees each.

Due to the vertical angle theorem, we also know that angles AEB and DEC are the same (we don't know the measure but we know they're equal angles).

So we have two pairs of congruent corresponding angles between the triangles, which is sufficient to let us use the AA (angle angle) similarity theorem. Therefore, the triangles have been proven to be similar. Triangle DCE is a reduced scaled down copy of triangle ABE. Or in reverse, triangle ABE is an enlarged copy of triangle DCE.

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

Since the triangles are similar, we can form the proportion below and solve for x

AB/AE = DC/DE

x/18 = 4/6

x*6 = 18*4 .... cross multiplication

6x = 72

x = 72/6

x = 12

Therefore, segment AB is 12 units long, and this is the radius of circle B.

Answer: x = 82°

Step-by-step explanation:

The angle on the other side of 108° can be calculated as 180° - 108° = 72°

All angles within a triangle add up to 180°, so the x-value can be found as:

x = 180° - 72° - 26° = 82°

An absolute value graph looks like a V. If the number attached to the x is positive, then the graph opens upwards. If the number attached to the x is negative, then the graph opens downwards.

In this case, the graph opens downwards.

To find the vertex, look at the |x - 1| part of the equation. This tells us that x is shifted 1 to the right (opposite of the sign). And, the 3 outside of the absolute value bars tells us that the graph is also shifted up 3. Therefore, the vertex is (1, 3).

Next, we need to figure out how to graph it. That's where the -2 in front comes in. We know the graph faces downwards already. So, from the vertex, we will go down 2 spaces and left or right 1 depending on the side you are working on. Continue this pattern just like you would graphing the slope of a regular line, but this one is two sided.

If you need to view the graph for further help, I would recommend an online graphing calculator such as Desmos.

Hope this helps!

Answer:

No solutions.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = 2x + 1

2x - y = 3

Step 2: Solve for x

Substitution

Answer:

The system has no solution.

Step-by-step explanation:

y = 2x + 1

2x - y = 3

2x - ( 2x +1) = 3

2x - 2x + 1 = 3

1 ≠ 3

Since system has no solution for x, the system has no solution.

Answer:

1/9

Step-by-step explanation:

You would multiply 1/3 by 1/3 since both of the spins are out of three for the probability of rolling on the same color two times.

Answer:

180=170+4x

180-170=4x

10=4x

2.5=x

Answer:

9pm + 6pn + 12qm + 8qn

Step-by-step explanation:

Use FOIL (firsts, outers, inners, lasts)

^ this tells you what to multiply

Multiply the firsts 3p × 3m = 9pm

Multiply the outers 3p × 2n = 6pn

Multiply the inners 4q × 3m = 12qm

Multiply the lasts 4q × 2n = 8qn

Answer:

I don't know your question sorry

Step-by-step explanation:

[tex] \tan(x \degree) = \frac{54}{32} \\ = \frac{3}{4} \\ x \degree = { \tan}^{ - 1} ( \frac{3}{2} ) \\ = 56.3 \degree[/tex]

Answer:

x = 7

Step-by-step explanation:

x + 5 = 12

Subtract 5 from both sides

5 - 5 cancels out

12 - 5 = 7

We're left with x = 7

Answer:

[tex]\underline{\underline{ -10x +2}}[/tex]

Step-by-step explanation:

A expression is given to us and we need to simplify out the expression . The given expression is ,

[tex]\implies 2(-3x +1)-4x [/tex]

Open the brackets .

[tex]\implies -6x +2-4x [/tex]

Simplify the like terms .

[tex]\underline{\underline{ -10x +2}}[/tex]

Hence the correct option is (4) .

Given:

The number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation:

[tex]x=1000-100p[/tex]

To find:

The selling price if the company wants the weekly revenue to be $1,600.

Solution:

We know that the revenue is the product of quantity and price.

[tex]R=xp[/tex]

[tex]R=(1000-100p)p[/tex]

[tex]R=1000p-100p^2[/tex]

We need to find the value of p when the value of R is $1600.

[tex]1600=1000p-100p^2[/tex]

[tex]1600-1000p+100p^2=0[/tex]

[tex]100(16-10p+p^2)=0[/tex]

Divide both sides by 100.

