Miguel received a $50 gift card to the bookstore. he would like to buy 3 books that cost$ 15.75 each including tax. he estmates that he cannot bey all three book because each book cost about $20, and all three book would cost $60 .is his estimate resonable?explain your reasoning.

According to the given statement, we can get the equation:

50 - 3x = 1/2 (50-x)

where x = amount removed from bag two, 3x removed from bag one

Then we multiply both sides by 2 (to eliminate the ½)

100-6x= 50-x

Add 6x to both sides

100= 50-5x

Then subtract 50 from both sides

50=5x

Lastly, divide by 5

10=x

Therefore 10 kg of sugar was removed from bag 2

further, 3x= 30, so 30 kg of sugar was removed from bag 1.

50-30=20 kg remaining in bag 1.

50-10=40 kg remaining in bag 2.

Answer:

40 kg in the first bag, 80 in the second

Step-by-step explanation:

The maximum possible length it could have been 44.49cm.

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

here, we have,

44cm is rounded to the nearest whole cm.

as, it is rounded to the nearest whole cm.

so, we get,

The maximum possible length it could have been 44.49cm.

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Final answer:

The quotient when dividing 6x³ + 13x² + x - 2 by x - 1 is 6x² + 19x + 20, and the remainder is 18. This solution can be found using synthetic division.

Explanation:

The question asks to find the quotient and remainder when the polynomial 6x³ + 13x² + x - 2 is divided by x - 1. To solve this, we can use polynomial long division or synthetic division. As the divisor is in the form of x - a, where a is 1, synthetic division is a streamlined approach.

We set up our synthetic division with 1 as our key number outside the division symbol and the coefficients of our polynomial (6, 13, 1, -2) inside:

Bring down the 6.

Multiply 1 by 6 to get 6, add this to the next coefficient 13 to get 19.

Continue the process: Multiply 1 by 19 to get 19, add this to 1 to get 20.

Repeat: Multiply 1 by 20 to get 20, add this to -2 to get 18.

The numbers now inside the division symbol represent the coefficients of the quotient polynomial, giving us 6x² + 19x + 20 with a remainder of 18. Therefore, the quotient is 6x² + 19x + 20, and the remainder is 18.

The two positive numbers are 10 and 5.

Given that,

The difference between two positive numbers is 5.

And the sum of their squares is 125.

Let us assume that,

The numbers are x and y.

Here, the difference between two positive numbers is 5.

x - y = 5

x = 5 + y  .. (i)

And, the sum of their squares is 125.

That is,

x² + y² = 125

Substitute the value of x from (i);

(5 + y)² + y² = 125

25 + y² + 10y + y² = 125

2y² + 10y + 25 = 125

2y² + 10y - 100 = 0

2 (y² + 5y - 50) = 0

y² + 5y - 50 = 0

y² + (10 - 5)y - 50 = 0

y² + 10y - 5y - 50 = 0

y (y + 10) - 5 (y + 10) = 0

(y - 5) (y + 10) = 0

This gives,

y = 5

y = - 10

Since the numbers are positive.

Hence, y = - 10 is not possible.

From (i);

x = 5 + y

Put y = 5;

x = 5 + 5

x = 10

Hence,

The two positive numbers are 10 and 5.

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The correct choice is D, where 'If next month is January' is the hypothesis, and 'then this month is the last of the year' is the conclusion, demonstrating the proper format and identification of a true conditional statement.

The question is concerning a true conditional statement and the identification of its hypothesis and conclusion. To form a proper conditional, we use the format 'If... then...' where the 'if' part represents the hypothesis and the 'then' part represents the conclusion. The hypothesis is the supposed condition, while the conclusion is the result or outcome that follows from the hypothesis.

Let's analyze the choices:

Choice A has the conclusion and hypothesis reversed.

Choice B is an incorrect format for a conditional because it uses 'so' instead of 'if... then...'.

Choice C has the same issue as choice B.

Choice D is in the correct format and has the hypothesis and conclusion properly identified. If next month is January is the hypothesis, and then this month is the last of the year is the conclusion.

Therefore, the answer is Choice D.

The  solution of the given equation is 5.5.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The given equation is 13=4x-9.

The collection of values used to replace the unknowns in an equation to make it true is known as the solution.

Here, add 9 on both the sides of an equation.

That is, 13+9=4x-9+9

4x=22

Divide 4 on both the sides of an equation.

4x/4 =22/4

x=5.5

Therefore, the value of x is 5.5.

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11(y-10) = 4y-5

11y-110 = 4y-5

7y -110 = -5

7y =105

y = 105/7 = 15

PTS = 11(15-10) = 11*5 = 55 degrees

Answer:

55

Step-by-step explanation:

We are given with two lines that intersects each other .

the vertical opposite angles are same.

So we equate the angles and solve for y

[tex]11(y-10)= 4y-5[/tex]

[tex]11y-110=4y-5[/tex]

Subtract 4y from both sides

[tex]7y-110=-5[/tex]

Now we add 110 on both sides

[tex]7y=105[/tex]

Now we divide by 7 on both sides

y=15

now we find m∠PTS

m∠PTS=[tex]11(y-10)[/tex]

Plug in 15 for y

m∠PTS=[tex]11(15-10)=55[/tex]

Answer:  2

Step-by-step explanation:

Let Set A represents the number of employees cooked​ food.

Set B represents the number of employees washed​ dishes.

Set C represents the number of employees operated the cash​ register .

Given : n(A)=9 ; n(B)=14 ; n(C)=22

n(A∩B)=4 ; n(A∩C) = 2 ; n(B∩C)=7 ; n(A∩B∩C)=1

Using the given information, we have made a Venn diagram below.

Using Venn diagram , we have

n(only A)= n(A)-(n(A∩B)+n(A∩C)+n(A∩B∩C))

⇒n(only A)=9-(4+2+1)=9-7=2

Hence, 2 employees only cooked​ food.

The length of the hypotenuse is 20 centimeters.

In order to solve this question, we'll use the Pythagoras formula which will be:

a² + b² = c²

where,

First leg = a = 12 centimeters

Second leg = b = 16 centimeters

Hypothenuse = c = Unknown

It should be noted that the hypothenuse is the longest side and therefore the formula will be:

a² + b² = c²

12² + 16² = c²

144 + 256 = c²

400 = c²

Therefore, c = ✓400

c = 20

Therefore, the length of the hypotenuse is 20 centimeters.

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we have

m∠P=[tex](2x)\°[/tex]

m∠Q=[tex](4x)\°[/tex]

m∠R=[tex](6x)\°[/tex]

1) By the triangle sum theorem, the sum of the angles in a triangle is equal to [tex]180\°[/tex]

therefore

m∠P+m∠Q+m∠R=[tex]180\°[/tex]

we know that

Substitution Property of Equality, states that If the values of two quantities are known to be equal, you can replace the value of one quantity with the other

so

2) Using the Substitution Property of Equality

[tex](2x)\°+(4x)\°+(6x)\°=180\°[/tex]

Simplifying the equation gets

[tex](12x)\°=180\°[/tex]

3) using the division property of equality

The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal

[tex](12x)\°/12=180\°/12[/tex]

[tex]x=15\°[/tex]

therefore

the answer is

Part a) Substitution Property of Equality

Part b)  [tex]x=15\°[/tex]

Answer:

Part a) Substitution Property of Equality

Part b) x=15

Step-by-step explanation:

Given triangle PQR with

[tex]m\angle P=(2x)^{\circ}[/tex]

[tex]m\angle Q=(4x)^{\circ}[/tex]

[tex]m\angle R=(6x)^{\circ}[/tex]

By the triangle sum property, the sum of the angles of a triangle is equal to [tex]180^{\circ}[/tex]

∴ m∠P+m∠Q+m∠R=180°

Substitution Property of Equality, states that If the values of two quantities are known to be equal, one can replace the value of one quantity with the other

[tex](2x)^{\circ}+(4x)^{\circ}+(6x)^{\circ}=180^{\circ}[/tex]

Simplifying the equation we get

[tex](12x)^{\circ}=180^{\circ}[/tex]

Using the division property of equality

The Division Property of Equality states that division with the same non zero number results that both sides remain equal

[tex]\frac{(12x)^{\circ}}{12}=\frac{180^{\circ}}{12}[/tex]

[tex]x=15[/tex]

Hence, the answer is

Part a) Substitution Property of Equality

Part b) x=15

PART A:

The function in vertex form by completing the square is:

            [tex]f(t)=(t+3)^2-29[/tex]

PART B:

The vertex is located at (-3,-29)

and the vertex is the minimum point of the graph.

PART C:

      The axis of symmetry of f(t) is:

                    t= -3

The function f(t) is given by:

             [tex]f(t)=t^2+6t-20[/tex]

We know that the vertex form of a equation is given by:

           [tex]f(t)=a(t-h)^2+k[/tex]

where a,h and k are real numbers.

and the vertex is located at (h,k)

The function is given by:

        [tex]f(t)=(t+3)^2-29[/tex]

Hence, the vertex is given by:

            (-3,-29)

Also, as the leading coefficient is positive.

Hence, the parabola is upward open parabola.

Hence, the vertex will be the minimum point of the graph.

Also, the axis of symmetry of a graph is given by:

                          t=h

Hence, here the axis of symmetry is:  t= -3

The complete data set will be 2, 5, 7, 9, 9, 9, 12. When the number 9 is added to the collection, the median and mode are both 9.

The median is defined as the value range. To get it, arrange the numbers in ascending order from smallest to largest, then hide one number on either end until you reach the center.

The median of a set is the middle number when the numbers are arranged in numerical order.

The mode of a set is the number that appears most frequently.

To find an entry that will make the median and mode equal, we first need to arrange the given numbers in numerical order: 2, 5, 7, 9, 9, 12.

The median of this set is the middle number, which is 9.

The mode is 9, since it appears twice while the other numbers appear only once.

To make the median and mode equal, we need to find a number that is between 1 and 12 and that is equal to 9. The only such number is 9.

Therefore, if we add the number 9 to the set, the median and mode will both be 9. The complete data set will be 2, 5, 7, 9, 9, 9, 12.

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