"Test I. Encircle the letter that corresponds your answer. 2 points each
1. How many solutions do you get when you solve by completing the square?
a. 1
b. 2
c. 3
d. 4
2. When completing the square, what do you do if your x squared term has a coefficient?
a. Divide both sides by this coefficient
c. Multiply both sides by this coefficient
b. Nothing
d. Move it to the other side
3. Find the value of b in the quadratic equation 2x²=-5 x+7
a. 2
b. 5
c. -7
d. -5
4. Which of the following mathematical statements is not a quadratic equation?
a. 2 r²-3r-5=0
c. 3t²+7t-2=0
b. 7h+12=h²
d. s²=-8s-15
5. It is a polynomial equation of degree two that can be written in the form ax²+bx+c=0, where a, b, and c are real numbers and a≠ 0.
a. Linear Equation
b. Linear Inequality
c. Quadratic Equation
d. Quadratic Inequality)
"

The number 3,675,000,000 represents 3,675,100,608 rounded off to the nearest million.

When we round off large numbers, we consider the digit to the right of the number occupying the place value for which we are rounding off to. If the digit to the right is 4 or less, we round down (we leave the number we are rounding to), but if the digit is 5 or higher, we round up (we increase the digit we are rounding by 1). and thus round to the indicated place value.

From the question, we have the large number;

3,675,100,608

the digit 5 indicates the place value (million)

and the digit 1 is to the right and will be rounded down.

Therefore, the number 3,675,000,000 represents 3,675,100,608, rounded to the nearest million.

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Owen went to Best Buy to purchase a new laptop. He put a down payment of $200 and will pay $75 each month until he pays it off. Use the

formula p= 200 + 75c to identify which statement below is false.

The ‘p’ is represented as the dependent variable [true]

The ‘c’ represents the number of months [true]

The independent variable is 75 [FALSE]

The ‘c’ is represented as the independent variable [true]

Answer:

42-48 pound" number.

Step-by-step explanation:

The correct values are;

⇒ a - d = - 2

⇒ c - a = 7

⇒ b - c = - 8

⇒ d - c = - 5

What is Number line?

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

The number line is shown in figure.

The values are,

a = - 3

b = - 4

c = 4

d = - 1

Now,

All the values are find as;

⇒ a - d = - 3 - (- 1)

           = - 3 + 1

           = - 2

⇒ c - a = 4 - (-3)

           = 4 + 3

           = 7

⇒ b - c = - 4 - 4

           = - 8

⇒ d - c = - 1 - 4

           = - 5

Thus, The correct values are;

⇒ a - d = - 2

⇒ c - a = 7

⇒ b - c = - 8

⇒ d - c = - 5

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a) The first term of the sequence is; ³¹/₆

b) The term to term rule is; aₙ = ³¹/₆ + (n - 1)²/₆

c) The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆

d) The 10th term in the sequence is; a₁₀ = ⁴⁹/₆

The first term of the sequence is given by the expression;

2 ÷ ¹²/₃₁ = ³¹/₆

The second term of the sequence is given by the expression;

3 ÷ ⁶/₁₁ = ³³/₆

The third term of the sequence is given by the expression;

5 ÷ ⁶/₇ = ³⁵/₆

These are the first three terms of a sequence and so the sequence is;

³¹/₆, ³³/₆, ³⁵/₆,....

d = ³³/₆ - ³¹/₆ = ²/₆

Thus, term to term rule is given by the nth term of an arithmetic progression;

aₙ = ³¹/₆ + (n - 1)²/₆

The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆

The 10th term in the sequence is;

a₁₀ = ³¹/₆ + (10 - 1)²/₆

a₁₀ = ³¹/₆ + ¹⁸/₆

a₁₀ = ⁴⁹/₆

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X + 7 is not a factor of [tex]x^{3}[/tex] -3[tex]x^{2}[/tex] +2x -8 because it gives a remainder when x + 7 divides it.

The remainder is the portion of the dividend that cannot be fairly divided by the divisor. After dividing whole numbers to find the quotient, the part that is left is called the remainder.

to know if x + 7 is a factor, x = -7 when substituted should give 0 as a remainder otherwise it is not a factor.

By substituting x = -7 we have

[tex](-7)^{3}[/tex] [tex]-3(-7)^{2}[/tex] +2(-7) - 8 = -343 -147 -14 - 8  which is -512

Therefore x + 7 is not a factor of the function.

In conclusion x + 7 is not a factor of [tex]x^{3}[/tex] -3[tex]x^{2}[/tex] +2x -8

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Answer:

What he said!

Step-by-step explanation:

Hello!

