Determine how much the bill will be if there are 50 text messages

The plane travels at 60 mph and the wind is blowing at 20 mph.  

By setting up and solving a system of equations, we find that the speed of the plane in still air is 63 mph and the speed of the wind is 21 mph.

To answer this question, you first need to set up equations to represent the speed of the plane and the speed of the wind. You can denote the speed of the plane in still air as 'p' and the speed of the wind as 'w'. The plane's speed with the wind (going to Phoenix) is represented by p+w and against the wind (coming back) is p-w.

For the trip to Phoenix, you know that distance = speed * time. That gives us the equation 1176 = 14(p+w). After simplification, we obtain the equation, p+w = 84.

For the return flight, our equation is 1176 = 28(p-w). On simplification, we find the equation p-w = 42.

Now you have a system of equations that you can solve: p+w = 84p-w = 42. Solving these equations together, you find that the speed of the plane (p) in still air is 63 mph, and the speed of the wind (w) is 21 mph.

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Answer:

For this expression, you will have to use the distribution property to get your answer.

First, distribute the 4 to the x and -1

[tex]4(x)=4x[/tex]

[tex]4(-1)=-4[/tex]

[tex]4x-4-3(x+2)[/tex]

Now do the same with the -3, x and 2

[tex]-3(x)=-3x[/tex]

[tex]-3(2)=-6[/tex]

[tex]4x-4-3x-6[/tex]

Now combine like terms to get your final answer

[tex]4x-3x=x[/tex]

[tex]-4-6=-10[/tex]

Thus, your solution is: x - 10

Step one: 4(x-1)-3(x+2)=0        (set equal to zero)

Step two: 4x-4-3x-6=0            (multiply numbers on the outside to inside of "( )")

Step three: x-10=0                   (combine like terms)

Step four: 0+10=10, x=10         (inverse operation)

Answer: x=10

27,515 is the actual answer.

Estimated, it is about 27,500

Hope I helped!

we are given

the quotient of y and 6

we always start from left to right order of operation

we know that

quotient means division

so, we can write as

the quotient of y and 6 is

[tex]\frac{y}{6}[/tex]...............Answer

For this case we have:

The general formula of the arithmetic sequence is given by:

[tex]a_n = a_1 + (n-1) d\\[/tex]

Where

[tex]a_n[/tex]: Last term

[tex]a_1[/tex]: First term

n: Number of terms

d: Difference

Rewriting according to the given common difference, we have:

[tex]a_n = a_1 + (n-1) (- 4.5)[/tex]

Answer:

[tex]a_n = a_1 + (n-1) (- 4.5)[/tex]

The explicit formula for an arithmetic sequence whose common difference is -4.5 is:

                      [tex]a_n=a_1-4.5(n-1)[/tex]

Explicit formula--

Explicit formula is the formula which is used to find the nth term of a sequence.

We know that the explicit formula for an arithmetic sequence is given by:

   [tex]a_n=a_1+(n-1)d[/tex]

where d is the common difference of the sequence and [tex]a_1[/tex] is the first term of the sequence.

We have: d= -4.5

Hence, the explicit formula is given by:

     [tex]a_n=a_1-4.5(n-1)[/tex]

145 + c   = 380

145 - 145 + c = 380 - 145              -Subtract 145 from both sides of the equation

c = 235

So, they collected 235 cans in the second week.

Hope this helps!

To find out how many cans of food were collected in the second week, subtract the number of cans collected in the first week from the total number of cans collected in two weeks. The inequality representing the problem is c + 145 > 380. Solving the inequality, we find that more than 235 cans were collected in the second week.

To find out how many cans of food were collected in the second week, we can subtract the number of cans collected in the first week from the total number of cans collected in two weeks. Let's assign a variable, c, to represent the number of cans collected in the second week. The inequality that represents the problem is: c + 145 > 380. To solve this inequality, we need to isolate the variable by subtracting 145 from both sides: c > 380 - 145. Simplifying further, we get c > 235. So, more than 235 cans of food were collected in the second week.

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Hello  Queengirl0

Past tense:

Melissa has a full chocolate bar 8/8

At lunch:

Melissa ate 2/8 of the candy bar, 8/8 - 2/8 = 6/8

After school:

Melissa ate 3/8 of the candy bar, 6/8 - 3/8 = 3/8

Melissa has 3/8 of a chocolate bar left

:)

Answer: B) The lengths of both transverse axes are the same.

Step-by-step explanation: Given Hyperbola equations :

[tex]\frac{x^2}{3^2}-\frac{y^2}{4^2}=1[/tex] and

[tex]\frac{y^2}{3^2}-\frac{x^2}{4^2}=1[/tex]

First one : [tex]\frac{x^2}{3^2}-\frac{y^2}{4^2}=1[/tex] is a Horizontal Hyperbola.

a = 3 and 2a = 6.

Length of transverse axis = 6.

And second one :  [tex]\frac{y^2}{3^2}-\frac{x^2}{4^2}=1[/tex] is a Vertical Hyperbola.

b=3 and 2b = 6

Length of transverse axis = 6.

The lengths of both transverse axes are the same.

Therefore, correct option is B option :

Answer:

B

Step-by-step explanation:

The answer for the first one is (x)°+(3x)°+(5x)°=180° and the answer for the second one is x=20. If you need me to explain how they got the answer, i'm here.

Answer:

Fill the blanks

1) (x)°+(3x)°+(5x)°=180°

2) x°=20°

Step-by-step explanation:

Consider the provided information.

Given: Triangle PQR with m∠P=(x)°, m∠Q=(3x)°, and m∠R=(5x)°.

We need to prove that x = 20

Consider the provided figure.

By the triangle sum theorem the sum of the angles in a triangle is equal to 180. Therefore using the give and triangle sum theorem,

m∠P+m∠Q+m∠R=180°

Now use substitution property.

(x)°+(3x)°+(5x)°=180°

Simplify the equation gets

9x°=180°

Finally, using the division property of equality.

9x°/9=180°/9

x°=20°

Hence proved

∠DAB and ∠BAD form a linear pair, so ∠DAB + ∠BAD = 180°

116° + ∠BAD = 180°   substituted

         ∠BAD = 64°   subtracted 116° from both sides

ΔABC

∠A + ∠B + ∠C = 180°    triangle angle sum theorem

64° + x + 60° = 180°      substitution

        x + 124° = 180°      added like terms

                   x = 56°       subtraction property

Answer: 56°

We are to convert 0.0167 to fraction.

Trick 1: Count the number of decimal values in our number which is 4.

Trick 2: Write 1 followed by 4 zeros (the four you counted to above). This gives 10000 which is our denominator.

Trick 3: Retrieve our denominator by writing down the whole number which can be observed in 0.0167. That whole number is 167.

Trick 4: Now put your results in the fraction form. That is in numerator/denominator form.

This gives 167/10000

Trick 5: Try to simplify further. You can't! So the answer is:

[tex]\frac{167}{10000}[/tex]

the answer is that it is false

(x/7)-12=-2

Add 12 to both sides.

x/7=10

Multiply both sides by 7.

x=70

Final answer: 70

hope this helps :)

g(x) = -3x² - 2x + 3

g(-2) = -3(-2)² - 2(-2) + 3

g(-2) = -12 + 4 + 3 = -5

8*10^6+5*10^9 should be

5,008,000,000

Answer:

The error student make is he multiply the terms instead of addition.

Step-by-step explanation:

Given : A student found the product of 8 × 10 to the 6 power + 5 × 10 to the 9th power to be 4 × 10 to 15 power.

To find : What is the error ?

Solution :

8 × 10 to the 6 power - [tex]8\times 10^6[/tex]

5 × 10 to the 9th power - [tex]5\times 10^9[/tex]

4 × 10 to 15 power -  [tex]4\times 10^{15}[/tex]

According to student, [tex]8\times 10^6+5\times 10^9=4\times 10^{15}[/tex]

We solve the expression,

[tex]=8\times 10^6+5\times 10^9[/tex]

[tex]=8\times 10^6+5000\times 10^6[/tex]

[tex]=10^6(8+5000)[/tex]

[tex]=5008\times 10^6[/tex]

The error student make is he multiply the terms instead of addition.

.0000156

Hope I helped!

Good Luck!

B would be the answer because if you were to search up a picture of alternate interior angles, it would be the same as <CAD and <ACB

Answer:

(B) ∠CAD≅∠ACB

Step-by-step explanation:

Given in the question quadrilateral ABCD is a rectangle and a table of two-column proof with missing statement for proves that the diagonals of the rectangle bisect each other.

If we want to prove that the diagonals bisects to each other, then for this  first we will prove that ΔADE≅ΔCBE. But given in the two-column proof  

∠ADB≅∠CBE , side BC= side AD .  ∠CAD ≅ACD must be  necessary for to prove that ΔADE≅ΔCBE (ASA postulate). Hence statement  ∠CAD ≅ACD can be used to fill in the blank space.

Lilliana's hair was 48 inches long and she cut off 2/3 of it. After calculating 2/3 of 48, which is 32 inches, we subtract this from the original length. Lilliana's hair was 16 inches long after her haircut.