[tex]p^2-10p+16=0[/tex]

Splitting the middle term, we get

[tex]p^2-8p-2p+16=0[/tex]

[tex]p(p-8)-2(p-8)=0[/tex]

[tex](p-8)(p-2)=0[/tex]

Using zero product property, we get

[tex]p-8=0[/tex] or [tex]p-2=0[/tex]

[tex]p=8[/tex] or [tex]p=2[/tex]

Therefore, the smaller value of p is $2 and the larger value of p is $8.

Answer:

LK = 38

Step-by-step explanation:

MN is the midsegment, and the midsegment is the average length of the top and bottom, so:

[tex]\frac{18 + LK}{2} =28[/tex]

solve for LK:

[tex]18+LK=56\\\\LK=38[/tex]

Answer:

80°

Step-by-step explanation:

Triangle ABC and CYZ are similar so the angles would also be same

Answer:

B

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

y - 6 = 5(x - 2) ← is in point- slope form

with slope m = 5 → B

Answer:

Step-by-step explanation:

In each option you need to find the number of outcomes of a single event and then multiply that by the number of times that event takes place.

1. 2 outcomes (heads and tails)

2. 6 outcomes (2 outcomes * 3 tosses)

3. 60 outcomes (6 outcomes per die * 10 rolls)

4. 12 outcomes (6 outcomes per die * 2 rolls)

5. 10 outcomes (10 numbers on the pad)

6. 52 outcomes (52 cards in a regular deck)

7. 32 outcomes (32 letters in the alphabet)

8. 7 outcomes (7 letters to choose from)

9. 10 outcomes (10 letters to choose from)

10. 36 outcomes (36 crayons to choose from)

Answer:

3x + 5 = 23

Step-by-step explanation:

Let x represents the number of persons in her group.

Since she brings 3 markers for each person, then number of markers brought for persons in her group = 3x.

She brings 5 extra markers for each person to share.

Thus, total markers she brought is now;

3x + 5

She brought 23 markers in all.

Thus, equation that represents the information is;

3x + 5 = 23

Answer:

Value of x:

[tex]{ \tt{(7x + 1) \degree + (18x + 4) \degree = 180 \degree}} \\ { \tt{25x + 5 = 180}} \\ { \tt{25x = 175}} \\ x = 7[/tex]

Finding m‹2 :

[tex]{ \tt{m \angle2 = (7x + 1) \degree}} \\ { \tt{m \angle2 = (7 \times 7) + 1}} \\ { \bf{m \angle2 = 50 \degree}}[/tex]

Answer:

m∠2 = 50

Step-by-step explanation:

7x + 1 and 18x + 4 are angles in a linear pair.

Sum of linear pair angles is supplementary.

7x + 1 + 18x + 4 = 180

7x + 18x + 1 + 4 = 180

25x + 5 = 180

25x = 180 - 5

25x = 175

x = 175 / 25

x = 7

Substitute x = 7 in 7x + 1,

7x + 1

= 7 ( 7 ) + 1

= 49 + 1

= 50

7x + 1 and ∠2 are vertically opposite angles and vertically opposite angles are equal.

∠2 = 7x + 1

∠2 = 50

Hello,

if A.P means arithmetic progression then

let's say a the first term and r the common difference.

[tex]\left\{\begin{array}{ccc}(a)+(a+r)+(a+2r)+...+(a+5r)&=&72\\a+r&=&7*(a+4r)\end{array}\right.\\\\\\\left\{\begin{array}{ccc}6a+15r&=&72\\6a+27r&=&0\end{array}\right.\\\\\\\left\{\begin{array}{ccc}a&=&\dfrac{-9}{2}*r\\-9r+5r&=&24\end{array}\right.\\\\\\\left\{\begin{array}{ccc}r&=&-6\\a&=&27\end{array}\right.\\\\[/tex]

Answer:

[tex]a)\ 5.06 * 10\³[/tex]

[tex]b)\ 6.079 * 10^6[/tex]

[tex]c)\ 3\ crore = 30\ million[/tex]

[tex]d)\ 999999[/tex]

[tex]e)\ 10478[/tex]

[tex]f)\ 78[/tex]

[tex]g)\ 2730[/tex]

Step-by-step explanation:

Solving (a): 5060 as a power of 10

We simply move the decimal between 5 and 6. The number of zeros to move backward is 4.

