find the exact value of x

Anna earns $8.50 per hour babysitting. For 3, 3.5 and 4 hours of work, she will earn $25.50, $29.75, and $34.00 respectively.

Anna earns $8.50 per hour for babysitting. To calculate her earnings, we simply need to multiply the number of hours she worked by her hourly rate.

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Answer:

2 1/2

Step-by-step explanation:

You divide and there are 2 two’s that can go into 5 with a remainder of 1

Answer: 2 1/2

Step-by-step explanation:

divide 5/2

you get 1 as a remainder and two at the top

2 1/2

Answer:

4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....

Step-by-step explanation:

Fifth term (a₅) =  [tex]\frac{1}{4}[/tex]

Common ratio (r) = [tex]\frac{1}{2}[/tex]

n = 5

The formula to find the [tex]n^{th}[/tex] term of a geometric sequence is

a₅ = a₁r⁽ⁿ⁻¹⁾

=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(5-1)}[/tex]

=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(4)}[/tex]

=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})[/tex]

=> [tex]\frac{1}{4}[/tex] = a₁* [tex]\frac{1*1*1*1}{2*2*2*2}[/tex]

=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{16})[/tex]

Flip the sides of the equation

a₁*[tex](\frac{1}{16})[/tex] = [tex]\frac{1}{4}[/tex]

Multiply both sides by 16

a₁*[tex](\frac{1}{16})[/tex]*16 = [tex]\frac{1}{4}[/tex]*16

Cancelling out the 16's from the top and bottom of the left side

a₁ = [tex]\frac{16}{4}[/tex]

=> a₁ = 4

So, first term of the geometric sequence is 4.

Common ratio = [tex]\frac{1}{2}[/tex]

Second term = First term * Common ratio

                      = 4* [tex]\frac{1}{2}[/tex]

                      = [tex]\frac{4}{2}[/tex]

                      = 2

Third term = Second Term * Common ratio

                  = 2 * [tex]\frac{1}{2}[/tex]

                  = [tex]\frac{2}{2}[/tex]

                  = 1

Fourth term = Third Term * Common ratio

                    = 1 * [tex]\frac{1}{2}[/tex]

                    = [tex]\frac{1}{2}[/tex]

Fifth term (given) = [tex]\frac{1}{4}[/tex]

So, the geometric sequence would be

4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....

sorry, put the wrong answer and cant delete

Answer:

4/15 distance

Step-by-step explanation:

We can use ratio's to solve this, putting distance over time

1/5 distance          x distance

----------------   = ----------------------

3/4 hour                 1 hour

Using cross products

1/5 * 1 = 3/4 x

1/5 = 3/4 x

Multiply by 4/3 to isolate x

1/5 * 4/3 = 4/3 * 3/4x

4/15 = x

The train can travel 4/15 of the distance in 1 hour

Answer:

Based on the number of cookies each girl made and if Kristina and Liz made the same number of cookies, then Heather made 4.2 dozen cookies.

Step-by-step explanation:

In order to find the number of cookies that Heather made, you need to set up two equations that represent the number of cookies that Kristina and Liz each made.  Since Kristina made 2.4 dozen less than 6 times as many dozen as Heather, we can represent that with the equation  6c - 2.4.  Since Liz made 1.8 dozen more than 5 times as many dozen as Heather, we can represent that with the equation 5c + 1.8.  We can set both equations equal to each other since Liz and Kristina made the same number, so 6c - 2.4 = 5c + 1.8.  Solving for 'c', which represents how many dozen cookies Heather made, we get 4.2  

Let's assign a variable to represent the number of dozens of cookies Heather made. We'll call this variable \( H \).

According to the problem:
- Kristina made \( 6 \times H - 2.4 \) dozen cookies.
- Liz made \( 5 \times H + 1.8 \) dozen cookies.

We are also given that Kristina and Liz made the same number of cookies, so we can set these two expressions equal to each other to find the value of \( H \):

\[ 6H - 2.4 = 5H + 1.8 \]

Now, we'll solve this equation for \( H \).

