Two cars leave an intersection. One car travels north: the other east. When the car traveling north had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled?

Answer:

149=19/9 (10) +b

130=19/9(1)+b

Step-by-step explanation:

for Loren to find a line passes through two points:(1,130), (10.149)

1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9

m=19/9

to find b in the equation y=mx+b for point (1,130)

y=130, x=1, m=19/9

130=19/9(1)+b

for point (10,149)

149=19/9 (10) +b

you have two options

The solution is, the equations of line passes through two points:(1,130), (10.149) is:

149=19/9 (10) +b

130=19/9(1)+b

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

for Loren to find a line passes through two points:(1,130), (10.149)

1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9

m=19/9

to find b in the equation y=mx+b for point (1,130)

y=130, x=1, m=19/9

130=19/9(1)+b

for point (10,149)

149=19/9 (10) +b

you have two options

Hence, The solution is, the equations of line passes through two points:(1,130), (10.149) is:

149=19/9 (10) +b

130=19/9(1)+b

To learn more on Equation 0f Straight-Line click:

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Answer:

10

Step-by-step explanation:

[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^2[/tex]

[tex]\left(x-6\right)^{2}+\left(y-0\right)^{2}=r^2\\[/tex]

We used (2,-3)

[tex]\left(2-6\right)^{2}+\left(-3-0\right)^{2}=25[/tex]

[tex]r^2=25\\[/tex] , so [tex]r = 5[/tex]

But this one is asking for the diameter, and to find it. It's simply 2r.

2*5 = 10

Answer:

B. x<27

Step-by-step explanation:

300-165=135

135/5=27

Answer:

B. x<27

Step-by-step explanation:

The shelter has 165 animals.  The shelter must keep its total occupancy below 300.  The shelter takes in an average of 5 animals per day. If x is the number of days, then in x days the shelter takes 5x animals. In total there will be  165+5x animals. This number must be less  than 300

         X<27

Answer:

24 of 18 is 75%

60 of 48 is 80%

1.052 is 105.2%

Step-by-step explanation:

Answer: 120

Step-by-step explanation:

Given: A bag contains two red marbles, two green ones, one lavender one, five yellows, and six orange marbles.

The total number of marbles in the bag : 2+2+1+5+6=16

Now, the number of ways of selecting sets of four marbles include one of each color other than lavender is

[tex]\( C(2,1) \times C(2,1) \times C(5,1) \times C(6,1)=2 \times 2 \times 5 \times 6\)=120[/tex]  [[tex]\because\ C(n,1)=n[/tex]]

Hence, the number of sets of four marbles include one of each color other than lavender = 120

Answer: 16,384

Step-by-step explanation:

The seven marbles have different colours, so we can differentiate them.

Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.

For the first marble, we have 4 options ( we have 4 jars)

For the second marble, we have 4 options.

Same for the third, for the fourth, etc.

Now, the total number of combinations is equal to the product of the number of options for each selection.

We have 7 selections and 4 options for each selection, then the total number of combinations is:

C = 4^7 = 16,384

Answer:

the answer is 16384

Step-by-step explanation:

have a nice day.

Answer:

y = 10

Step-by-step explanation:

y = 2x + 6

Let x  =2

y = 2*2 +6

y = 4+6

y = 10

Answer:

Step-by-step explanation:

[tex]y = 2x + 6 \\ x = 2 \\ y = 2(2) + 6 \\ y = 4 + 6[/tex]

[tex]y = 10[/tex]

Answer: 90 degrees clockwise rotation

Step-by-step explanation:

Common rotations about Origin :

90° clockwise    (x,y)→(y,-x)

90° counterclockwise    (x,y)→(-y,x)

180°       (x,y)→ (-x,-y)

270°  clockwise     (x,y)→(-y,x)

Given:  Julio’s rotation maps point K(–6, 9) to K’(9, 6).

Rotation corresponding to this is (x,y) → (y,-x) since K(–6, 9) → K’(9, -(-6)) = K(9,6).

Therefore, Julio’s rotates 90° clockwise to map point K(–6, 9) to K’(9, 6).

so , correct answer is "90 degrees clockwise rotation".

