The ares of a rectangle is 46 square inches, if the length is 4 times the width , the find the dimensions of the rectangle.

Answer:

#9 x=21

#10 a. QP  b. 8  c. 18

Step-by-step explanation:

#9 use the theorem where the ratio between a midline and the base of the triangle is 1:2

as we know the midline and the base is 1:2

this means

2(4x-65)=2x-4

  4x-65=x-2

    3x=63

      x=21

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

#10

a. RS|| QP (Remember to write the letters accordingly)

b. 8 (As mentioned before of the ratio 1:2)

c. 18

Answer:

the percent decrease is approximately 47 %

Step-by-step explanation:

Since the quantity started at 170 and then changed to 90, there was clearly a decrease in its value.

We use the following formula to calculate the percent of decrease:

[tex]\%\,decrease = \frac{original-final}{original} \,100\\\%\,decrease = \frac{170-90}{170} \,100\\\%\,decrease = \frac{80}{170} \,100\\\%\,decrease \approx 47\,\%[/tex]

Step-by-step explanation:

Hey, there!!

Let's solve it simply,

angle ONP = 60°+55° { as exterior angle is equal to the sum of opposite interior angle}.

Therefore, angle ONP = 115°.

Now, let's solve for x,

x+ 115°=180° { because the sum of co-interior angle is 180°}.

x= 180°-115°

Therefore, the measure of angle x is 65°.

Hope it helps...

Answer:

[tex]\Huge \boxed{{x=65\° }}[/tex]

Step-by-step explanation:

l and m are parralel lines.

The third angle in the triangle is also x, because of corresponding angles.

Angles in a triangle add up to 180 degrees.

Create an equation and solve for x.

x + 60 + 55 = 180

Add the numbers.

x + 115 = 180

Subtract 115 from both sides.

x = 65

Answer:

Mercury, Venus, Earth, Mars, and Uranus

Step-by-step explanation:

Calculate the escape velocity for each planet, using the equation v = √(2gR).

[tex]\left[\begin{array}{cccc}Planet&R(m)&g(m/s^{2})&v(m/s)\\Mercury&2.43\times10^{6}&3.61&4190\\Venus&6.07\times10^{6}&8.83&10400\\Earth&6.37\times10^{6}&9.80&11200\\Mars&3.38\times10^{6}&3.75&5030\\Jupiter&6.98\times10^{7}&26.0&60200\\Saturn&5.82\times10^{7}&11.2&36100\\Uranus&2.35\times10^{7}&10.5&22200\\Neptune&2.27\times10^{7}&13.3&24600\end{array}\right][/tex]

The rocket's maximum velocity is double the Earth's escape velocity, or 22,400 m/s.  So the planets the rocket can escape from are Mercury, Venus, Earth, Mars, and Uranus.

Complete Question

The  complete question is shown on the first uploaded image  

Answer:

a

  [tex]n(t) = 120 e^{(0.056t)}[/tex]

b

  [tex]n(36) = 901 \ rats[/tex]

c

 [tex]t = 50 \ months[/tex]

Step-by-step explanation:

From the question we are told that

    The  original number of  rats that swim from the wreckage to a deserted island is

   The population on the island grows exponentially according to the model

          [tex]n(t) = n_o e^{rt}[/tex]

     The  number of rats after t =  15 months is  280

So

     [tex]n(15) = 120 e^{15 * r } = 280[/tex]

=>   [tex]120 e^{15 * r } = 280[/tex]

=>   [tex]e^{15r} = 2.33[/tex]

=>  [tex]15r = 0.8459[/tex]

=>   [tex]r = 0.056[/tex]

Therefore the population t months after the arrival of the rats is mathematically represented as

      [tex]n(t) = 120 e^{(0.056t)}[/tex]

Here t is in months

Considering question b

   For  t =  3 years  =  12 * 3 =  36 months

   Then the number of rats that will be present is mathematically represented as

     [tex]n(36) = 120 e^{0.056 * 36 }[/tex]

      [tex]n(36) = 901 \ rats[/tex]

Considering question c

Now  the number of rats considered is  n(t) =  2000

So  

     [tex]n(t) = 2000 = 120e^{0.056t}[/tex]

=>    [tex]2000 = 120e^{0.056t}[/tex]

=>  [tex]16.67 = e^{0.056t}[/tex]

Taking natural log of both sides

=>   [tex]0.056 t = 2.81[/tex]

=>   [tex]t = 50 \ months[/tex]

Answer:

AC

Step-by-step explanation:

First, let's find m∠B and m∠C by solving for x. Since the sum of interior angles in a triangle is 180°, we know that:

60 + 3x - 2 + 2x + 7 = 180

5x + 65 = 180

5x = 115

x = 23° so m∠B = 3(23) - 2 = 67° and m∠C = 2(23) + 7 = 53°. The longest side of a triangle is always opposite to the largest angle of the triangle, and since m∠B is the largest, we know that the side opposite to ∠B is the longest. That side is AC.

In triangle ABC, the longest side is AC, since it is opposite the biggest angle ∠B.

According to the angle sum property of a triangle, the sum of the three interior angles is 180°.

In a triangle, the longest side is on the opposite side of the biggest angle, and the shortest side is on the opposite side of the smallest angle.

We are given the angles of the triangle ABC. We are asked to find the longest side in the triangle ABC.

By the angle sum property of a triangle, we know that,

m∠A + m∠B + m∠C = 180°

or, 60° + (3x - 2)° + (2x + 7)° = 180°

or, 5x + 65° = 180°

or, 5x = 180° - 65° = 115°

or, x = 115/5 = 23.

∴ m∠A = 60°.

m∠B = (3x - 2)° = (3(23) - 2)° = (69-2)° = 67°.

m∠C = (2x + 7)° = (2(23) + 7)° = (46 + 7)° = 53°.

∵ m∠B is the largest angle, the side opposite to it, that is, AC is the longest side of the triangle.

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Answer:

x is greater than 4

Step-by-step explanation:

4x + 5 is greater than 13

you want to find out what x is

4 - 4 x + 5 is greater than 13 - 4 ( whatever you do to one side you have to do to the other)

x + 5 is greater than 9

x + 5 - 5 is greater than 9 - 5

x is greater than 4

Answer:

The answer is A.

Do you need an explanation?

387,500 /100 = 3,875

3,875 * 0.43 = 1,666.25

I multiplied, because, if you divide with a decimal, the number increases, instead of decreasing... hope this helps!

the answer is 7-7y i think if not the it should be 7+7y

Answer:

1/4x + 3

Step-by-step explanation:

The question said one-third(1/3) not one-fourth(1/4).

1/3x + 4 can also be written as x/3 + 4.

Answer:

1/4x + 3

Step-by-step explanation:

expressions does not represent "four more than one-third x"

1/3x + 4 --- No.

x/3 + 4  --- No.

1/4x + 3 --- Yes. it does not represent 4 + 1/3x. you can tell it by +3

Answer:

1.00o2

Step-by-step explanation:

You dont need this explained come on

Answer: 12.96

Step-by-step explanation:

given data:

Poisson distributio = 3.60

solution:

The Poisson distribution expected value is same as Variance.

which is expressed as = SD^2

therefore;

the expected value

= SD^2

= 3.60^2

= 12.96

Answer:

2/10 because if the two fraction

The equivalent fractions of 8/11 = 16/22 , 24/33 , 32/44

The equivalent fractions of 1/10 = 2/20 , 3/30 , 4/40

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the first fraction be represented as A

Now , the value of A = 8/11

Let the second fraction be represented as B

Now , the value of B = 1/10

And , the equivalent fractions of A is given by

A = 8/11 , 16/22 , 24/33 , 32/44

And , the equivalent fractions of B is given by

B = 1/10 , 2/20 , 3/30 , 4/40

Hence , the fractions are solved

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Answer:

newzz new new me he new new

Answer:

oiuhj90pkomnjhb vcfgtyu789i0op,lmkn bvghyu7890opklmnjbhgvfty67890-p[lkjhngvty67u890-op[l;',

Step-by-step explanation:

Answer:

b would be a negative number

Answer:  The sign of b is negative or  -

Step-by-step explanation:

If you multiply two negative numbers you will have a positive number. And if you multiply a positive and negative numbers you will have  a negative answer.

