Avery had $25.88 in her wallet. If she bought lunch with dollars from her wallet, how much money did she have in her wallet after lunch?
A. $14.38
B. $15.88
C. $15.38
D. $15.68

Answer:

Substitute 7 for a.

Simplify the equation after substituting the value for a.

Verify that a = 7 is correct when the result is a true statement.

Step-by-step explanation:

 –9(a – 5) = –18  

Distribute

-9a +45 = -18

Subtract 45 from each side

-9a +45-45 = -18-45

-9a = -63

Divide each side by -9

-9a/-9 = -63/-9

a = 7

To check the solution put a =7 back into the original equation

 –9(a – 5) = –18  

  -9(7-5) = -18

Simplify

-9(2) = -18

-18 = 18

This is true  so 7 is the solution

Answer:

Substitute 7 for a.

Simplify the equation after substituting the value for a.

Verify that a = 7 is correct when the result is a true statement.

Step-by-step explanation:

Here, the given equation is,,

[tex]-9(a-5)=-18[/tex]

And, after solving it the result is,

a = 7

We can check whether a result is the solution of an equation by substituting the result in the given equation.

If we get a true statement, then the result is the solution of the equation.

Thus, for verifying the solution, steps are as follow,

Step 1 : Substitute 7 ,

-9(7-5) = -18

Step 2 : Simplify the equation after substituting the value of a  

-9(2) = -18    

Step 3 : Verify that a = 7 is correct when the result is a true statement.

-18 = -18      

Answer:

$852.5

Step-by-step explanation:

$11 * 40 hours = $440 for reg. hours

$16.5 * 9 hours = $148.5 for overtime

$22 * 12 hours = $264 for holiday time

$440 + $148.5 + $264 = $852.5 in total

Answer: $12.15

Step-by-step explanation:

5.70 + 2.15 = $7.85

$20 - 7.85 = $12.15

Answer:

The height of the statue is 21.4 feet

Step-by-step explanation:

We are given

A person is standing 50 ft from a statue

The person looks up at an angle of elevation of 16 degree when staring at the top of the statue

hen the person looks down at an angle of depression of 8 degree when staring at the base of the statue

Firstly, we will draw diagram

In triangle ABF:

FC=50

we can use trig formula

[tex]tan(16)=\frac{y}{50}[/tex]

[tex]y=50tan(16)[/tex]

[tex]y=14.33727ft[/tex]

now, we can find x

In triangle DEF:

we can use trig formula

[tex]tan(8)=\frac{x}{50}[/tex]

[tex]x=50tan(8)[/tex]

[tex]x=7.0270ft[/tex]

we can see that

height of statue =x+y

so, the height of statue is

[tex]=14.33727+7.0270[/tex]

[tex]=21.4ft[/tex]

The height of the statue to the nearest tenth of a foot is 21.4 ft and this can be determined by using the trigonometric properties

Given :

Refer to the diagram attached below.

From the diagram in triangle ABF:

[tex]\rm tan(16)=\dfrac{a}{50}[/tex]

a = 14.33 ft

From the diagram in triangle DEF:

[tex]\rm tan(8)=\dfrac{b}{50}[/tex]

b = 7.02 ft

Now, the height of the statue is given by:

[tex]\rm Height = a +b[/tex]

Height = 14.33 + 7.02

Height = 21.4 ft

The height of the statue to the nearest tenth of a foot is 21.4 ft.

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Answer:

BE : EC = 1 : 3

Step-by-step explanation:

Consider triangles AKD and EKB. In these triangles

Then ΔAKD is similar to ΔEKB by AAA theorem.

Similar triangles have proportional corresponding sides:

[tex]\dfrac{AD}{EB}=\dfrac{AK}{EK}=\dfrac{DK}{KB}.[/tex]

Since [tex]\dfrac{DK}{KB}=\dfrac{4}{1},[/tex] then [tex]AD=4BE.[/tex]

Opposite sides in parallelogram have the same lengths, then [tex]BC=AD.[/tex]

Now

[tex]BC=BE+EC,\\ \\BC=\dfrac{1}{4}BC+EC,\\ \\EC=BC-\dfrac{1}{4}BC=\dfrac{3}{4}BC.[/tex]

Find the ratio

[tex]\dfrac{BE}{EC}=\dfrac{\frac{1}{4}BC}{\frac{3}{4}BC}=\dfrac{1}{3}.[/tex]

The ratio of BE:EC is 1:2.