Answer:

90 degrees clockwise

Step-by-step explanation:

EDGE2020

Answer:

[tex]\dfrac{1}{x^{48}y^{36}z^{6}}[/tex]

Step-by-step explanation:

[tex] (\dfrac{(x^2y^3)^{-2}}{(x^6y^3z)^{2}})^3 = [/tex]

[tex] = (\dfrac{1}{(x^6y^3z)^{2}(x^2y^3)^{2}})^3 [/tex]

[tex] = (\dfrac{1}{x^{12}y^6z^{2}x^4y^6})^3 [/tex]

[tex]= (\dfrac{1}{x^{16}y^{12}z^{2}})^3[/tex]

[tex]= \dfrac{1}{x^{48}y^{36}z^{6}}[/tex]

Answer:

[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]

Step-by-step explanation:

[tex]\displaystyle[\frac{(x^2 y^3)^{-2}}{(x^6 y^3 z)^2 } ]^3[/tex]

[tex]\displaystyle \frac{(x^2 y^3)^{-6}}{(x^6 y^3 z)^6 }[/tex]

[tex]\displaystyle \frac{(x^{-12} y^{-18})}{(x^{36} y^{18}z^6 ) }[/tex]

[tex]\displaystyle \frac{x^{-48} y^{-36}}{z^6 }[/tex]

[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]

Answer:

60 cents or $0.60

Step-by-step explanation:

9.00/15 = 0.6

Answer:

$.60

Step-by-step explanation:

This is just 9 divided by 15 which is $.60

Answer:

B since the correlation between the numbers in x raise at a higher rate than any other chart

Answer:

in day 44 it covered half the area.

Step-by-step explanation:

A bacterial culture doubles every two days, so if today it covers [tex]3 cm^2[/tex], in two days it will cover [tex]6cm^2[/tex]. In other words, if today it covered x space, two days ago it covered half the space [tex](\frac{x}{2})[/tex].

Now, following that reasoning, we have that after 46 days the bacterial culture covered the entire surface area in the Petri dish, therefore, two days ago it covered half the area and we can conclude that in day 44 it covered half the area.

Answer:

The sampling method used is a stratified sampling method

Step-by-step explanation:

sampling is the selection of a predetermined representative subpopulation from a larger population, to estimate the characteristics of the whole population.

Stratified sampling: Here, the total population are divided into subcategories (strata) before sampling is done. The strata are formed based on some common characteristics. In our example, the times of the day (morning, afternoon and evening) has widely varying atmospheric conditions which will add biases to the measurement of air quality. For example, the air in the morning if compared to the afternoon in an industrial area may be purer because of minimal industrial activity, hence effective comparison will be made by stratification.

Answer:

y = -3x - 11

Step-by-step explanation:

(y - y1)/(x - x1) = (x2 - x1)/(y2 - y1)

(y - 7)/(x + 6) = (-3 + 6)/(6 - 7)

(y - 7)/(x + 6) = 3/-1 = -3

y - 7 = -3(x + 6)

y - 7 = -3x - 18

y = -3x -18 - 7

y = -3x - 11

Answer:

[tex]5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex].

Step-by-step explanation:

The given expression is

[tex]\sqrt[3]{5xy^2}[/tex]

We need to find the expression in rational exponent form.

It can be written as

[tex](5xy^2)^{\frac{1}{3}}[/tex]           [tex][\because \sqrt[n]{x}=x^{\frac{1}{n}}][/tex]

[tex]=(5)^{\frac{1}{3}}(x)^{\frac{1}{3}}(y^2)^{\frac{1}{3}}[/tex]           [tex][\because (ab)^m=a^mb^m][/tex]

[tex]=5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex]           [tex][\because (a^m)^n=a^{mn}][/tex]

Therefore, the required expression is  [tex]5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex].

Answer:

D. 4z^3

Step-by-step explanation:

First, you see what cubed is 64, which is 4, so you know it is either A or D, but it can not be A because it is not z to the power 5 but x to the power of 3

Hope this helps, if you want me to explain more, feel free to ask questions.