What does this problem want:

What we need to find: rate of bagels made per hour

    [tex]\text{Rate}=\frac{\text{Total number of bagels}}{\text{Number of hours}} =\frac{640}{4} =160 \text{ bagels per hour}[/tex]

Thus

                 8 * 160 = 1280 bagels

                6 * 160 = 960 bagels

Hope that helps!

The only solution the system of the equation has is x = -1/3.

The number of solutions is one.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The system of equations:

y = -3x - 1

y = x² - 3x + 4

The solutions of the equation.

y = 0

So,

-3x - 1 = 0

-3x = 1

x = -1/3

x² - 3x + 4 = 0

It is in the form of ax² + bx + c = 0

a = 1, b = -3, and c = 4

Now,

x = -b ± √(b² - 4ac) / 4a

x = 3 ± √(9 - 16) / 4

x = 3 ±√-7 / 4

x = 3 ±i√7 / 4

This is a complex root.

So,

These are not real solutions.

Thus,

The only solution the system of the equation has is x = -1/3.

The number of solutions is one.

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Answer:

Step-by-step explanation:

6(6p-9)-10p-6(6p-9)-10p

36p-54-10p-36p+54-10p

36p-36p-54+54-10p= -10p

Answer:

-4

Step-by-step explanation:

3x+15+2=5

3x=-15-2+5

3x=-12

x=-12/3

x=-4

Answer:

x=-4

Step-by-step explanation:

Given:

[tex]3(x+5)+2=5[/tex]

To find:

The value of x.

Explanation:

It is given that,

[tex]3(x+5)+2=5[/tex]

That implies,

[tex]3(x+5)+2=5\\3x+15+2=5\\3x+17=5\\3x=5-17\\3x=-12\\x=-\frac{12}{3} \\x=-4[/tex]

Hence, the value of x is -4.

Answer: x=5

Step-by-step explanation:

4x-3=17 Add three to both sides

4x=20 Divide both side by 4 to isolate x

x=5

Las expresiones algebraicas que completan la tabla son 200+x, 2(200+x), 650+ 2(200+x),  y -5, y+ 10, y+8, 75- y

El lenguaje algebraico es simbólico es decir se expresa mediante consonantes o vocales, el lenguaje algebraico nos permite expresar de manera sencilla y practica el valor desconocido de una determinada cantidad.

A partir de la información dada es decir  "x" naranjas y "Y" que es la edad de José vamos a expresar las respuestas en lenguaje algebraico.  Para esto se debe relacionar la x o y con el valor dado y el signo matemático correspondiente:                                                

Luis tiene 200 naranjas mas que Soraya  =  200+x

Susana tiene el doble de Luis  = 2(200+x)

Juan tiene 650 naranjas mas que susana   = 650+ 2(200+x)

Considerando que Y es la edad de José

Los años que tenia hace 5 años = y -5

Los años que tendrá en 10 años  = y+ 10

Los años que tendrá dentro de 8 años = y+8

Los años que faltan para que cumpla 75 años = 75- y

Podemos concluir que el lenguaje algebraico nos permite representar de manera practica un valor desconocido y de igual manera obtener respuestas practicas y sencillas a partir de variables.

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The formula for the volume of a cone is given by the following equation:

V = 1/3 * π * r2 * h

where V is the volume of the cone, r is the radius of the cone, and h is the height of the cone.

In this case, we are given that the radius of the cone is 2.5 units and the volume of the cone is 19 cubic units. We can use this information to complete the expression that represents the height of the cone as follows:

V = 1/3 * π * r2 * h

19 cubic units = 1/3 * π * 2.5 units2 * h

19 cubic units = 1/3 * π * 6.25 units2 * h

19 cubic units = 1/3 * 19.63 units2 * h

19 cubic units = 6.54 units2 * h

h = 19 cubic units / 6.54 units2

h = 2.9 cubic units / 6.54 units

Therefore, the expression that represents the height of the cone is 2.9 cubic units / 6.54 units.

Answer:

Irrational

Step-by-step explanation:

A rational number can be expressed as p/q where p and q are integers

3.04 is rational since it can be expressed as 304/100

√20 is not rational. √20 = √(4·5) = √4·√5 = 2√5
While 2 is a rational number, √5 is irrational since 5 is a prime number and square roots of primes are not rational

An irrational number multiplied by a rational number is irrational so √20 is irrational

An irrational number added to a rational number results in an irrational number.

So 3.04 + √20  is irrational

Answer:

22 people

Step-by-step explanation:

First, let's convert the percentage into a decimal so we can multiply the two.

55% = 0.55

Next, we'll multiply 40 times 0.55. This is so we can find the amount of people who said yes. (55% of people said yes.)

0.55*40 = 22

22 people said yes.