We have Parallelogram ABCD

Point K on diagonal BD such that BK:DK = 1:4

The extension of AK meets BC at point E

Since BK:DK = 1:4,

we know that BK = 1/5 * BD

and DK = 4/5 * BD.

AK extends to meet BC at point E means that AE is parallel to BD and BE is parallel to AK.

pair A,B,C,D,K,E;

A = (0,0);

B = (5,0);

C = (5,5);

D = (0,5);

K = (3.5,0);

E = (3.5,2.5);

Since AE is parallel to BD and BD is a diagonal of parallelogram ABCD, we know that AE bisects BD. This means that AE = BD/2 = 3/5 * BD.

Since BE is parallel to AK and AK is a diagonal of parallelogram ABCD, we know that BE bisects AK. This means that BE = AK/2 = 1/5 * BD.

Therefore, the ratio of BE:EC = 1/5 * BD

: 2/5 * BD

= 1:2.

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Answer:

$15.61

Step-by-step explanation:

483.62 - 218.25 = 265.37

265.37/17 = $15.61

If each student raises the same amount, how much more money must each student raise is: $15.61.

Using this formula

Amount raised=Current amount to raised-Old Amount raised /Number of students

Where:

Current amount to raised=$483.62

Old Amount raised =$218.25

Number of students=17

Let plug in the formula

Amount raised=483.62 - 218.25/17

Amount raised= 265.37/17

Amount raised= $15.61

Thus, if each student raises the same amount, how much more money must each student raise is: $15.61.

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Answer:

It took Latisha 2 hours and 18 minutes to finish hiking the trail.

Step-by-step explanation:

Speed = Distance traveled / Time taken

Given:

Distance traveled = 9.66 miles

Speed = 4.2 miles/hour

Time taken = Distance traveled/Speed

                   = 9.66/4.2 =2.3 hours = 2 hours 18 minutes.

∴ It took Latisha 2 hours and 18 minutes to finish hiking the trail.

The margin of error is 0.97849

we are given

mean=235

so,

[tex]n=235[/tex]

standard deviation =7.5

so,

[tex]\sigma=7.5[/tex]

we know that

ME=2*standard error

and

[tex]SE=\frac{\sigma }{\sqrt{n} }[/tex]

If confidence level is 95%, then we can multiply by 1.96

so, we can multiply by 2 to get ME

now, we can use marginal error formula

[tex]ME=\frac{2\sigma }{\sqrt{n} }[/tex]

now, we can plug values

and we get

[tex]ME=\frac{2\times 7.5 }{\sqrt{235} }[/tex]

[tex]ME=0.97849[/tex]

Answer: 15

Step-by-step explanation:

Answer:

D) (4, -1)

Step-by-step explanation:

When a point is translated down 4 units you need to subtract 4 from the y-coordinates. The x-coordinates will not change. Therefore (4, 3) will become (4, -1).

Answer:

4.5 feet

Step-by-step explanation:

Because one yard is 3 feet and half a yard is 1.5 feet and 3 plus 1.5 equals 4.5.

The top-left graph is the correct representation of the function[tex]\( f(x) = 0.75^x \)[/tex]. It shows a decreasing function as [tex]\( x \)[/tex] increases, and the y-intercept is at (0, 1).

The correct option is (A).

To determine which graph represents the function [tex]\( f(x) = 0.75^x \)[/tex], we should consider the key characteristics of an exponential function where the base is between 0 and 1:

1. As [tex]\( x \)[/tex]  increases, [tex]\( f(x) \)[/tex] should decrease because 0.75 raised to a higher power becomes smaller.

2. As [tex]\( x \)[/tex] decreases (becomes more negative), [tex]\( f(x) \)[/tex] should increase because 0.75 raised to a negative power becomes larger.

3. The graph will never touch the x-axis, as an exponential function does not cross the axis when the base is positive.

4. The y-intercept should be at [tex]\( f(0) = 0.75^0 = 1 \)[/tex] because any non-zero number to the power of 0 is 1.

Now let's evaluate the provided graphs with respect to these characteristics:

- Top-left graph:This graph shows a decreasing function as [tex]\( x \)[/tex] increases, and the y-intercept is at (0, 1), which matches the behavior of [tex]\( f(x) = 0.75^x \)[/tex].

- Top-right graph:This graph increases as [tex]\( x \)[/tex] increases, which is not correct for [tex]\( f(x) = 0.75^x \)[/tex].

- Bottom-left graph:This graph also increases as [tex]\( x \)[/tex] increases, which does not match the expected behavior.

- Bottom-right graph:This graph shows a decreasing function as [tex]\( x \)[/tex]increases, but the y-intercept is not at (0, 1), so it does not represent [tex]\( f(x) = 0.75^x \)[/tex].

Based on this analysis, the top-left graph is the correct representation of the function[tex]\( f(x) = 0.75^x \)[/tex]. It shows a decreasing function as [tex]\( x \)[/tex] increases, and the y-intercept is at (0, 1).

complete question given below:

Which graph represents the function f(x) =0.75^x

Answer:

h =  2A / (b1 + b2)

Step-by-step explanation:

A = 1/2h (b1 + b2)

Divide both sides by 1/2 (b1 + b2)

h  =  A / 1/2 (b1 + b2)

h =  2A / (b1 + b2)

Answer:

2A /  (b1+b2)  = h

Step-by-step explanation:

The formula for the area of a trapezoid is

A = 1/2 (b1+b2) *h

We want to solve for h

Multiply each side by 2

2A = 2*1/2  (b1+b2) *h

2A =  (b1+b2) *h

Divide each side by  (b1+b2)

2A /  (b1+b2)  =  (b1+b2) / (b1+b2) *h

2A /  (b1+b2)  = h

In one year, $ 9,000 with a profit of 7.75%, is $ 697.5

697.5 × 18 = 12555

After 18 years old, it is $ 15,222

Answer:

The answer is 34494.79

Step-by-step explanation:

Y=ab^x

A= starting value= 9000

r=rate = 7.75% = 0.0775

Exponential growth

Y= 9000(1.0775)^x

Plug in time for x

Y= 9000(1.0775)^18

Y=34494.7918323

ROUND the number and your answer will be Y= 34494.78

Answer:

The length of side BC is 18 units

Step-by-step explanation:

Perimeter of the rectangle: P=76 units

AB=4z

BC=3z+3=?

We need to determine z

The formula to calculate the perimeter of a rectangle is:

P=2(w+l)

Width: w=AB=4z

Length: l=BC=3z+3

Replacing in the formula:

76 = 2 [4z+(3z+3)]

Eliminating the parentheses:

76 = 2 [4z+3z+3]

Adding like terms:

76 = 2 (7z+3)

Solving for z: Dividing both sides of the equation by 2:

76 / 2 = 2 (7z+3) / 2

38 = 7z+3

Subtracting 3 both sides of the equation:

38-3 = 7z+3-3

Subtracting:

35 = 7z

Dividing both sides of the equation by 7:

35 / 7 = 7z / 7

Dividing:

5 = z

z = 5

Then:

BC=3z+3

Replacing z by 5 in the formula above:

BC = 3(5)+3

Multiplying:

BC = 15 + 3

Adding:

BC = 18 units

Answer:

12 total

Step-by-step explanation:

green : orange  

4               0          

We add in a ratio of

1                  2

So we need to multiply by 4

green : orange  

4*1            4*2

4                8

We have 4 green  and we need to add 8 orange  to get the right ratio

4 green + 8 orange = 12 total

Answer:

-15

63 but in simplified form, it's like this: -5

                                                              21

Step-by-step explanation: For multiplication and division, you don't need a common denominator, but for addition and subtraction you have to find the common denominator...

For this problem, since your multiplying, you just multiply straight accross, and if it needs to be simplified, then simplify:

5/9 x -3/7

-15

63

SIMPLIFIED because both -15 & 63 can be divided by 3 and end up like this:

-5

21

Answer:

There are 264 pints in 33 gallons.

Step-by-step explanation:

Because there are 8 pints in 1 gallon.

Answer: 264 pints

Step-by-step explanation:

There are 8 pints in a gallon so you multiply that by 33 and you get your answer.

Answer:

it has no solution

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

Life

Answer:

ASA

Step-by-step explanation:

We're already given a pair of congruent angles and sides

∠DEA and ∠BEC are congruent because they are verticle angles

So we can use ASA to prove the triangle ADE and triangle CBE congruent

To prove that triangle ADE is congruent to triangle CBE, you can use the SSS, SAS, or ASA congruence theorems depending on the given information. The Pythagorean theorem or trigonometry can be used if applicable. You must match corresponding sides or angles to decide which theorem to use.