Step 1: Isolate the variable \( H \) on one side.
To do this, we'll first subtract \( 5H \) from both sides of the equation:

\[ 6H - 5H - 2.4 = 5H - 5H + 1.8 \]
\[ H - 2.4 = 1.8 \]

Step 2: Now we need to get \( H \) alone, so we'll add \( 2.4 \) to both sides:

\[ H - 2.4 + 2.4 = 1.8 + 2.4 \]
\[ H = 4.2 \]

So, Heather made \( 4.2 \) dozen cookies.

To ensure this is the correct number of dozens Heather made, we can plug this value back into the original expressions for Kristina and Liz's cookies to verify that they made the same amount:

Kristina: \( 6 \times 4.2 - 2.4 = 25.2 - 2.4 = 22.8 \) dozen cookies
Liz: \( 5 \times 4.2 + 1.8 = 21 + 1.8 = 22.8 \) dozen cookies

Both Kristina and Liz made 22.8 dozen cookies, confirming our solution that Heather made 4.2 dozen cookies.

By increasing her speed from 55 mph to 60 mph, Rachel can save approximately 1.5 hours on her 1034-mile trip from New York to Dayton, Florida.

The subject of this question is Mathematics, specifically dealing with the concept of speed, distance, and time. To answer your question, we need to calculate how long the trip would take at each speed and then find the difference.

First, we calculate the time taken when the average speed is 55 mph. The formula to calculate time is distance divided by speed. So, 1034 miles divided by 55 mph equals about 18.8 hours.

Next, we do the same for 60 mph. 1034 miles divided by 60 mph equals about 17.2 hours.

The difference between the two times will give the time saved by increasing the speed to 60 mph from 55 mph. So, 18.8 hours - 17.2 hours equals 1.6 hours, which is approximately 1.5 hours when rounded to the nearest half hour.

Therefore, Rachel can save about 1.5 hours driving at an average speed of 60 mph compared to 55 mph over the distance of 1034 miles.

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Answer:

[tex]x=8[/tex]

Step-by-step explanation:

In similar triangles, corresponding sides' ratio are equal.

We can set up a ratio of [tex]\frac{SideAB}{Side XY}=\frac{SideCA}{Side ZX}[/tex]

Hence, we can write (and solve):

[tex]\frac{Side AB}{Side XY}=\frac{Side CA}{SideZX}\\\frac{2}{4}=\frac{x+7}{4x-2}\\2(4x-2)=4(x+7)\\8x-4=4x+28\\8x-4x=28+4\\4x=32\\x=\frac{32}{4}=8[/tex]

So, x = 8

624.75

first get the numeric values simplified

2/13h=0.153h

so 18.20÷0.153=119

meaning he earned 119 dollars every hour

now you can multipy this number with 5.25 to get the answer which is 624.75 dollars

Answer:

m = 1

Step-by-step explanation:

Given ->  3m + 5 = 8

Subtraction -> 3m = 3

Division -> m = 1

Answer:

m= 1

Step-by-step explanation:

3m +5 = 8     Substract 5 to both sides

 3m = 3         Divide 3 in both sides

  m = 1

Answer:

450

Step-by-step explanation:

Answer:

option A

-2x + 4y = 4

-3x + 6y = 6

Step-by-step explanation:

In option A, if the student multiply the first equation by 3 and the second equation by -2, then the equations become

-6x+12y = 12 and

6x-12y =-12

If she adds both equations, she will get 0 = 0

This means that the system has infinite number of solutions.

Hence, the student could have started with equations -2x + 4y = 4 and -3x + 6y = 6.

Answer:

$7. Based on the assumption that both offices paid the same amount for delivery, the difference in the total cost paid is due to the difference in the number of turkey sandwiches ordered, which is 4. The cost of each sandwich is a quarter of this difference in cost.

Step-by-step explanation:

In mathematical working, the explanation above can be written in the form of equations, where we work to solve the value of a variable. In this case, we are interested to find the value of t.

Define variables:

Let the cost of a turkey sandwich be $t while the delivery fee be $d.

Form 2 equations:

Assuming that the sandwich stores charges the same delivery fee for both offices,

4t + d= 33 -----(1)

8t + d= 61 -----(2)

Solve by elimination:

(2) - (1):

4t= 61 - 33

4t= 28

Divide both sides by 4:

t= 7

Thus, each turkey sandwich adds $7 to the cost of the delivery.

To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.

To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.

For the first office, they paid $33 for 4 turkey sandwiches. Let's assume the cost of delivery is 'x'. So the equation to represent the total cost is: 4x + 33 = total cost.

Similarly, for the second office, they paid $61 for 8 turkey sandwiches. Let's assume the cost of delivery is 'y'. So the equation to represent the total cost is: 8y + 61 = total cost.

Now we can solve both equations to find the values of 'x' and 'y' which will represent the cost of delivery. Once we have those values, we can calculate how much each turkey sandwich adds to the cost of delivery by dividing the cost of delivery by the number of turkey sandwiches ordered.

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Answer:

A.) Linear

B.) Continuous function

Step-by-step explanation:

Its linear because it is not all over the place and continuous because it does not stop it will keep going because it is a ray  

Answer: The graph is A) Linear

The graph represents a B) Continuous function.

Step-by-step explanation:

Since we have given a figure which depicts the total cost of purchasing blueberries at Blue Basket Farm at certain price per pound.

Since the graph is linear .

As we can write it as :

At x = 1, y = 4

At x = 2 , y = 8

At x = 3, y = 12

So, it will become

[tex]y=kx[/tex], where k = 4 units.

So, it is linear graph.

The graph is continuous function as it does not break any where and it is unbroken line.

hence,  the graph is A) Linear

The graph represents a B) Continuous function.

Answer:

X-intercept:(-4/3,0)

Y-intercept:(0,-3/2)

Step-by-step explanation:

The x-intercept is (-4/3, 0) and the y-intercept is (0, -3/2).

To find the x-intercept of the equation 8y= -9x-12, we substitute y with 0 and solve for x. This gives us:

8(0) = -9x-12

0 = -9x-12

-9x = 12

x = -12/9

x = -4/3

Therefore, the x-intercept is (-4/3, 0).

To find the y-intercept, we substitute x with 0 and solve for y. This gives us:

8y = -9(0)-12

8y = -12

y = -12/8

y = -3/2

Therefore, the y-intercept is (0, -3/2).

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Answer:

The scale factor used was 1/2

hope this helped

Step-by-step explanation:

Final answer:

The value of any number raised to the power of 1 is the number itself, as it implies a single multiplication of the number by 1.

Explanation:

The value of a number raised to the power of 1 is always the number itself. This is because an exponent represents how many times to multiply the number by itself. When the exponent is 1, you are simply multiplying the number by 1, which does not change its value.

For example:

[tex]\left\{\begin{array}{ccc}2x+3y=17\\x+5y=19&|\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+3y=17\\-2x-10y=-38\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad-7y=-21\qquad\text{divide both sides by (-7)}\\.\qquad\qquad \boxed{y=3}\\\\\\\text{Substitute the value of y to the second equation}\\\\x+5(3)=19\\\\x=15=19\qquad\text{subtract 15 from both sides}\\\\\boxed{x=4}\\\\Answer:\ x=4\ and\ y=3.[/tex]

Answer:

16

Step-by-step explanation:

We want to divide 1/2 pound in 8 equal parts

1/2 dividend by 8/1 is the same as  

1/2 multiplied by 1/8 =1•1/2•8=1/16

Each package will weigh 1/16 of a pound  

Or 1 ounce since 1 pound = 16 oz

[tex]f(x)=x^2-2x-8;\ g(x)=\dfrac{1}{4}x-1\\\\f(x)=g(x)\iff x^2-2x-8=\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4x^2-8x-32=x-4\qquad\text{subtract x from both sides}\\\\4x^2-9x-32=-4\qquad\text{add 4 to both sides}\\\\4x^2-9x-28=0\\\\4x^2-16x+7x-28=0\\\\4x(x-4)+7(x-4)=0\\\\(x-4)(4x+7)=0\iff x-4=0\ \vee\ 4x+7=0\\\\x=4\ \vee\ 4x=-7\\\\\boxed{x=4\ \vee\ x=-\dfrac{7}{4}}[/tex]

Answer:

(2i,0) (-2i,0)

(1,0) (-1,0).

Step-by-step explanation:

The graph below shows that there are only 2 real solutions at x = 1 and x = - 1

Expressed as points, these two are (1,0) and (-1,0). However that is not the complete answer. There are 2 complex points.

y = x^4 + 3x^2 - 4

y = (x^2 - 1)(x^2 + 4)

These two binomials can be equated to 0

================

Answer: Kate expression: 2(50-t)

2 : represents twice,

50 : represents Initial number of tickets Kate has,

t : The lost tickets

50-t : represents Number of ticket Kate has After loosing t tickets

Jack expression: 100 - 2t

100 : Twice of initial ticket Kate has,

t :  The lost tickets

2t : represents twice of the lost tickets,

100-2t : represents Final number of ticket Kate has.

Step-by-step explanation:

Since, According to the question,

Initially Kate has 50 tickets.

She lost tickets = t

And, after losing t ticket she has tickets = 50 - t

But, His father doubled the amount, Thus she has final tickets = 2(50-t)= 2×50 -2× t = 100 - 2t  

Final answer:

Kate's expression, 2(50−t), represents the number of tickets she has now by doubling the tickets she had left after losing some. Jack's expression, 100−2t, represents the number of tickets Kate has now by subtracting twice the number of tickets she lost from the total number of tickets she initially had.

Explanation:

Kate wrote the expression 2(50−t) to find the number of tickets she has now. In this expression, t represents the number of tickets she lost. The expression is simplified as follows: multiply 2 by the quantity (50−t). This means that Kate's dad doubled the tickets she had left after losing some tickets.

Jack's expression, 100−2t, also determines the number of tickets Kate has now. In this expression, t represents the number of tickets she lost. The expression is simplified as follows: subtract 2 times the quantity t from 100. This means that Jack found the number of tickets Kate has by subtracting twice the number of tickets she lost from the total number of tickets she initially had.

Answer:

60

Step-by-step explanation:

The required result is 60 when 480 is divided by 8, with no remainder.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

To divide 21,900 by 25, we can perform long division as follows:

  8 ) 480 ( 60

     - 480

     ________

          0

When we divide the first digit of 480 (which is 4) by the divisor 8, which gives us 60 with a remainder of 0.

Therefore, 480 divided by 8 is 60, with no remainder.

To learn more about the division operation click here :

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The complete question would be as:

What is the result when 480 is divided by 8 long division?

Answer:

Step-by-step explanation:

1.  <3 = <4                                      1 Given

2.  <2 <3 are supplementary      2.  non common   sides in  opposite  rays

3. <2 + <3 = 180                             3.  Definition of supplementary angles

4.  <2 + < 4 = 180                              4  substitution

5.  <1 = <4                                       5  Opposite angles are equal

6 <2 + <1 = 180                                6     Substitution

7.  <1, <2 are supplementary            7.  Definition of supplementary angles

The only word I am not sure of is the last word in 2

Answer:

The graph is shown below.

Step-by-step explanation:

Let x be the weight of fruit in pounds and P(x) be the price of fruit.

For fruit weighing greater than or equal to 0.01 pounds and less than or equal to 0.5 pounds, the amount charged is $2.00.

P(x) = $2.00 for 0.01 ≤ x ≤ 0.5

For fruit weighing greater than 0.5 pounds and less than or equal to 1.0 pounds, the amount charged is $3.50.

P(x) = $3.50 for 0.5 < x ≤ 1.0

For fruit weighing greater than 1.0 pounds and less than or equal to 1.5 pounds, the amount charged is $5.00.

P(x) = $5.00 for 1.0 < x ≤ 1.5

For fruit weighing greater than 1.5 pounds and less than or equal to 2.0 pounds, the amount charged is $6.50.

P(x) = $6.50 for 1.5 < x ≤ 2.0

For fruit weighing greater than 2.0 pounds and less than or equal to 2.5 pounds, the amount charged is $8.00.

P(x) = $8.00 for 2.0 < x ≤ 2.5

It is a piecewise floor function. We have open circle on left side of each floor except first floor because the sign of inequality in all other is < .

We have closed circle on right side of each floor because the sign of inequality is ≤ .

The graph is shown below.