Have a good day! :)

Answer:

4 z^3

Step-by-step explanation:

( 64 z^9) ^ 1/3

Rewriting 64 as 4^3

( 4^3 z^9) ^ 1/3

We know that ( ab) ^c = a^c  * b^c

4^3 ^ 1/3 z^9  ^ 1/3

We know that a^ b^c = a^ ( b*c)

4^(3 * 1/3) z^ (9  * 1/3)

4 ^ ( 1)  z^ ( 3)

4 z^3

Answer:

9 years i think

Step-by-step explanation:

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

Work Shown:

Plug in f(x) = 37. Solve for x. Use logarithms.

f(x) = 20(1.05)^x

37 = 20(1.05)^x

20(1.05)^x = 37

1.05^x = 37/20

1.05^x = 1.85

log( 1.05^x ) = log( 1.85 )

x*log( 1.05 ) = log( 1.85 )

x = log( 1.85 )/log( 1.05 )

x = 12.6088044498867

Round up to the nearest whole number to get x = 13.

In the year 2013, sales exceed 37 million.

Answer:

Hello! The answer to your question will be below.

Step-by-step explanation:

The answer would be clockwise.

So point k was rotated 90 degrees clockwise.....

Review.....

Question:

Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.

THE DIRECTION OF THE ROTATION WAS CLOCKWISE.

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Answer:

clockwise.

So point k was rotated 90 degrees clockwise.....

Review.....

Question:

Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.

Step-by-step explanation:

Answer:

-1+2-4+8-10+12-14+16-18+20

=

-47+68

= +21

hope youlike this

stay at home stay safe

keep rocking

Answer: 2,500 blocks

Step-by-step explanation:

Hi, to answer this question we have to calculate both volumes:

Volume of a rectangular prism= length x width x height

Volume of the block = 22 x 11 x 7 = 1,694 cm3

Before calculating the volume of the wall, we have to convert the measures in m to cm:

Since:

1m = 100 cm

5 1/2 m x 100 = 550 cm (length)

3 1/2 m x 100 =350 cm (height)

Volume of the wall = 550 x 22 x 350= 4,235,000 cm3

Finally:

Volume of the wall /Volume of the block = 4,235,000 / 1,694 = 2,500 blocks.

Feel free to ask for more if needed or if you did not understand something.  

Answer:

Step-by-step explanation:

Hello!

a)

You have three triangles and you have to find the ratio of the adjacent sides to the angle 23.1º

Remember, considering a specific angle ∠, "the adjacent sides" are those that make contact with the angle and the "opponent side" is the one that is in the opposite side of the angle and the hypotenuse is the longest side of the right triangle, always opposed to the right angle.

First triangle, the adjacent sides, are

JL= 20.17m (hypotenuse)

JK= 18.55m

Ratio: [tex]\frac{JK}{JL}= \frac{18.55}{20.17}= 0.9196= 0.92[/tex]

Second triangle, adjacent sides:

PR= 141.19m (hypotenuse)

PQ= 129.85m

Ratio: [tex]\frac{PQ}{PR} = \frac{129.85}{141.19}= 0.9196= 0.92[/tex]

Third triangle, adjacent sides:

XZ= 181.53m (hypotenuse)

XY= 166.95m

Ratio: [tex]\frac{XY}{XZ} = \frac{166.95}{181.53} = 0.9196= 0.92[/tex]

b)

Using the calculator you have to calculate the trigonometric ratios of 23.1º:

sin(23.1º)= 0.392= 0.39

cos(23.1º)= 0.9198= 0.92

tan(23.1º)= 0.426= 0.43

c)

To calculate the trigonometrical ratios manually you have to do as follows:

Consider the angle A

[tex]sinA= \frac{opposite}{hypotenuse}[/tex]

[tex]cosA= \frac{adjacent}{hypotenuse}[/tex]

[tex]tanA= \frac{opposite}{adjacent}[/tex]

In item a) you calculated the ratios of the adjacent sides of the angle by the hypotenuse, this is equal to the cosine of the given angle.

I hope this helps!

Answer:

C. 97.5 yd

Step-by-step explanation:

The distance between Marsha, the ball and the tee for the fourth hole, forms a triangle.