The student's question concerns the length of Lilliana's hair after she has asked her hairdresser to cut 2/3 of it off. If we know that Lilliana's hair was originally 48 inches long, we need to calculate 2/3 of this length and then subtract it from the original length to find the new length of her hair after the haircut.

Calculate 2/3 of 48 inches: (2/3) times 48 = 32 inches.

Subtract the amount cut from the original length: 48 inches - 32 inches = 16 inches.

Therefore, after Lilliana's haircut, her hair was 16 inches long.

a + b + c = 180

b = 2a

c = 3a

a + 2a + 3a = 180

6a = 180

a = 30

b = 2(30)

b = 60

c = 3(30)

c = 90

Answer:

a = 30

b = 60

c = 90

A) is 164 because 6 times 6 is 36. 500 - 36 is 164

Answer:

28 questions

Step-by-step explanation:

In the first 10 mins she answered 2/5 of 40 which is 16. The remaining amount is 24 questions and half of that is 12. So she answered 12 questions in 15 mins. Finally you add them to get 28 questions in 25 minutes.

f(x)=40

x=8

so if x=2 it would be 40/8 which is 5

C

since the quantities vary directly then

x = kf(x) ( where k is the constant of variation )

to find k use the given condition , f(x) = 40 when x = 2

k = [tex]\frac{x}{f(x)}[/tex] = [tex]\frac{8}{40}[/tex] = [tex]\frac{1}{5}[/tex]

thus x = [tex]\frac{1}{5}[/tex]f(x)

when x = 2

f(x) = [tex]\frac{x}{k}[/tex] = [tex]\frac{2}{\frac{1}{5} }[/tex] = 10

4 (1/5 ) = 21/5

21 / 5 divided by 2 / 3 equals

21 / 5 * 3 / 2 equals 63 / 10 equals

6 (3 / 10)

Answer:

The Quiz Was Updated This Is It Now

Step-by-step explanation:

DO IN ORDER!

Thee steps for using a compass and straightedge to construct the bisector of ∠G is given in the image attached.

So, the correct order of the steps from beginning is:

Learn more about bisector  from

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The correct answer is A) g≥5

This is because when you look at an absolute value function, the constant at the end is the y value of the vertex. Since it is an absolute value equation, we know that the values can only go up. Therefore, it must be greater than or equal to the constant at the end (5)

d - 2 < -1 is how this inequality would be displayed.

However, we can solve for the value of d by treating this like a standard algebraic equation.

d - 2 < -1

Add 2 to both sides.

d < 1

The value of d is less than 1.

Let me know if you have any other questions.

Answer:

Given phrase,

a number d minus 2 is less than -1

∵ '-' is the sign of minus,

⇒ d minus 2 = d - 2

Also, '<' is the sign of less than,

⇒ d minus 2 is less than -1 = d - 2 < - 1

Hence, the required inequality would be,

[tex]d-2 < -1[/tex]

Now, by further solving,

Add 2 on the both sides of inequality ( additive property of inequality )

[tex]d < -1 + 2\implies d < 1[/tex]

⇒ d ∈ ( -∞, 1 )

ANSWER

The correct answer is E

EXPLANATION

Polygon IJKL is a rectangle.

The area is given by;

[tex]Area=l\times w[/tex]

The coordinates of I are [tex](5,8)[/tex] and L[tex](-5,8)[/tex].

This is a horizontal line so it will be faster using the absolute value method rather than the distance formula

The length is

[tex]|IL|=|5--5|[/tex]

[tex]|IL|=|5+5|[/tex]

[tex]|IL|=|10|[/tex]

[tex]|IL|=10[/tex]

units

The coordinates of K are [tex](-5,-7)[/tex] and L[tex](-5,8)[/tex].

The width is

[tex]|LK|=|8--7|[/tex]

[tex]|LK|=|8+7|[/tex]

[tex]|LK|=|15|[/tex]

[tex]|LK|=15[/tex]

units

Therefore

[tex]Area=10\times 15[/tex]

[tex]Area=150[/tex] square units

The coordinates of K are [tex](-5,-7)[/tex] and L[tex](-5,8)[/tex].

Answer:

The correct answer option is E. 150 square units.

Step-by-step explanation:

A polygon is figure with at least 3 straight or definite sides or typically 5 or more straight sides.

Here the polygon we are given is a rectangle.

We know that,

Area of a rectangle = l x w

so we need to measure the length and width of the rectangle to find its area.

If we look closely, we can see the length of the rectangle above the x-axis is 8 units and the length below the x-axis 7 units which makes a total og 15 units.

While the width is 10 units (5 units on each side of the y-axis).

Area of the rectangle = 15 x 10 = 150 square units.

Therefore, the area of the polygon is 150 square units.