Answer:

[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]

Step-by-step explanation:

The question is incomplete; However

[tex]A = (-2, -4)[/tex]

[tex]B = (6, 1)[/tex]

Required

Determine coordinates of P

When line segment is divided in ratios, the following formula calculates the coordinates;

[tex]P(x,y) = \{\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\}[/tex]

In this case;

[tex]m:n = 2:1[/tex]

[tex](x_1,y_1) = (-2, -4)[/tex]

[tex](x_2,y_2) = (6, 1)[/tex]

So, the coordinates of P is calculated as thus

[tex]P(x,y) = \{\frac{2 * 6 + 1 * (-2)}{2+1}, \frac{2 * 1 + 1 * (-4)}{2+1}\}[/tex]

[tex]P(x,y) = \{\frac{12 -2}{3}, \frac{2 -4}{3}\}[/tex]

[tex]P(x,y) = \{\frac{10}{3}, \frac{-2}{3}\}[/tex]

Hence, the coordinates of P is

[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]

The question is incomplete, the points A and B are:

A = (-2, -4)

B = (6, 1)

We want to find a point P in the segment AB such that the ratio of AP to PB is 2:1

We will find that:

[tex]P = (\frac{2}{3} , \frac{7}{3} )[/tex]

The general formula for two points (x₁, y₁) and (x₂, y₂), the coordinates of a point that separates the segment in a ratio j:k is

[tex]P = (\frac{j*x_1 + k*x_2}{j + k} , \frac{j*y_1 + k*y_2}{j + k})[/tex]

So we only need to use that general formula:

[tex]P = P = (\frac{2*(-2) + 1*6}{3} , \frac{2*(-4) + 1*1}{3})\\\\P = (\frac{2}{3} , \frac{7}{3} )[/tex]

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Answer:

True

Explanation:

1/2 (up the hill) - 1/2 (down the hill) = 0

Answer:

D. $10,909.09

Step-by-step explanation:

The class recovery period for residential rental property each year = 27.5 years

The cost basis for the residential property = $300,000

The amount he will be able to depreciate

= Cost basis/ Number of years

= $300000/ 27.5 years

=$10, 909.090909

Approximately ≈ $10,909.09

The amount he will be able to depreciate  using the class recovery period for residential rental property each year is: D. $10,909.09.

Using this formula

Depreciation=Rental unit amount/ MACRS residential rental property recovery period

Where:

Rental unit amount=$300,000

MACRS Residential rental property recovery period=27.5 years

Let plug in the formula

Depreciation=$300,000/27.5

Depreciation=$10,909.09

Inconclusion the amount he will be able to depreciate  using the class recovery period for residential rental property each year is: D. $10,909.09.

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Answer:

1684

Step-by-step explanation:

x ÷ 17 > 99

x > 17 * 99

x > 1683

The least whole number that is greater than 1683 is 1684.

Answer: 1684

Answer:

1683

Step-by-step explanation:

To undo the problem you do 99 times 17 which is 1683. Then you know that 1683 divided by 17 is 99.

Answer:

324 miles divided by 18 gallons = 18 miles per gallon (mpg)  

Therefore, 41 gallons x 18 mpg = 738

Step-by-step explanation:

Answer:

It should take her father four hours to reach her.

Step-by-step explanation:

Since Madison takes an hour to travel 10 miles, by the time she reaches 3 hours, shes at 30 miles. (At this point her father has begun traveling towards her) And since he goes 15 miles per hour, four hours later (for her father), they will both be at the same distance.

(So in 6 hours, Madison goes 60 miles, and in 4 hours her father also goes 60 miles since hes faster)

Please tell me if I did anything wrong!

It will take the time that Madison's dad 8 hours to catch up with her.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

Let's call the distance from Madison's house to the point where her dad catches up with her "D".

distance Madison traveled = rate × time = 10 mph × 2 hours = 20 miles.

This means that when Madison's dad starts driving, Madison is 20 miles ahead of him.

For Madison's dad, his rate is 15 mph, and the time it takes him to catch up to Madison is "t" hours.

So his distance traveled is:

distance traveled by Madison's dad = 15 mph × t

For Madison, her rate is 10 mph, and she has already traveled for 2 hours. So her distance traveled is:

distance traveled by Madison = 10 mph × (t + 2)

Now, their distances are equal to each other:

15t = 10(t + 2) + 20

Simplifying and solving for "t", we get:

15t = 10t + 40

5t = 40

t = 8

Therefore, it will take Madison's dad 8 hours to catch up with her.

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Answer:

D?

Step-by-step explanation:

¯\_(ツ)_/¯

Answer:

p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]

Step-by-step explanation:

Given equations:

2p - 3q = 4        -----------(i)

3p + 2q = 9       ------------(ii)

Let's solve this equation simultaneously using the elimination method

(a) Multiply equation (i) by 3 and equation (ii) by 2 as follows;

[2p - 3q = 4]        x 3

[3p + 2q = 9]       x 2

6p - 9q = 12            -------------(iii)

6p + 4q = 18            -------------(iv)

(b) Next, subtract equation (iv) from equation (iii) as follows;

     [6p - 9q = 12]        

 -   [6p + 4q = 18]    

            -13q = -6      -----------------(v)

(c) Next, make q subject of the formula in equation (v)

      q = [tex]\frac{6}{13}[/tex]

(d)  Now substitute the value of q = [tex]\frac{6}{13}[/tex] into equation (i) as follows;

     2p - 3([tex]\frac{6}{13}[/tex]) = 4

(e)  Now, solve for p in d above

Multiply through by 13;

26p - 18 = 52

Collect like terms

26p = 52 + 18

26p = 70

Divide both sides by 2

13p = 35

p = [tex]\frac{35}{13}[/tex]

Therefore, p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]

...... ❤

[tex] \frac{ - 4}{ \: \: 7} x = - 1[/tex]

Now firstly we have to take 7 to right hand side and multiply -1 by 7

[tex] - 4x = - 1 \times 7[/tex]

[tex] - 4x = - 7[/tex]

Now we have to take -4 to the right hand side and divide -7 by -4

[tex]x = \frac{ - 7}{ - 4} [/tex]

As we know that in case of division - and - are cancelled so ,

[tex]x = \frac{7}{4} [/tex]

Hope it helps u mate

Answer:

21

Step-by-step explanation:

tcctvucycyccyctctctchu ycuvuvuvy t r y y g g t g

Answer:

399.17 miles

Step-by-step explanation:

Gunnar's car gets 22.4 miles per gallon. His gas tank can hold 17.82 gallons of gas.

Gunnar's car travels with one gallon of gas = 22.4 miles

He can travel with 17.82 gallon of gas = 17.82 × 22.4

                                                             = 399.168 ≈ 399.17 miles

Gunnar can travel 399.17 miles if he uses all of the gas in the gas tank.

Answer: A

16 minutes

Step-by-step explanation:

The required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.

The rate of change is defined as the change in value with the rest of the time is called rate of change.

Here,
radius = 55 / 2 = 27.5
Since volume is directly proportional to the cube of the radius,
So,
For maximum volume,
V ∝ R³

and
2/3V = v
2/3R³ = r³
r = 27.5 ∛2/3
r = 24
Now,
the radius increases at a rate of 1.5 feet per minute.
Time to reach a radius of 24 feet,
= 24 / 1.5
= 16 minutes

Thus, the required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.

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