· Amani and Danielle are buying hair spray. They can buy 4 bottles of Rave and 5 bottles of Max for $30.00, or
they can by 1 bottle of Rave and 1 bottle of Max for $6.50. If r is the cost of a bottle of Rave and m is the cost
Fa bottle of Max, how much does each bottle of hair spray cost?

Answer:

7

Step-by-step explanation:

1.5 x 1.5 = 2.25

2.25 x 3.14 = 7.065

[tex]Area \: = \pi {r}^{2} = 3.14 \times {1.5cm}^{2} \\ = 7.065 \: \: {cm}^{2} [/tex]

= 7 cm^2

Answer:

10

Step-by-step explanation:

There are several ways to solve this problem which I’ll demonstrate these ways and see which method is way easier to understand.

First Method

This method is to convert the fractional expression to a single exponent expression using a law of exponent.

[tex]\displaystyle \large{\frac{m^a}{m^b} = m^{a-b}}[/tex]

In words, it means if both divisor (denominator) and dividend (numerator) have same values or are same, we can subtract the exponent from dividend (numerator) with divisor (denominator).

The dividend (numerator) exponent is unknown, let’s say it’s got ‘x’ as an exponent and this ‘x’ is what we are going to find since we don’t know its value.

Now we have the equation:

[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]

Apply the exponent rules above.

[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]

Solve an exponential equation - If both sides of equation have same base, we can solve the exponents.

Since LHS (Left-Handed Side) and RHS (Right-Handed Side) both have same base which is ‘m’ therefore, solve exponents.

[tex]\displaystyle \large{x-7=3}\\\displaystyle \large{x=7+3}\\\displaystyle \large{x=10}[/tex]

Therefore, the missing exponent is 10.

Additional Info

You can also use logarithm to solve an exponential equation.

[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]

Take a logarithm of base ‘m’ both sides so we can apply other properties.

[tex]\displaystyle \large{\log_m m^{x-7} = \log_m m^3}[/tex]

From the property [tex]\displaystyle \large{\log_a b^n = n \log_a b}[/tex]

[tex]\displaystyle \large{(x-7) \log_m m = 3 \log_m m}[/tex]

From the property [tex]\displaystyle \large{\log_a a = 1}[/tex]

[tex]\displaystyle \large{(x-7)1 = 3 \cdot 1}\\\displaystyle \large{x-7=3}\\\displaystyle \large{x=10}[/tex]

______________________________

Second Method

This method is to isolate the term with missing exponent.

[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]

Transport m^7 to multiply with m^3 via transportation property.

[tex]\displaystyle \large{m^x = m^3 \cdot m^7}[/tex]

We also have to apply another law of exponent as well.

[tex]\displaystyle \large{m^a \cdot m^b = m^{a+b}}[/tex]

Similar to the one with division (fraction), this one, when same bases multiply each other, we have to add both exponents while the other one subtracts exponents.

[tex]\displaystyle \large{m^x = m^{3+7}}\\\displaystyle \large{m^x = m^{10}}[/tex]

In the first method, we know that when solving an exponential equation, if two bases from left and right sides are same, we solve the exponent.

Therefore, [tex]\displaystyle \large{m^x = m^{10} \to \boxed{x=10}}[/tex]

______________________________

Summary

  Laws of Exponent

[tex]\displaystyle \large{a^m \cdot a^n = a^{m+n}}\\\displaystyle \large{\frac{a^m}{a^n} = a^m \div a^n = a^{m-n}}\\[/tex]

For what I demonstrate in my explanation only.

  Exponential Equation

When two bases from left side and right side are same, we can solve through exponents.

Examples:

[tex]\displaystyle \large{2^{x-3} = 2^{4}}\\\displaystyle \large{x-3=4}\\\displaystyle \large{x=4+3}\\\displaystyle \large{x=7}[/tex]

You can also substitute x-value in an equation to see if both sides are equal or not.

[tex]\displaystyle \large{2^{x-4} =2^3}[/tex]

Substitute x = 7 for check.

[tex]\displaystyle \large{2^{7-4} = 2^3}\\\displaystyle \large{2^3 = 2^3 \ \ \checkmark}[/tex]

  Logarithm

This is not necessary used in this question. This is mostly used for converting to exponential and more advanced mathematics.

[tex]\displaystyle \large{\log_a b^n = n\log_a b}\\\displaystyle \large{\log_a a = 1}[/tex]

Only from what I demonstrate in my explanation.

______________________________

If you are still stuck or need clarification regarding my answer and explanation, you may ask in comment below.

