A train left a station at noon going at 40 mph. A second train left at 3 pm going in thte same direction at 6o mph. At what time iwll the second train catch up with the first

Answer:

Step-by-step explanation :

Given :

To Find :

Solution :

Let the angles be 7x and 8x respectively

As We know that, Sum of supplementary angles is always 180°

So, Adding Both the angles,

→ 7x + 8x = 180°

→ 15x = 180°

→ x = 180/15

→ x = 12

Hence,

Therefore,

Using proportions, it is found that the coordinates of the other end of the fence are (-1,-7).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The midpoint of a segment is the mean of the coordinates of the endpoints, hence:

[tex]3.5 = \frac{x + 8}{2}[/tex]

x + 8 = 7

x = -1.

[tex]-1 = \frac{y + 5}{2}[/tex]

y + 5 = -2.

y = -7.

The coordinates of the other end of the fence are (-1,-7).

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Answer:

6/7

Step-by-step explanation:

all fractions have a common denominator which allows us to add all numerators and maintain the same denominator. 2+3+1=6, and put it back over 7. so 6/7.

The probability that the spinner is multiple of 4 or multiple of 7 is 1/3

Probability is the likelihood or chance that an event will occur, Mathematically;

Probability = expected/total

If a game has a spinner with 15 equal sectors labeled 1 through 15, the total outcome is 15

P(multiple of 4) = 3/15 =1/5

Pr(multiple of 7 )= 2/15

p(multiple of 4 or multiple of 7) = 1/5 + 2/15
p(multiple of 4 or multiple of 7) = 5/15 =1 /3

Hence the probability that the spinner is multiple of 4 or multiple of 7 is 1/3

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[tex]\\ \rm\Rrightarrow \sqrt{x²-10x+25}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{x²-5x-5x+25}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{x(x-5)-5(x-5)}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{(x-5)(x-5)}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{(x-5)^2}[/tex]

[tex]\\ \rm\Rrightarrow\pm (x-5)[/tex]

Solution set(for x-5)

for 5-x

Answer:

First, simplify the expression under the square root sign by factoring:

[tex]\implies x^2-10x+25[/tex]

[tex]\implies x^2-5x-5x+25[/tex]

[tex]\implies x(x-5)-5(x-5)[/tex]

[tex]\implies (x-5)(x-5)[/tex]

[tex]\implies (x-5)^2[/tex]

Therefore:

[tex]\implies \sqrt{x^2-10x+25}=\sqrt{(x-5)^2}[/tex]

[tex]\implies \sqrt{x^2-10x+25}=\pm(x-5)[/tex]

[tex]\implies \sqrt{x^2-10x+25}=|x-5|[/tex]

As the domain is -5 ≤ x < 5, then:

[tex]\implies y=-x+5[/tex]

and the range is 0 < y ≤ 10

Answer:

1.5 Oz because it's just a random guess hopefully I'm right

I think

Answer:

63 quizzes= 7 weeks

90 quizzes= x weeks

63x = (7)(90)

x= (7)(90)/63

x= 10 weeks

The inside of a baking pan is to be lined with tinfoil. Then the amount of tinfoil needed will be 171 square inches.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

The inside of a baking pan is to be lined with tinfoil. the pan is 12 inches long, 9 inches wide, and 1.5 inches tall.

Then the amount of the tinfoil will be

The surface area of the rectangle with an open lid is given as

Surface area = 2(LH + WH) + LW

Then the surface area of the tinfoil will be

Surface area = 2(12 x 1.5 + 9 x 1.5) + 12 x 9

Surface area = 2 (18 + 13.5) + 108

Surface area = 2 x 31.5 + 108

Surface area = 63 + 108

Surface area = 171 square inches

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The recursive formula is; 1.02(an-1 + 15) a1=200 based on the question.

The term recursive formula can be used to describe the derivation of a term in a sequence based on the previous term.

Given the information in the question, the recursive formula is; 1.02(an-1 + 15) a1=200.

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Answer:

f(- 2) = - 7

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = [tex]\frac{3}{2}[/tex] × - 2 - 4 = - 3 - 4 = - 7

The volume of the cone that has a radius of 8 in. and a height of 10.5 in. is: 703.7 in.³

Volume = 1/3πr²h

Given the parameters:

Volume of the cone = 1/3πr²h = 1/3π(8²)(10.5)

Volume of the cone = 1/3π(64)(10.5)

Volume of the cone = 703.7 in.³

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Answer:

224Pi inches cubed

Step-by-step explanation:

Answer:

1 hour and 30 minutes

[tex]t = ch + td = fh[/tex]

where ch is current hour, td is time distance, and fh is final hour.

to find td, we must subtract the number of minutes in ch and fh and then base how many hours passed off of the minutes.

[tex]cm(45) - fm(15) = 30[/tex]

If half an hour passed, we can guess that only another hour passed, therefore we can make a final equation using eh for "estimated hour".

[tex]t = (cm - fm) + eh = 1:30[/tex]

using Indices we can simplify the square root of 10,000,000 using powers of ten is: [tex]10^{7/2}[/tex]

Indices in mathematics can be defined as a value that takes up in index form but still retain its magnitude.

It is writing big or complicated values in a simpler and smaller way.

Indices is so important for simplicity purposes.

in conclusion, using Indices we can simplify the square root of 10,000,000 using powers of ten is: [tex]10^{7/2}[/tex]

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Answer:

40 customers

Step-by-step explanation:

40% brown,

25% black

20% blonde

15% red

100% = 160

(40* 160)/ 100

6400 / 100 = 64

40% = 64 customers

(15 * 160)/100

2400/100 = 24

15% = 24 customers

64 customers - 24 customers =40 customers.

Answer:

a standard unit is a fixed value this value cannot be changed.

Step-by-step explanation:

it’s a fixed value that can’t be changed.

Standard unit is a unit of measurement that is accepted by the world as a universal unit of measurement that cannot be changed

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{-4}\\ b=\stackrel{opposite}{-5}\\ \end{cases} \\\\\\ c=\sqrt{(-4)^2 + (-5)^2}\implies c=\sqrt{41} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(\theta )\implies \cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{\sqrt{41}}}\implies \cfrac{-4}{\sqrt{41}}\cdot \cfrac{\sqrt{41}}{\sqrt{41}}\implies -\cfrac{4\sqrt{41}}{41} \\\\\\ sec(\theta )\cfrac{\stackrel{hypotenuse}{\sqrt{41}}}{\underset{adjacent}{-4}}\implies -\cfrac{\sqrt{41}}{4}~\hfill cot(\theta )\implies \cfrac{\stackrel{adjacent}{-4}}{\underset{opposite}{-5}}\implies \cfrac{4}{5}[/tex]

Answer:The answer iis 1810.3cm^2

Step-by-step explanation:

Question :-

Answer :-

[tex] \rule{180pt}{3pt}[/tex]

Diagram :-

[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{12 \: cm}}\end{picture}[/tex]

Solution :-

As per the provided information in the given question, we have been given that the radius of the sphere is 12 cm. We have been asked to find or calculate the surface area of the sphere.

To calculate the surface area of the sphere, we will use the formula below :-

[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]

Substitute the given values into the above formula and solve for surface area:

[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(12 \: cm)^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(144 \: cm^2)[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(452.16 \: cm^2)[/tex]

[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 1809 \: cm^2}[/tex]

Therefore :-

[tex]\\[/tex]

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Have a great day! <33

Answer:

Option D. [tex]\sf 2\sqrt{10}[/tex]

Answer:

They bought 32 pencils

Step-by-step explanation:

5.76 divided by 0.18 = 32

Answer:

The answer is B

Please read the explanation... it always helps!!!

Step-by-step explanation:

All of the choices ask for difference.... it really helps when you draw a number line to solve these types of questions....

but for B you will need to imagine a compass..

alrighty for option B lets examine why it is correct....

Imagine you were standing on a dot (lol)

you walked 1.5 steps to the left  <--

then you walked 1.5 steps to the right -->

you can see that you walked in opposite directions and in the end you will be back where you started (aka on the dot, still lol)

meaning the displacement is zero

that is why option B is correct

i really hope this isn't confusing and it helps!!!

The coordinates for the line segment E'F' are (3, 3) and (3, -5) and the length of the segment E'F' is 8 units.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

Line segment EF begins at (-1, 5) and ends at (-1, -3). The segment is translated right 4 units and down 2 units to form line segment E'F'. Then the coordinate of E' and F' will be:

E' = (-1 + 4, 5 – 2) = (3, 3)

F' = (-1 + 4, -3 - 2) = (3, -5)

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The length of the E'F' = √(0 + 64) = 8 units

Thus, the coordinates for the line segment E'F' are (3, 3) and (3, -5) and the length of the segment E'F' is 8 units.

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The equation of the circle of radius 4 and center at (-1, 1) is given as follows:

[tex](x + 1)^2 + (y - 1)^2 = 16[/tex]

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In this problem:

Hence, the equation is given as follows:

[tex](x - (-1))^2 + (y - 1)^2 = 4^2[/tex]

[tex](x + 1)^2 + (y - 1)^2 = 16[/tex]

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Answer: 4

Step-by-step explanation:

Answer:

307.916cm^3

Step-by-step explanation:

[tex]volume \: of \: a \: cone \: = \frac{1}{3}\pi \: r {}^{2} h \\ v = \frac{1}{3} \times 3.142 \times 3.5 {}^{2} \times 24 = 307.916cm {}^{3} [/tex]

Answer:

0.0064

Step-by-step explanation:

Probability (2 sets of twins) :

Answer:

6 tables

Step-by-step explanation:

54 chairs divided by 9 chairs = 6 tables have 9 chairs :)

Answer:

Step-by-step explanation:

Given:

To find:

Solution:

⇒ 1 : Based on the given conditions, formulate

⇒ 54 ÷ 9

⇒ 2 : Calculate

54

----

9

= 6.75

Round down in this case, so

⇒ Answer: 6.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Since, the Area of smaller rectangle is 35,

Let's calculate it's length ~

[tex]\qquad \sf  \dashrightarrow \:a = l \cdot w[/tex]

[tex]\qquad \sf  \dashrightarrow \:35 = l \cdot5[/tex]

[tex]\qquad \sf  \dashrightarrow \:l = 35 \div 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:l = 7 \: ft[/tex]

And the two rectangles are similar ~ so the ratio of their sides are equal as well ~

Assume length of greater rectangle be x

[tex]\qquad \sf  \dashrightarrow \: \dfrac{25}{5} = \dfrac{x}{7} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 5 \times 7[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 35[/tex]

Now, since the length and width of the greater rectangle is known, let's find it's Area ~

[tex]\qquad \sf  \dashrightarrow \:a = l \cdot w[/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 35 \sdot25[/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 875 \: \: ft {}^{2} [/tex]

So, Area of the greater rectangle is 875 ft²

Answer:

root of 15 or in decimal form 3.87 (rounded)

Step-by-step explanation:

You just multiply both together

Answer:

  all are NO

Step-by-step explanation:

No integer ratio with 8 in the denominator can be equal to any integer ratio with 3 in the denominator.

__

The denominators 8 and 3 are relatively prime, so equivalent fractions using them cannot be formed with integers.

The equivalent to 4/3 has a mixed-number numerator that is greater than 8.

  [tex]\dfrac{4}{3}=\dfrac{10\frac{2}{3}}{8}[/tex]

This matches none of the offered choices.

The percentage increase from 5 laps of race on the first day to 9 laps after several weeks is 80%

The distance ran are given as:

Initial = 5 laps

Final= 9 laps

The percentage increase is calculated using:

Percentage = (Final - Initial)/Initial

So, we have:

Percentage = (9 - 5)/5

Evaluate

Percentage = 0.8

Express as percentage

Percentage = 80%

Hence, the percentage increase is 80%

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