The graph of the equation is shown below

The x-intercept is -2

The y-intercept is undefined

From the question, we are to solve the equation by graphing and determine the x- and y-intercepts

The given equation is

3x + 1 = -5

To determine the x-intercepts, we will solve the equation

3x + 1 =-5

3x = -5 - 1

3x = -6

Divide both sides by 3

x = -2

Since, y is not defined in the equation, the y-intercept is undefined

The graph of the equation is shown below.

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The answer choice which must be a factor of the polynomial in discuss is; (x - 1).

It follows from the vertex form equation of a parabola; f(x) = a ( x - h )² + k where the vertex of the parabola is; (h, k).

Therefore, the equation of the parabola in discuss is;

f(x) = a (x - 3.5)² + 3.

Recall that the x coordinates of the vertex, h is given by; h = (p + q) / 2

where p and q are the zeroes of the quadratic function.

Therefore, since one of the zeroes is given as; 6 ( from (6, 0) ); it follows that the second zero can be determined as follows;

3.5 = ( 6 + q ) / 2

7 = 6 + q

q = 1

Therefore, since the second zero is; 1. It follows that the associated factor as required is; ( x - 1 ).

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Answer:

Step-by-step explanation:

443

Answer:

Step-by-step explanation:

Given the values in the table, you want to know if they represent a linear or exponential relation, along with the common difference or ratio, as applicable.

The first attachment shows the differences and ratios between successive table values. Neither the differences nor the ratios are constant. The wide variation in ratios and the relatively smaller variation in differences suggests the table is best modeled by a linear function.

Changes when the function is linear are additive. That is, the function values have a common difference.

The average difference between table values is (949.92 -229.44)/3 = 240.16. A linear regression analysis gives a slope of 240.12 as the "best fit" to the table values.

You can see from the first attachment that the differences are not constant, so there isn't really a common difference. The difference is approximately 240.12.

__

Additional comment

The second attachment shows linear and an exponential regression applied to this data. The residuals are much smaller for the linear approximation.

The slope of the line (common difference) is estimated at 240.12 using the regression formula. This makes the mean square residuals a minimum. As we show above, this slope is different (slightly lower) than the slope of the line through the first and last data points.

Answer:

GM = 18

Step-by-step explanation:

JK = KL = 2

GJ = LM =7

GM = 7+2+2+7 = 18!

So the answer it is 18.

Answer: Radio

Step-by-step explanation:

An electromagnet wave with a wavelength of 100m is a Radio. These signals are invisible to the human eye, humans are only able to detect visible light.

The gas for the Trip cost is $8.39

The amount of gas motorcycle needed is 12 Liter of gas.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Jackson’s motorcycle gets 28 kilometers per liter.

He drives 336 kilometers and gas is $1.43 per liter.

The amount of gas motorcycle needed

= 336/28

= 12 Liter of gas

and, The gas for the Trip cost = 12/1.43

                                                  = $8.39

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Answer:

y - 9 = 7(x - 1)

Step-by-step explanation:

The given equation is in Point Slope Form:  y - y₁ = m(x - x₁)

m is the slope, and parallel lines have the same slope (7)

x₁ and y₁ are the coordinates of a point on the line

The inequality that represents the situation given will be  

7x + 13y ≤ 91.

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

The inequality that represents the situation given will be  7x + 13y ≤ 91.

From the information given, Crawford is ordering pizzas and breadsticks for a school pizza party and has a budget of $91, but no more and an order of breadsticks costs $7 while a pepperoni pizza costs $13.

Therefore, the inequality that represents the situation given will be  

7x + 13y ≤ 91.

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Answer:172 cm²

Step-by-step explanation:

when we use the formula, and we can  solve out is like 172.05 and round to tenth and will have the answer

Formula is 1/2 × p × a  

The function of reflect x-axis is g(x) =  -(1/2)*x - 8, according to the question.

What do you mean by function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

According to the given question,

First, let's define a reflection over the x-axis.

If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).

Now, when we have a function

f(x) = y, the points can be written as:

(x, y = f(x) ) = (x, f(x))

Then, after the reflection over the x-axis, we have:

(x, y = g(x)) = (x, -f(x))

So now we have g(x) = -f(x)

and we know that f(x) = (1/2)*x + 8

then our new function is g(x) =  y = -f(x) = -( (1/2)*x + 8) = -(1/2)*x - 8.

g(x) =  -(1/2)*x - 8.

Therefore, the required answer is g(x) =  -(1/2)*x - 8.

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Answer: 29000

Step-by-step explanation:

12000 + 2500 = 14500

14500 * 2 = 29000

Answer:7

Step-by-step explanation:

What it is asking you is what multiplied by it self gets you to 49. the answer would be 7 because 7*7=49

Answer: 12

Step-by-step explanation:

       1 2  

   5 ⟌ 6 0  

     - 5    

       1 0  

     - 1 0  

         0