Hope this helps! And wish you luck in your assignment.

The above pic is your answer mate.

Answer:

See below!

Explanation:

equation for distance:

Lets Ben hours be x and Landon hours be y,

60x + 56y = 820 .........equation 1

equation for time:

[tex]\frac{60x}{60}+ \frac{56x}{56} =14[/tex]

x + y = 14 .........equation 2

Make x the subject:

60x + 56y = 820

x = (820 - 56y)/60 ..........equation 3

x + y = 14

x = 14 - y ........equation 4

Solve equation 3 and 4 simultaneously:

             [ Therefore Landon drove 5 hours ]

Extra's further investigated:

if y = 5

              [ Therefore Ben drove 9 hours ]

Answer:

Landon drove 5 hours (and Ben drove 9 hours)

Step-by-step explanation:

Let B = number of miles Ben drove

Let L = number of miles Landon drove

Given The trip took them 14 hours

⇒ B + L = 14

Given, Ben averaged 60 miles per hour and Landon averaged 56 miles per hour. Ben and Landon took turns driving on a 820 mile road trip:

⇒ 60B + 56L = 820

Rewrite B + L = 14 to make B the subject, substitute into 60B + 56L = 820, and solve for L:

⇒ B = 14 - L

⇒ 60(14 - L) + 56L = 820

⇒ 840 - 60L + 56L = 820

⇒ 20 = 4L

⇒ L = 5

Therefore, Landon drove for 5 hours

Answer:

B

Step-by-step explanation:

We will divide 18 by 3 and 30 by 5, and if the results are the same, then this relationship is proportional.

18/3 = 6

30/5 = 6

The two answers are the same, so this relationship is proportional.

Answer: x= -20/3 and y= 34/3

hope this helps :)

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Domain : 0 ≤ x ≤ 8

Range : 0 ≤ y  ≤ 56

Answer:

= f(x) = x²+16

is correct.

Step-by-step explanation:

[tex] \dashrightarrow f( \rm x) = (x - 4)(x - 4)[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow f( \rm x) = \: {x}^{2} - 4x - 4x + 16[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow f( \rm x) = \: {x}^{2} - 8x + 16[/tex]

Answer:

$46.27¢

Step-by-step explanation:

Good thing I was a teacher

Answer:

1/2 or 0.5

Step-by-step explanation

1/2 of 10 = 5

We can write 1/2 as a decimal.

Do you need a decimal or fraction as the answer?

Still stuck? Get 1-on-1 help from an expert tutor now.

Answer:

15 units

Step-by-step explanation:

you have to use pythagoras to solve (c²=a²+b²)

AB is the longest side of the triangle which is c in the pythagoras

so counting the units for AC, you get 9 units, and CB you get 12 units

now solve for c in pythagoras

c²=9²+12²

c = 15 units

Inequality is the comparison of mathematical expressions which are not strictly equal. The needed inequality is: 18.45 ≥ 3 + h

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given case, we've got:

Amount spent by Leticia = $18.45

Amount spent by Humberto = h dollars

Since amount spent by Leticia is at least $3. 00 more than what  Humberto spends, thus:

18.45 is at least h + 3 (all in dollars)

(we usually skip stuffs like currency sign or units in equations or inequalities, to keep things as minimized as possible. It is known from the context what unit or currency or such thing is being discussed).

At least can be thought of as equal to that quantity or greater than that quantity but not less than that quantity.

This more than or equal to is written as ≥

Thus, the inequality we get is:

18.45 ≥ 3 + h

Learn more about inequalities here:

https://brainly.com/question/11901702

Answer:

completing the division operation: numerator divided by denominator.

Step-by-step explanation:

If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Step-by-step explanation:

I'll do it on my laptop.......

Step-by-step explanation:

that a picture of what you need. Go through it and get back to me.

Answer:

y = - 6x - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 10) and (x₂, y₂ ) = (- 1, - 2) ← 2 points on the line

m = [tex]\frac{-2-10}{-1-(-3)}[/tex] = [tex]\frac{-12}{-1+3}[/tex] = [tex]\frac{-12}{2}[/tex] = - 6

the line crosses the y- axis at (0, - 8 ) ⇒ c = - 8

y = - 6x - 8 ← equation of line

Answer:

its 135

Step-by-step explanation:

Answer:

623 mm²

Step-by-step explanation:

I am going to split this shape into a 15mm x 19mm rectangle and a 26mm x 13mm rectangle. (the 19mm comes from 32mm at the bottom minus 13mm at the top to find how long the first rectangle is)

Rectangle 1: 15mm • 19mm = 285mm²

Rectangle 2: 26mm • 13mm = 338mm²

Total Area: 285mm² + 338mm² = 623mm²

It should be noted that the area of the rectangle given will be 918 inches².