So,

[tex]5 0 6 0 = 5.06 * 10^3[/tex]

Solving (b): 6079000 as a power of 10

We simply move the decimal between 6 and 0. The number of zeros to move backward is 4.

So,

[tex]6079000 = 6.079 * 10^6[/tex]

Solving (c): 3 crore to millions

[tex]1\ crore = 10\ million[/tex]

Multiply by 3

[tex]3\ crore = 30\ million[/tex]

Solving (d): The greatest 6 digits

The greatest unit digit is 9. So, we simply write out 9 in 6 places

[tex]Greatest= 99999[/tex]

Solving (e): The least 5-digit formed from 4,1,8,0,7

To do this, we start the number from the smallest non-zero digit.

The remaining 4 digits will then be in an increasing order

So, we have:

[tex]Least = 10478[/tex]

Solving (f):

[tex]18 - 7 + 9 * \frac{48}{6} - 5[/tex]

Using BODMAS

Evaluate the division, first

[tex]18 - 7 + 9 * 8 - 5[/tex]

Then multiplication

[tex]18 - 7 + 72 - 5[/tex]

Add up the remaining digits

[tex]78[/tex]

Solving (g): This question is not clear.

I will assume the expression is:

[tex]\frac{72}{ 12}* [ \frac{180}{4}*{10 +(15 - \frac{45}{9}*2)}][/tex]

Evaluate all divisions

[tex]6* [ 45*{10 +(15 - 5*2)}][/tex]

Solve the multiplication in brackets

[tex]6* [ 45*{10 +(15 - 10)}][/tex]

Remove the inner bracket

[tex]6* [ 45*{10 +5}][/tex]

Evaluate 45 * 10

[tex]6* [ 450 +5}][/tex]

Remove the bracket

[tex]6* 455[/tex]

Multiply

[tex]2730[/tex]

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Its area includes all Sahara's locations in North Africa, South Arabia, Iran's and Iraq's larger parts, North-Western India, California throughout the United States, South Africa but most of Australia.

Half-arid temperatures include places like the Utah, Montana, and Gulf Coastal regions of sagebrush. Also, it comprises regions in Iceland, Russia, Scandinavia, Greenland, and Northeast India. Semi-arid thankless than tube called per year of rain and up to 20 inches per year at much more than arid deserts.

Regions from of the latitude of 25° to 35° usually develop desert, because air sinks and is heated under pressures in this area. The world's dry and semi-arid desert regions are between 20°C and 35°C north latitude and between 20°C and 35°C South latitude.

which one.

................................

Step-by-step explanation:

................

Answer:

x = 15

Step-by-step explanation:

If A parallel to B then ∠ 2 and ∠ 4 are same- side interior angles and sum to 180° , then

2x + 10 + 4x + 80 = 180 , that is

6x + 90 = 180 ( subtract 90 from both sides )

6x = 90 ( divide both sides by 6 )

x = 15

Answer:

c

Step-by-step explanation:

got it right

Answer:

y = 4x - 3

Step-by-step explanation:

y2 - y1 / x2 - x1

5 - (-3) / 2 - 0

8 / 2

= 4

y = 4x + b

5 = 4(2) + b

5 = 8 + b

-3 = b

Answer:

20 units

Step-by-step explanation:

Let the length be x. According to the question,

➝ Width = 15% of the length

➝ Width = 15/100x

➝ Width = 3/20x

We have the perimeter of the rectangle that is 46 units.

[tex]\longrightarrow \sf {Perimeter_{(Rec.)} = 2(L + W) } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{20x + 3x}{20} \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{23x}{20} \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {\dfrac{46}{2}= \dfrac{23x}{20}} \\ [/tex]

[tex]\longrightarrow \sf {23= \dfrac{23x}{20}} \\ [/tex]

[tex]\longrightarrow \sf {23 \times 20 = 23x} \\ [/tex]

[tex]\longrightarrow \sf {460= 23x} \\ [/tex]

[tex]\longrightarrow \sf {\cancel{\dfrac{460}{23}} = x} \\ [/tex]

[tex]\longrightarrow \underline{\boxed{ \bf {20\; units = x}}} \\ [/tex]

Therefore, length of the rectangle is 20 units.