Samantha is riding a raft down a stream that is moving at a rate of 65 feet per minute. How far downstream does she travel in 5 minutes?

8-6z=26

8-8-6z=26-8

-6z=18

divide by -6 for -6z and 18

-6z/-6=18/-6

z=-3

Check answer by using substitution method

8-6(-3)=26

8+18= 26

26=26

Answer is z=-3

Answer:

answer - 3

Step-by-step explanation:

8 - 6z = 26                    Subtract 8 from both sides.

8-8 - 6z = 26 - 8

- 6z = 18                         Divide by - 6

-6z/-6 = 18/-6                 Do the division. Note: you must leave the letter with 1 in front of it.

z = - 3

Answer:

Option 2: 14.06 minutes

Step-by-step explanation:

For the first scenario, we will convert the minutes into hours first to get all the quantities in same unit

So,

15 minutes = 1/4 hours = 0.25 hours

Speed = 7.5 miles per hour

Now using the speed, distance and time formula

Speed = distance/time

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

[tex]7.5 = \frac{distance}{0.25}[/tex]

[tex]7.5 * 0.25 = Distance[/tex]

Distance = 1.875 miles

So the distance for 1st day is 1.875 miles.

For next day

Speed = 8 miles per hour

Distance = 1.875

So,

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

[tex]8 = \frac{1.875}{time}[/tex]

[tex]time = \frac{1.875}{8}[/tex]

[tex]time = 0.234375 hours[/tex]

Converting the hours into minutes will give

0.234375 * 60 min =  14.0625 minutes

Rounding off to two decimals = 14.06 min

So 2nd option is correct..

For this case we have a factored expression, of a second degree equation:

([tex](x-3) (x + 8) = 0[/tex]

To find the solutions:

we add 3 to both sides of the equation:

[tex]x=3[/tex]

We subtract 8 on both sides of the equation:

[tex]x = -8[/tex]

Thus, the solutions of the equation are:

[tex]x_ {1} = 3\\x_ {2} = - 8[/tex]

Answer:

[tex]x_ {1} = 3\\x_ {2} = - 8[/tex]

Answer:

Step-by-step explanation:

It is a right angle triangle with height and base = 3. The 4.24, for area, is not relevant.

Area = h * b / 2

Area = 3 * 3/2

Area = 9/2

Area = 4.5

Answer:

4.5 units

Step-by-step explanation:

A=1/2(b×h)

b=base

h=height

plug in what we know ...

A=1/2 (3×3)

A=1/2 (9)

A=4.5

Answer:

Part 1) 0.08

Part 2) $75.6

Part 3) y=230+0.08x

Part 4) The minimum amount to sell is $3,500

Step-by-step explanation:

Part 1) Give the decimal form of 8%

we know that

To convert percentage number to decimal number, divide by 100

8%=8/100=0.08 ----> decimal form

Part 2) If you make $945 in sales, how much will you make from your 8% commission?

Multiply the percentage of commission in decimal number by the total amount in sales

so

0.08*($945)=$75.6

Part 3) Create an expression representing how much you will make in one week if you sell  

x amount of sales.

Let

x-----> amount of sales in a week

y ----> total earned in a week

we know that

The linear equation that represent this situation is

y=230+0.08x  

Part 4) Create an inequality using the expression in problem 3 to find how much you need  to sell at a MINIMUM to make your goal

we know that

The inequality that represent the situation is

[tex]230+0.08x \geq 510[/tex]

Solve for x

Remember that x is the amount of sales in a week

[tex]0.08x \geq 510-230[/tex]

[tex]0.08x \geq 280[/tex]

[tex]x \geq 280/0.08[/tex]

[tex]x \geq 3,500[/tex]

The minimum amount to sell is $3,500

Answer:

Step-by-step explanation:

The 9 is in the tens place in 75, 293 so rounding to the tens place means we need to round to the place the 9 is in, and we can sort of disregard the number after that, which is a 3. It will eventually round to a 0, but if that number is 5 or greater, it rounds the 9 up. It's a 3, so the 9 stays a 9: 75, 290.