There are several congruence theorems for triangles including Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA). To determine which theorem to use in order to prove that triangle ADE is congruent to triangle CBE, you need to determine what information is given in the problem. For example, if you know that corresponding sides and angles are equal, you might use the SSS postulate, the SAS postulate, or the ASA postulate respectively.

If right angles are involved, we could also factor in the Pythagorean theorem to help establish side lengths - this theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), expressed as: a² + b² = c². Solving for c gives us c = √a² + b². Similarly, if vectors and trigonometry are relevant factors in deriving your triangle sides or angles, they can also be used in establishing congruence.

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Final answer:

Each term is matched with its correct concept, revealing the fundamental concepts of biological macromolecules and their formation and breakdown through dehydration synthesis and hydrolysis.

Explanation:

Let's match each concept with its correct term:

Macromolecules such as proteins, carbohydrates, and nucleic acids are essential for life and are composed of smaller organic molecules called monomers. When these monomers join together through dehydration synthesis, they release a water molecule and form covalent bonds to create larger structures known as polymers. The opposite process, hydrolysis, involves adding water to break down polymers into monomers.

Answer:

x=0 , y=2

Step-by-step explanation:

x=y-2

4x+y =2

We can substitute the first equation in for x into the second equation

4*(y-2) +y =2

Distribute the 4

4y-8 +y =2

Combine like terms

5y-8 =2

Add 8 to each side

5y-8+8 = 2+8

5y= 10

Divide each side by 5

5y/5 =10/5

y=2

But we still need to find x

x = y-2

x = 2-2

x=0

Answer:

The answer is 7.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

9.75 divided by 1.3 equals 7.5

I used a calculator... :)

Answer:

Y=2x-3

Step-by-step explanation:

Hi there! :)

Answer:

y = 2x - 3

Step-by-step explanation:

The slope intercept equation looks like this : y = mx + b

Where "m" is the slope and "b" is the y-intercept.

Your y-intercept = -3 → SO, b = -3

Your slope = 2 → SO, m = 2

Replace the values of "b" and "m" in the equation, and you're done:

y = mx + b

y = 2x - 3

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:

Alright well solve for y by simplifying both sides of the equation, then isolating the variable

Exact form: y = - 65/4

Decimal form: y = - 16.25 Hope this helps Have a nice day :)

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

the rate of change is the measure of the slope m of the line

To calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, 27) and (x₂, y₂ ) = (5, - 8)

m = [tex]\frac{-8-27}{5-0}[/tex] = [tex]\frac{-35}{5}[/tex] = - 7 ← rate of change

the initial value is the y-coordinate of the starting point

That is y = 27 ← starting value

The rate of change for the linear function is -7 and the initial value is 27.

The probability that the first 2 ribbons removed from the bag are yellow is [tex]\(\frac{1}{51}\)[/tex].

First, let's calculate the probability of drawing the first yellow ribbon. There are 3 yellow ribbons and a total of 8 red, 7 green, and 3 yellow ribbons, which sums up to 18 ribbons in total. So, the probability of drawing the first yellow ribbon is:

[tex]\[ P(\text{first yellow}) = \frac{\text{Number of yellow ribbons}}{\text{Total number of ribbons}} = \frac{3}{18} = \frac{1}{6} \][/tex]

After drawing the first yellow ribbon, there are now 17 ribbons left in the bag, with 2 yellow ribbons remaining. The probability of drawing the second yellow ribbon is:

[tex]\[ P(\text{second yellow | first yellow}) = \frac{\text{Number of remaining yellow ribbons}}{\text{Total number of remaining ribbons}} = \frac{2}{17} \][/tex]

Now, we multiply the two probabilities to find the probability that the first two ribbons drawn are yellow:

[tex]\[ P(\text{first two yellow}) = P(\text{first yellow}) \times P(\text{second yellow | first yellow}) = \frac{1}{6} \times \frac{2}{17} \]\[ P(\text{first two yellow}) = \frac{1 \times 2}{6 \times 17} = \frac{2}{102} = \frac{1}{51} \][/tex]

Answer:

4≥x

Step-by-step explanation:

The person has to be at least four feet (=) or he can be higher (>).