1 Round the number 5.014937 to the nearest hundredth.

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}}\implies \cfrac{-1+2}{3+4}\implies \cfrac{1}{7}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{\cfrac{1}{7}}[x-\stackrel{x_1}{(-4)}]\implies y+2=\cfrac{1}{7}(x+4) \\\\\\ y+2=\cfrac{1}{7}x+\cfrac{4}{7}\implies y=\cfrac{1}{7}x+\cfrac{4}{7}-2\implies y=\cfrac{1}{7}x-\cfrac{10}{7}[/tex]

Each new term is found by multiplying the last term by 2

1*2 = 2

2*2 = 4

2*4 = 8

2*8 = 16

and so on

Therefore the common ratio is r = 2.

The starting term is a = 1

The general nth term is [tex]a*(r)^{n-1} = 1*(2)^{n-1} = 2^{n-1}[/tex] where n is an integer (aka whole number) and n starts at n = 1.

Answer:

- 12

Step-by-step explanation:

The rate of change is measured by the slope m of the data

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, - 2) and (x₂, y₁ ) = (5, - 26) ← 2 ordered pairs from the table

m = [tex]\frac{-26+2}{5-3}[/tex] = [tex]\frac{-24}{2}[/tex] = - 12

Rate of change = - 12

Answer:

1 1/2 hours

Step-by-step explanation:

divide 3/2 and whatever you got is your answer

Answer:

[tex]\$973.80[/tex]  

Step-by-step explanation:

The complete question is

How much money will Alondra make if she invests $900 in an account that pays 8.2% interest compounded annually for one year?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=1\ year\\ P=\$900\\ r=8.2\%=8.2/100=0.082\\n=1[/tex]

substitute in the formula above

[tex]A=900(1+\frac{0.082}{1})^{1*1}[/tex]  

[tex]A=900(1.082)^{1}[/tex]  

[tex]A=\$973.80[/tex]  

Answer:

(e) =1/2x^3y^4      (f)=y/3x^2

Answer:

Step-by-step explanation:

8+?=19

19-8=11

Y=11

Final answer:

To solve the equation 19 = 8 + y for y, you subtract 8 from both sides which gives you y = 11.

Explanation:

The equation provided, 19 = 8 + y, is a simple linear equation where you are solving for the variable y. To find the value of y, you need to isolate y on one side of the equation.

Here is the step-by-step process:

Start with the original equation: 19 = 8 + y.

To isolate y, you need to get rid of the 8 on the right side of the equation. You can do this by subtracting 8 from both sides of the equation.

Subtracting 8 from both sides gives us: 19 - 8 = y.

Simplify the left side: 11 = y.

Therefore, y equals 11.

Answer:

Step-by-step explanation:

f = v + at....solving for t

f = v + at....subtract v from both sides

f - v = at....divide both sides by a

(f - v) / a = t or could also be : t = f/a - v/a <==

The equivalent equation for the given expression f = v + at  is (f - v) / a = t. The correct option is C.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

The given expression is f = v + at, where, the final velocity of an object, f, with an initial velocity, V, and an acceleration rate, a, over time, t.

The given expression for ' t ' is calculated as:-

f = v + at....solving for t

f = v + at....subtract v from both sides

f - v = at....divide both sides by a

(f - v) / a = t

The above expression can also be written as given below:-

t = f/a - v/a <==

Hence, the expression  f = v + at for t will be equal to (f - v) / a = t. Then the correct option is C.

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Step-by-step explanation:

Check out the pic, if it doesn't help you can ask me whichever part you don’t understand

The velocity of plane is 379 kilometer per hour

Solution:

Given that, plane was traveling from Florida to Canada

It flew 5 hours and went 1895 km

To find: Velcoity

The velocity can be found by dividing the distance traveled by time taken

[tex]velocity = \frac{distance}{time}[/tex]

Here in this sum,

distance = 1895 km

time = 5 hours

Substituting the values in formula,

[tex]velocity = \frac{1895}{5}\\\\velocity = 379[/tex]

Thus velocity of plane is 379 kilometer per hour

Answer:

y = -21

Step-by-step explanation:

Answer:

The smallest amount is [tex]\£6,911[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1[/tex]  

substitute in the formula above

[tex]8,000=P(1+\frac{0.05}{1})^{1*3}[/tex]  

solve for P

[tex]8,000=P(1.05)^{3}[/tex]  

[tex]P=8,000/(1.05)^{3}[/tex]  

[tex]P=\£6,910.70[/tex]  

Round to the nearest pound she can invest

The smallest amount is [tex]\£6,911[/tex]

Answer:

132 ft squared

Step-by-step explanation:

One way is to divide the shape into a rectangle and a triangle, by drawing a vertical line.

This gives a rectangle that is 9 by 11, so has area 99.

The triangle has a base of 11 and height of 15 - 9 = 6.

So the area of the triangle = 1/2 x b x h = 1/2 x 11 x 6 = 33

So the total area is 99 + 33 = 132.

Answer:

first C then B

Step-by-step explanation:

The distance Raphael needs to travel goes down by time. Therefore the y-value (the amount of distance) will go down as the x-value (the amount of time) will go up. So C.

The speed of the rollercoaster is increasing as time goes by. Therefor the y-value (the speed) will go up and the x-value (the amount of time) will also go up. So B.

Time is almost always moving forward so you can almost always assume x will go up.

Answer:

4u+16

Step-by-step explanation:

first multiply the outside bumber(in this case its 4) by each of the numbers and variables inside. (making u turn into 4u) and ( making 4 turn into 16 bcs 4x4=16

Answer:

Step-by-step explanation:

Because 4 to the power of -3 divided by 4 to the power of -1 switched (Like when there is a negative exponent you move the number or variable to the other side of the fraction) and scince both have a negative number you switch both. and 1-3 is -2 so you switch it to the bottem and put a 1 at the top.