The 2 is in the hundreds place, so just like above, we can change everything after the 2 to a 0, after we use the 9 for rounding. 9 is greater than 5, so the 2 rounds up to a 3: 75, 300.

The 5 is in the thousands place, so everything after that will become 0's, but use the 2 for rounding first. 2 is less than 5, so the 5 stays a 5: 75, 000.

For this case we solve the following equation:

[tex]3 (x + 10) + 6 = 3 (x + 12)[/tex]

We apply distributive property to the terms within parentheses:

[tex]3x + 30 + 6 = 3x + 36[/tex]

We add similar terms:

[tex]3x + 36 = 3x + 36\\36 = 36[/tex]

Since 36 equals 36, then the equation will always be true for any value of x.

ANswer:

Infinite solutions

I believe the answer would be B. Hope this helps!

Graph B. best represents all the possible dollar amounts that it can save to buy a   Skateboard.

calculation:-

amount Nita needed to buy a skateboard=$85

  amount had=$61

∴ amount Nita needed more= $85-$61

                                    =$24

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Answer:

 π units^2.

Step-by-step explanation:

The area = π r^2   where  r = the radius and the radius = 1/2 * the diameter.

So the radius of this circle = 1/2 * 2 = 1.

The required area =  π * 1^2

= π units^2.

ANSWER

Exact form: π units square.

Or 3.14 square units.

EXPLANATION

The area of a circle is calculated using the formula:

[tex]Area = \pi \times {r}^{2} [/tex]

From the diagram, the diameter of the circle is d=2 units.

The radius is half of the diameter which is 1 unit.

We substitute r =1 into the formula to obtain;

[tex]Area = \pi \times {1}^{2} [/tex]

[tex]Area = \pi \: [/tex]

In decimal form, the area is

[tex]Area =3.14 \: square \: units[/tex]

Below is an image of the vertical line test.

The vertical line test is passed only when a vertical line only intersects the graph once. As you can see this graph intersects the graph twice, and therefore is not a function.

The answer you selected was correct!

Hope this helped!

Word form: 4 to 15

Fraction form: 4/15

Ratio form: 4:15

The ratio has been written in three different forms as 4:15, 0.266:1 or 1:3.75.

When a number is divisible by another number then it can be written in the form of p:q, if two ratios are equal then they are said to be in proportion.

The number of walks in the baseball game is 4

The number of hits in the baseball game is 15

The ratio of walks to hits is 4 :15

The ratio of walks to hits is 0.2666 : 1

The ratio of walks to hits is 1 : 3.75

Therefore, the ratio has been written in three different forms as 4:15, 0.266:1 or 1:3.75.

To know more about Ratio

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Answer:

A. 24

Step-by-step explanation:

! = 2 multiplied by the maximum

So, 4! = 2 × 3 × 4 [24]

This is what is known as Factorials.

I am joyous to assist you anytime.

Answer:

[tex]\Huge\boxed{24}[/tex]

Step-by-step explanation:

Apply by the factorial rule.

[tex]\displaystyle 4!=1*2*3*4[/tex]

Then multiply to find the answer.

[tex]\displaystyle 1*2*3*4=4*3=12*2=24*1=24[/tex]

24, which is our answer.

½ = v; multiply the divisor to remove the variable from the denominator.

Answer:

x = -2; x = -3

Step-by-step explanation:

(-x - 3)(x + 2) = 0

(-x - 3) = 0

x = -3

(x + 2) = 0

x = -2

Answer:

Final answer is -63.

Step-by-step explanation:

Given expression is [tex]-|-9| \times |7|[/tex].

Now question says to simplify that expression [tex]-|-9| \times |7|[/tex]

| | indicates absolute function which results only in positive output so |-9| gives 9 only

and |7| gives 7.

then we can rewrite the expression as :

[tex]-|-9| \times |7|[/tex]

[tex]=-(9) \times (7)[/tex]

[tex]=-9 \times 7[/tex]

[tex]=-63[/tex]

Hence final answer is -63.

Answer:

b

Step-by-step explanation:

Answer:

9/10

Step-by-step explanation:

step 1

Compare the slopes

[tex]1/10=0.10[/tex]

[tex]9/10=0.9[/tex]

[tex]0.9 > 0.10[/tex]

therefore

An experienced skier would like the 9/10 hill slope because it is steeper, while the 1/10 is a softer slope.

Answer:

a. [tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]

b. [tex]100x+225y=100x+225[/tex] Which means it is an identity

Step-by-step explanation:

The Pythagorean Theorem states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.

If in a right triangle there are legs of length a, and b, and the measure of the hypotenuse is c, then The following relationship is fulfilled:

[tex]a^{2} +b^{2}=c^{2}[/tex]

a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram

From the exercise shown in the image, we can get the values of a, b, and c.

a = 8x+12y, b = 6x+9y, and c = 10x+15y

Write an equation using the Pythagorean Theorem

We obtain:

[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]

b. Transform each side of the equation to determine if it is an identity.

In mathematics, an identity is the realization that two objects that are mathematically written differently, are in fact the same object. In particular, an identity is an equality between two expressions, which is true whatever the values ​​of the different ones are.

So, we transform each side of the equation

[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]

[tex](8x)^{2} +(12y)^{2} +(6x)^{2} +(9y)^{2}= (10x)^{2}+(15y)^{2}\\64x+144y+36x+81y=100x+225y\\(64x+36x)+(144y+81y)=100x+225y\\100x+225y=100x+225[/tex] Which means it is an identity

.

Answer:

a). (10x + 15y)² = (8x + 12y)² + (6x + 9y)²

b). It's an identity

Step-by-step explanation:

a). Pythagoras theorem says

(Hypotenuse)² = Height² + Base²

Therefore, form the given picture

(10x + 15y)² = (8x + 12y)² + (6x + 9y)² will be the equation.

b). For an identity we have to prove Right hand side of the equation(R.H.S.) = Left hand side of the equation(L.H.S.)

Now we solve the L.H.S. of the equation

(10x + 15y)²

= 100x² + 225y² + 300xy  [ (a + b)² = a²+ b² + 2ab

Now we solve R.H.S. of the equation

(8x + 12y)² + (6x + 9y)²

= 64x²+ 144y² + 36x² + 81y² + 108y + 192xy + 108xy

= 100x² + 225y²+ 300xy

Therefore, L.H.S. = R.H.S.

The given equation is an identity.

just substitute 10 into the equation

10=2x-6

add 6 to both sides

16=2x

divide both sides by 2

x=8

Answer:

Option B. [tex]212.1\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the central angle of the shaded sector

Remember that the diameter divide the circle into two equal parts ( 180 degrees each part)

so

Let

x -----> the measure of the central angle of the shaded sector

∠x+72°=180°

∠x=180°-72°=108°

step 2

Find the area of the circle

The area of the circle is

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=15\ cm[/tex]

assume

[tex]\pi=3.1416[/tex]

substitute

[tex]A=(3.1416)(15)^{2}[/tex]

[tex]A=706.86\ cm^{2}[/tex]

step 3

Find the area of the shaded sector

Remember that the area of the complete circle subtends a central angle of 360 degrees

so

by proportion find the area of a sector by a central angle of 108 degrees

[tex]\frac{706.86}{360}=\frac{x}{108}\\ \\x=706.86*108/360\\ \\x=212.1\ cm^{2}[/tex]

B it is horizontally stretched by a factor of of 3 and reflected over the y

Answer:

itś C on edge :)

Step-by-step explanation:

{y|1 > y}, (-∞, 1); you did not specifically mention what notation you needed, so I wrote both [Internal Notation and Set Notation].

Answer:

all real numbers less than or equal to 0

Step-by-step explanation:

EDGE 2020

x: females

x+14: males

so 34=x+x+14

To find the number of males and females in the biology class, we can create a system of equations based on the given information and then solve for the variables. After solving the equation, we find that there are 10 females and 24 males in the biology class.

To find the number of males and females in the biology class, we can create a system of equations based on the given information:

Let's assume the number of females in the class is 'x'.

The number of males in the class is then 'x + 14'.

Since the total number of students in the class is 34, we can write the equation:

x + (x + 14) = 34

Simplifying the equation, we have 2x + 14 = 34.

Subtracting 14 from both sides, we get 2x = 20.

Dividing both sides by 2, we find x = 10.

Therefore, there are 10 females and 24 males in the biology class.

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a. The speed is represented by 7 miles an hour

b. f(t)=7t

c. 28 miles

Answer:

She'll owe each friend $40.

Step-by-step explanation:

That's a total of $200 borrowed from 5 friends, which comes to:

$200

------------- = $40/friend

5 friends

Answer: A. $200 ÷ 5

Step-by-step explanation:

Sorry about the answer above mine.. that's kinda embarrassing considering how easy this question is. Anyways, the correct answer is A because the outcome will be 40 which is what we want because if you did the math for any other answer, the outcome will be negative.

Answer:

[tex]\boxed{\bold{21h+13}}[/tex]

Explanation:

Group Like Terms

= [tex]\bold{13h-4h+12h+10-6+9}[/tex]

Combine Similar Elements: [tex]\bold{13h-4h+12h=21h}[/tex]

= [tex]\bold{21h+10-6+9}[/tex]

Subtract: [tex]\bold{10-6+9=13}[/tex]

= [tex]\bold{21h+13}[/tex]

Mordancy.

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ \cline{1-1} r=0.8\\ a_1=10\\ n=5 \end{cases} \\\\\\ a_5=10(0.8)^{5-1}\implies a_5=10(0.8)^4\implies a_5=4.096[/tex]

Answer:

[tex]\large\boxed{\dfrac{5\pm3\sqrt7}{4}}[/tex]

Step-by-step explanation:

[tex]m^2-\dfrac{5}{2}m=-\dfrac{11}{2}\qquad\text{add}\ \dfrac{11}{2}\ \text{to both sides}\\\\m^2-\dfrac{5}{2}m+\dfrac{11}{2}=0\qquad\text{multiply both sides by 2}\\\\2m^2-5m+11=0[/tex]

[tex]\text{Use the quadratic formula:}[/tex]

[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\text{We have}[/tex]

[tex]a=2,\ b=-5,\ c=11[/tex]

[tex]\text{substitute:}[/tex]

[tex]\sqrt{b^2-4ac}=\sqrt{(-5)^2-4(2)(11)}=\sqrt{25-88}=\sqrt{63}=\sqrt{9\cdot7}=\sqrt9\cdot\sqrt7=3\sqrt7\\\\m=\dfrac{-(-5)\pm3\sqrt7}{2(2)}=\dfrac{5\pm3\sqrt7}{4}[/tex]

Regroup terms

(3 + 16V)(6 - 64)

Simplify 6 - 64 to -58

(3 + 16V) * -58

Simplify

= -58(3 + 16V)

Heathe lives halfway up: 42 / 2 = 21st floor.

Raveen = 42 x 4/7 = 168/7 = 24th floor.

Alveera = 42 x 3/14 = 126/14 = 9th floor.

Rafi = 42 x 4/6 = 168/6 = 28th floor.

Suha = 28-24 = 4 /2 = 2 = 24+2 = 26th floor.

Arabi = 42 x 2/3 = 84/3 = 28th floor