Thus, the distance between Marsha's ball and the hole can be calculated using the Cosine formula below:

c² = a² + b² - 2abcos(C)

Where,

c = distance between Marsha's ball and the hole = ?

a = distance between the tee for the fourth hole and the tee = 300 yd

b = distance between tee and the hole = 255 yd

C = 18°

c² = 300² + 255² - 2(300)(255)cos(18)

c² = 90000 + 65025 - 153000 × 0.951

c² = 155025 - 145503

c² = 9522

c = √9522 ≈ 97.5

c = distance between Marsha’s ball and the hole = 97.5 yd (nearest tenth)

Answer:

19

Step-by-step explanation:

To calculate this, all we need to do is 150 * 0.125 ≈ 18.75 which rounds to 19. We round to the nearest integer because you can't land on the 4 18.75 times.

Answer: 19

Step-by-step explanation:

.125 is equal to 1/8, so it will be roughly 1/8 of the 150 times so we can multiply

150(.125)=18.75, which rounded up, or normally becomes 19

Answer:  [tex]\sum\limits_{i=1}^{n} n^2[/tex] , where n is a natural number.

Step-by-step explanation:

A series can be represented in a summation or sigma notation.

Greek capital letter, ∑ (sigma), is used to represent the sum.

For example: [tex]\sum\limits_{n=1}^{\infty} n=1+2+3+4+5+...[/tex], where n is a natural number.

The given series : 1,4,9,16 which can be written as [tex]1^2, 2^2, 3^2,...[/tex] .

So , we can write it as

[tex]\sum\limits_{n=1}^{\infty} n^2[/tex] , where n is a natural number.

Answer:

B=6

C=n^2

Just did the test

Step-by-step explanation:

Answer: C: -10

Step-by-step explanation:

An output is another word for y. If we set y to -15, we can solve for x, or the input variable.

[tex]-15=2x+5[/tex]

Subtract 5 from both sides of the equation.

[tex]-20=2x\\[/tex]

Divide both sides of the equation by 2.

[tex]-10=x[/tex]

Therefore, x = -10.

Hope this helps!

Answer:

the answer is -25

Step-by-step explanation:

y = 2x + 5

y = 2x(-15) + 5

2 times -15 = -30

-30 + 5 = -25

Hope this helps! :)

Answer:

x = 1/(a-b)

Step-by-step explanation:

The given equation is ax = bx + 1

Collecting like terms:

ax - bx = 1

Factorizing x out of the equation:

x(a - b) = 1

Dividing both sides by (a - b):

[tex]\frac{x(a - b)}{(a - b)} = \frac{1}{a - b} \\x = \frac{1}{a - b}[/tex]

Therefore, x is related to the difference of a and be by the equation

x = 1/(a-b) where a - b is the difference of a and b

Answer:

x = 1/(a-b)

Step-by-step explanation:

Answer:

2 CDs and 6 movies

Step-by-step explanation:

Let the number of CD you bought be x, and the number of movies you bought be y.

Since you bought 8 items in total,

x + y = 8 ______(1)

The sum of money spent is 78, so

9x + 10y = 78 ________(2)

From equation (1),

x = 8 - y ________(3)

Substitute (3) into (2),

9 (8-y) + 10y = 78

72 - 9y + 10y = 78

- 9y + 10y = 78-72

y = 6

Now substitute y=6 into (3).

x = 8 - y

x = 8-6

x = 2

Therefore, you bought 2 CDs and 6 movies.

Answer:

Hey mate... I don't know the first three... But mayb I can help u in last one.

Step-by-step explanation:

The answer is : 2: 6: 18: 54: 162: 426

I can see the pattern by multiplying.. As from 3

2x3=6 :6x3=18 :18x3= 54 :54x3=162 :162x3=426

So I guess this is the ans

Hope it helped u!

Answer:

216 elements

Step-by-step explanation:

the total number of elements of a dice is :

6^n

6 stand for the 6 faces of the dice

n stands for the number trial

then total number of elements in 3 trials of rolling a 6-sided die is 6^3=216 elements