Answer:

[tex]\pi,\ \dfrac{7\pi}{6},\ \dfrac{3\pi}{4},\ \dfrac{4\pi}{3},\ \dfrac{3\pi}{2},\ \dfrac{5\pi}{3},\ \dfrac{7\pi}{4},\ 2\pi.[/tex]

Step-by-step explanation:

Convert each angle in degree measure:

[tex]\dfrac{3\pi}{4}=135^{\circ},\\ \\\pi=180^{\circ},\\ \\\dfrac{7\pi}{6}=210^{\circ},\\ \\\dfrac{5\pi}{3}=300^{\circ},\\ \\\dfrac{7\pi}{4}=315^{\circ},\\ \\\dfrac{4\pi}{3}=240^{\circ},\\ \\\dfrac{3\pi}{2}=270^{\circ},\\ \\2\pi=360^{\circ}.[/tex]

Then

[tex]\cos \dfrac{3\pi}{4}=\cos 135^{\circ}=-\dfrac{\sqrt{2}}{2},\\ \\\cos \pi=\cos 180^{\circ}=-1,\\ \\\cos \dfrac{7\pi}{6}=\cos 210^{\circ}=-\dfrac{\sqrt{3}}{2},\\ \\\cos \dfrac{5\pi}{3}=\cos 300^{\circ}=\dfrac{1}{2},\\ \\\cos \dfrac{7\pi}{4}=\cos 315^{\circ}=\dfrac{\sqrt{2}}{2},\\ \\\cos \dfrac{4\pi}{3}=\cos 240^{\circ}=-\dfrac{1}{2},\\ \\\cos \dfrac{3\pi}{2}=\cos 270^{\circ}=0,\\ \\\cos 2\pi=\cos 360^{\circ}=1.[/tex]

Therefore, the angles in increasing order of their cosines are

[tex]\pi,\ \dfrac{7\pi}{6},\ \dfrac{3\pi}{4},\ \dfrac{4\pi}{3},\ \dfrac{3\pi}{2},\ \dfrac{5\pi}{3},\ \dfrac{7\pi}{4},\ 2\pi.[/tex]

Answer:

Step-by-step explanation:

Answer:

The length of side KM is [tex]\sqrt{109}[/tex] units.

Step-by-step explanation:

Given information:  KLMN is a trapezoid, ∠N= ∠KML, FD=8, LM:KN=3:5, F∈ KL, D∈ MN , ME ⊥ KN KF=FL, MD=DN, [tex]ME=3\sqrt{5}[/tex].

From the given information it is noticed that the point F and D are midpoints of KL and MN respectively. The height of the trapezoid is [tex]3\sqrt{5}[/tex].

Midsegment is a line segment which connects the midpoints of not parallel sides. The length of midsegment of average of parallel lines.

Since LM:KN=3:5, therefore LM is 3x and KN is 5x.

[tex]\frac{3x+5x}{2}=8[/tex]

[tex]\frac{8x}{2}=8[/tex]

[tex]x=2[/tex]

Therefore the length of LM is 6 and length of KN is 10.

Draw perpendicular on KN form L and M.

[tex]KN=KA+AE+EN[/tex]

[tex]10=6+2(EN)[/tex]                (KA=EN, isosceles trapezoid)

[tex]EN=2[/tex]

[tex]KE=KN-EN=10-2=8[/tex]

Therefore the length of KE is 8.

Use pythagoras theorem is triangle EKM.

[tex]Hypotenuse^2=base^2+perpendicular^2[/tex]

[tex](KM)^2=(KE)^2+(ME)^2[/tex]

[tex](KM)^2=(8)^2+(3\sqrt{5})^2[/tex]

[tex]KM^2=64+9(5)[/tex]

[tex]KM=\sqrt{109}[/tex]

Therefore the length of side KM is [tex]\sqrt{109}[/tex] units.

The answer is [tex]\sqrt{70}[/tex]

Answer:

First box: 6x

Second box: 24

Step-by-step explanation:

9(16)=6x

144 = 6x   | divide by 6

144/6 = 6x/6

24 = x

Answer:

y =  8x + 6

Step-by-step explanation:

The slope intercept form is: y = mx + c

where m ⇒ slope

          c ⇒ y-intercept

          (x,y) is a point on the graph the  satisfy the equation representing that graph.  x is the x-coordinate of a point on the line and y is the y-coordinate of a point on the line.

m  = 8

Y-intercept = 6

y = mx + c   ⇒ y =  8x + 6