                                         ^^Hope this helps!

The expressions equivalent to 4^-3 / 4^-1 are 1/4^2 and (4^-1)^-3.

In the subject of mathematics, the given expression is 4^-3 / 4^-1. To simplify this expression, you need to understand two rules of exponents:

Applying these two rules, 4^-3 / 4^-1 = 4^-3 * 4^1 = 4^(1 - 3) = 1/4^2.

Another way to simplify the expression is to use the rules of exponents to rewrite each part independently. 4^-3 = 1/4^3 and 4^-1 = 1/4. Therefore, 4^-3 / 4^-1 = (1/4^3) / (1/4) = 4, which is equivalent to (4^-1)^-3.

Therefore, the equivalent expressions are (B) 1/4^2 and (D) (4^-1)^-3.

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Answer:

x= 40°

Step-by-step explanation:

Please see attached picture for full solution.

Key concepts:

- Corresponding angles are equal to each other

- The sum of the angles in a triangle add up to 180°

Answer:

$ 16.84

Step-by-step explanation:

First take 40 percent of 26 by doing 26 times .4 which gives you 10.4 and then do 26- 10.4 (because it was marked down) which gives you 15.6 and then you multiply 15.6 by .08 giving you 1.248 and then you add 1.248 + 15.6 to give you 16.84

Answer:

To find out the length of AB you are trying to figure out how long it is

If B is at 45, and A is at 16

You need to figure out how far it is from 16 to 45

In order to do this the easiest way, you would go 45-16

45-16=29

AB=29

Hope this helps ;)

Answer:

There are 8 more girls than boys.

Step-by-step explanation:

First, find how many girls and boys are in the class. Add the two parts of the ratio together, 3 and 5 to get 8. Then divide 32 by 8 to get 4. Since the total number of students in the class is 4 times the ratio of boys to girls, multiply both sides of the ratio by 4. You then get 12 boys : 20 girls. You can check this by adding 12 + 20 to get 32. Next, subtract the number of girls from the boys. 20 - 12 = 8. Therefore, there are 8 more girls than boys.

Therefore there are 8 girls more than boys

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Answer:

Slope= -3/4

Step-by-step explanation:

Measure of one of the vertical angle is 156°

Solution:

The measure of angles given are (x + 104)° and 3x°.

The given angles are vertical in order.

If two lines meet at a point, then the angle formed in vertical positions are equal.

That is vertically opposite angles are equal.

⇒ 3x° = (x + 104)°

⇒ 3x° = x° + 104°

Subtract x° on both sides of the equation to equal the expression,

⇒ 3x° – x° = x° + 104° – x°

⇒ 2x° – x° = 104°

⇒ 2x° = 104°

Divide both sides of the expression by 2, we get

⇒ x° = 52°

Substitute x° = 52° in one of the vertical angle.

3x° = 3 × 52° = 156° (or)

x° + 104° = 52°+ 104° = 156°

Hence the measure of one of the vertical angle is 156°.

Answer:

Step-by-step explanation:

It takes 9 minutes to fill a depth of [tex]\frac{3}{5}[/tex] meters.

Filling  [tex]\frac{3}{5}[/tex] meters take 9 minutes time.

Filling 3 meters of the aquarium takes [tex]5\times9[/tex] = 45 minutes time (Multiplying by 5 both the numbers).

In order to fill 1 meter of the aquarium it will take [tex]\frac{9\times5}{3} = 15[/tex] minutes (Dividing by 3 both the numerical values).

Answer:

The rate is 15 minutes per meter.

Step-by-step explanation: please give brainliest

The number 28 is divided by the number 3 in fraction form is  9 1/3.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The number 28 is divided by the number 3.

This can be written in fraction form as 28/3.

Now, 3×9 = 27.

Therefore, 28/3.

= 9 1/3.

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Answer:

x = 6

y = 0

Explanation:

−2x+y=−12;3y−2x=−12

Rewrite equations:

−2x+y=−12;−2x+3y=−12

Solve −2x+y=−12 for y

−2x+y=−12

−2x+y+2x=−12+2x(Add 2x to both sides)

y=2x−12

Substitute 2x−12 for y in −2x+3y=−12

−2x+3y=−12

−2x+3(2x−12)=−12

4x−36=−12 (Simplify both sides of the equation)

4x−36+36=−12+36 (Add 36 to both sides)

4x=24

Divide both sides by 4

4x / 4 = 24 / 4

x = 6

Substitute 6 for x in y=2x−12

y=2x−12

y=(2)(6)−12

y=0 (Simplify both sides of the equation)

Answer: X = 8.67

Step-by-step explanation:

Answer:

I believe the answer to this question is: X=5.

Answer;

Given that;

n/8=9

Here n is the numerator and 8 is the denominator we know that 8 is divided here so when we take it to the left side we get;

n=9 * 8. (9 multiplied with 8)

n=72

Hence answer only;

n/8=9

n=9 *8

n=72

Hence answer only;

n=72

After solving  n/8=9 you will get n = 72.

To solve the equation n/8 = 9 for n, we need to isolate the variable by performing inverse operations.

Step 1: Multiply both sides of the equation by 8 to eliminate the fraction:

8 * (n/8) = 8 * 9

This simplifies to n = 72.

Therefore, the solution to the equation n/8 = 9 is n = 72. When n is divided by 8, the result is 9. This means that 72 is the value that satisfies the equation and makes it true.

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