From the information given, it was stated that a rectangular poster is 17 inches by 54 inches long.

The area of the rectangle will be:

Area = Length × Width

Area = 17 × 54

Area = 918 inches²

Learn more about area on:

https://brainly.com/question/25292087

Answer:

[tex]x = 22.5[/tex]

Explanation:

Given Sides:

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

using all these sides, create similarities equation:

[tex]\frac{HB}{HD} = \frac{HM}{HT}[/tex]

[tex]\frac{6}{21} = \frac{9}{9+x}[/tex]

[tex]6(9+x) = 9(21)[/tex]

[tex]54 + 6x = 189[/tex]

[tex]6x = 189 - 54[/tex]

[tex]6x = 135[/tex]

[tex]x = \frac{135}{6}[/tex]

[tex]x = 22.5[/tex]

From the coordinate points, we can see that the data point that differs significantly is (−4,−8)

An outlier in statistics is a data point that differs significantly from other observations in the given data

This may be due to variability in the measurement or it may indicate an experimental error.

From the coordinate points, we can see that the data point that differs significantly is (−4,−8). This gives the possible outlier of the given coordinate

Learn more on outlier here: https://brainly.com/question/3631910

Answer:

It's would be -4,-8 Have a great day

Based on the amount Peyton invested, and the interest rate, the amount in the account 15 years later would be $2,848.09.

The amount in the account after 15 years would be:

= Amount x ( 1 + rate) ^ number of years

Solving gives:

= 1,700 x ( 1 + 3.5%)¹⁵

= $2,848.09

Find out more on future value at https://brainly.com/question/24978019.

Answer:

2848.1

Step-by-step explanation:

Answer:

  (a)  -8

  (b)  6x +4 +3h

Step-by-step explanation:

Sometimes, it works well to find the general solution first, then use that to solve the specific problem. That's what we'll do here.

The average rate of change on the interval [x, x+h] is defined as ...

  m = (f(x+h) -f(x))/h

For the given f(x), this is ...

  [tex]m=\dfrac{((3(x+h)^2+4(x+h)-4)-(3x^2+4x-4)}{h}\\\\m=\dfrac{3x^2 +6xh+3h^2+4x+4h-4-3x^2-4x+4}{h}\\\\m=\dfrac{6xh+3h^2+4h}{h}\\\\\boxed{m=6x+4+3h}\qquad\text{average rate of change on $[x,x+h]$}[/tex]

__

Using the above result for the interval [-4. 0], we have x=-4 and h=4. The average rate of change on that interval is ...

  m = 6(-4) +4 +3(4) = -24 +4 +12 = -8

The average rate of change on [-4, 0] is -8.

_____

Additional comment

In the above, we worked the generic problem first. That way, we only needed to expand f(x+h)-f(x) once. If you're not terribly comfortable with doing algebra on literal expressions, sometimes it is more comfortable to work the numerical problem--as this question would have you do. This lets you get an idea of the kinds of operations that are involved and the way terms combine.

We note that the average rate of change is the instantaneous rate of change (derivative of the function) at the midpoint of the interval. That derivative is the value of m when h=0: 6x+4. The midpoint of the interval [-4,0] is x=-2, and the derivative there is 6(-2)+4 = -8, as above.

Answer:

Two points, (0,4) & (8,5)

Step-by-step explanation:

In this equation, we can easily find the first point by looking at the +4 in this equation. This should automatically signal to you that the point is (0,4)

Now, we have to look at the 1/8x in the equation.

This 1/8 means that the slope is 1/8!

Now we use the slope and to rise/run to find our next point

We go up 1 from 4 (this is the rise) to get to 5 on the y-axis

Next, we go over 8 horizontally to get to 8 for your x-axis point.

So therefore, our next point is, (8,5)

You can use this rise/run system infinitely and is very useful

Answer:

q = -1 and p = 3

Step-by-step explanation:

make q the subject of the formula

q = 2p - 7

Let use the other equation to manipulate data

3p + 2q = 7

:3p + 2 (2p - 7) = 7

:3p + 4p - 14 = 7

:3p + 4p = 7 + 14

:7p = 21

7. 7

like terms cancel each other

thus

p = 3

we the first equation to find the value of q

q = 2p - 7

since we have find p as 3, let's substitute

q = 2 (3) - 7

q = 6 - 7

q = -1

Answer: c

Step-by-step explanation: