need help with 7 A & B? “Quadratic Functions” algebra 1

Subtracting -2y² from -4y² + 5d will give us -2y² + 5d.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.

To subtract the two polynomials, we first need to distribute the negative sign to the second polynomial.

So, (-4y² + 5d) - (-2y²) becomes -4y² + 5d + 2y².

Now, combine the like terms, which are the terms that contain y²:

-4y² + 5d + 2y² = (-4 + 2)y² + 5d

So, our final answer is:

-2y² + 5d.

Since our answer is in simplest terms, the final answer is -2y² + 5d.

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Answer:

We can start by simplifying each parentheses separately and then adding the resulting expressions:

(2^4 – 5^3 – 7) + (−5^5 − 5^2 + 9 + 17)

= (16 - 125 - 7) + (-3125 - 25 + 9 + 17) (using the fact that 2^4 = 16 and 5^3 = 125)

= (-116) + (-3124) (combining like terms)

= -3240

Therefore, the answer is -3240. To express this number in standard form, we write it as:

-3.24 x 10^3

The negative sign indicates that the number is less than zero, and the 3.24 tells us the value of the number. The "x 10^3" part means that we need to multiply 3.24 by 10^3 (which is 1000) to get the actual value of the number:

-3.24 x 10^3 = -3.24 * 1000 = -3240

So, the answer in standard form is -3.24 x 10^3.

Answer:

Part A

a = 1

b = 3

c = -4

Part B

[tex]x = \dfrac{ -3 \pm \sqrt{3^2 - 4(1)(-4)}}{ 2(1) }[/tex]

Part C

[tex]\mathrm{x = \dfrac{ -3 + \sqrt{25}}{ 2 } :and\: x = \dfrac{ -3- \sqrt{25}}{ 2 }}[/tex]

Part D

Option B:   x = 1 and x = -4

Step-by-step explanation:

The standard form of the quadratic equation is [tex]ax^2 + bx + c=0[/tex]

1.The given equation is [tex]x^2 + 3x - 4 = 0[/tex]

Part A

Comparing the given equation with the generalized standard equation we see that

[tex]a[/tex]  = coefficient of [tex]x^2[/tex] = 1

[tex]b[/tex]= coefficient of [tex]x = 3[/tex]

[tex]c[/tex]= constant term = [tex]-4[/tex]

Part B.

The quadratic formula for the roots of the equation is:
[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

Plugging in values for a, b and c from Part A:
[tex]x = \dfrac{ -3 \pm \sqrt{3^2 - 4(1)(-4)}}{ 2(1) }[/tex]

Part C

[tex]\mathrm{x = \dfrac{ -3 + \sqrt{25}}{ 2 } :and\: x = \dfrac{ -3- \sqrt{25}}{ 2 }}[/tex]

part D
Simplifying we get

[tex]x = \dfrac{ -3 + 5\, }{ 2 } = \dfrac{2}{2} = 1\\\\x = \dfrac{ -3 - 5\, }{ 2 } = \dfrac{-8}{2} = -4\\\\[/tex]

Correct answer for Part C:
B. x = 1 and x = -4

Answer:$7.49

Step-by-step explanation:

just subtract 42.50 from 49.99
49.99-42.50=7.49

Answer:

A. X = -4

Step-by-step explanation:

[tex]-6x-24=3x+12\\-9x=36\\x=-4[/tex]

The probabilities are:

(a) P(diamond or heart) = 0.5

(b) P(diamond or heart or spade) = 0.75

(c) P(seven or heart) ≈ 0.308.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

(a) To compute the probability of randomly selecting a diamond or heart from a standard deck of 52 cards, we need to count the number of diamond cards and heart cards in the deck. There are 13 diamond cards and 13 heart cards, so the total number of cards that are either diamonds or hearts is 13 + 13 = 26. Therefore, the probability of randomly selecting a diamond or heart is:

P(diamond or heart) = number of diamond cards + number of heart cards / total number of cards

P(diamond or heart) = 26/52

P(diamond or heart) = 1/2

P(diamond or heart) = 0.5

(b) To compute the probability of randomly selecting a diamond or heart or spade from a standard deck of 52 cards, we need to count the number of cards that belong to any of these three suits. There are 13 diamond cards, 13 heart cards, and 13 spade cards in the deck, so the total number of cards that are either diamonds, hearts, or spades is 13 + 13 + 13 = 39. Therefore, the probability of randomly selecting a diamond or heart or spade is:

P(diamond or heart or spade) = number of diamond cards + number of heart cards + number of spade cards / total number of cards

P(diamond or heart or spade) = 39/52

P(diamond or heart or spade) = 3/4

P(diamond or heart or spade) = 0.75

(c) To compute the probability of randomly selecting a seven or a heart from a standard deck of 52 cards, we need to count the number of seven cards and the number of heart cards in the deck. There are 4 seven cards and 13 heart cards, but we need to be careful not to double-count the seven of hearts. Therefore, the total number of cards that are either sevens or hearts is 4 + 12 = 16. Therefore, the probability of randomly selecting a seven or a heart is:

P(seven or heart) = number of seven cards + number of heart cards - number of seven of hearts / total number of cards

P(seven or heart) = 16/52

P(seven or heart) = 4/13

P(seven or heart) ≈ 0.308

Hence, The probabilities are:

(a) P(diamond or heart) = 0.5

(b) P(diamond or heart or spade) = 0.75

(c) P(seven or heart) ≈ 0.308.

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Answer:

Step-by-step explanation:

18

Answer:

slope = 4 , point on line (- 1, 3 )

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y - 3 = 4(x + 1) ← is in point- slope form

with slope m = 4 and (a, b ) = (- 1, 3 )

The angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.

To find the angle between two vectors \( \mathbf{u} \) and \( \mathbf{v} \), we can use the formula:
\[ \cos \theta = \frac{\mathbf{u} \cdot \mathbf{v}}{\| \mathbf{u} \| \| \mathbf{v} \|} \]
where \( \theta \) is the angle between the vectors, \( \mathbf{u} \cdot \mathbf{v} \) is the dot product of the vectors, and \( \| \mathbf{u} \| \) and \( \| \mathbf{v} \| \) are the magnitudes of the vectors.

First, we need to find the dot product of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \mathbf{u} \cdot \mathbf{v} = (-4)(-5) + (-1)(-2) = 20 + 2 = 22 \]

Next, we need to find the magnitudes of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \| \mathbf{u} \| = \sqrt{(-4)^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17} \]
\[ \| \mathbf{v} \| = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \]

Now we can plug these values into the formula and solve for \( \theta \):
\[ \cos \theta = \frac{22}{\sqrt{17} \sqrt{29}} \]
\[ \theta = \cos^{-1} \left( \frac{22}{\sqrt{17} \sqrt{29}} \right) \]

Using a calculator, we find that \( \theta \approx 12.5 \) degrees.

Therefore, the angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.

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The number is 30.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum

Given that,

The sum of the digits of a certain two-digit number is 3.

Since it is a two digit number, there will be a tens place and a ones place.

Let x be the digit in tens place and y be the digit in ones place.

x + y = 3

The number can also be written as 10x + y, since x is in the tens place.

When the number is reversed, tens place changed to ones place and vice versa.

The reversed number is 10y + x.

Given that the value of the number is decreased by 27 when the digits is reversed.

Original number - 27 = Reversed number

10x + y - 27 = 10y + x

9x - 9y = 27

x - y = 3

Also, we have,

x + y = 3  [Equation 1]

x - y = 3   [Equation 2]

Adding the equations,

2x = 6

x = 6/2 = 3

Substituting in equation 1, y = 0

Hence the number is 30.

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The value of x for the similar triangles is 8 units.

The value of x is determined by applying the principle of similar triangles as shown below.

In the given diagram, we can assume the following for the similar triangles;

length 10 is congruent to length 10 + (3x + 1 )

length 22 is congruent to length 7x -1  + 22

So we will have the following equation;

(3x + 1  + 10 )/ 10 = (7x - 1 + 22 ) / 22

(3x + 11 ) / 10 = ( 7x + 21 ) / 22

22(3x + 11 ) = 10 (7x + 21 )

66x + 242 = 70x + 210

32 = 4x

x = 32 / 4

x = 8

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Solving a linear equation we can see that he can afford to pay the monthly fee for 28 months

We know that there is an initial fee of $300 plus $7 per month, so the total cost after x months is:

C = 300 + 7*x

And we know that Julio has $500 set aside, then the equation that we need to solve is:

500 = 300 + 7x

500 - 300 = 7x

200 = 7x

200/7 = x = 28.5

Rounding down we get 28.

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The total surface area of the given figures is:

1) 376 sq. feet

2)92sq. feet

What is meant by surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. A solid object's surface area is a measurement of the overall space that the object's surface takes up. Every geometric shape has a different surface area formula, but the goal of all of them is to determine the total area occupied by all of the objects' faces.

1) This figure is a cuboid.

  It has six faces and the opposite faces are of equal dimensions.

The surface area of a cuboid is the sum of the areas of each face.

Length l = 10 ft

Width w = 6 ft

Height h = 8 ft

Surface area = 2lw+2lh+2hw = 2 ( lw+ lh+ hw)

                                     = 2 ( 10*6 + 10*8 + 8*6) = 376 sq. feet

2) This figure has 2 similar right triangle faces.

Sum of area of both triangles = 2 * 1/2 * base * height = 3 * 4 = 12 sq. feet

There are two rectangular faces.

Area of front rectangular face = 10 * 5 = 50 sq. feet

Area of base rectangular face = 10*3 = 30 sq. feet

 Total surface area = 12 + 50 + 30 = 92sq. feet

Therefore the total surface area of the given figures is:

1) 376 sq. feet

2)92sq. feet

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Answer:

To find the total surface area of a square pyramid, we need to find the sum of the areas of its base and its four triangular faces.

In this case, the base is a square with side length 11.5 inches. Therefore, its area is:

Area of base = 11.5^2 = 132.25 square inches

Each triangular face has a base length equal to the side length of the square base, which is 11.5 inches. To find the height of each triangular face, we can use the Pythagorean theorem. Since the pyramid is a square pyramid, the height of each triangular face is also the slant height of the pyramid.

The slant height of the pyramid can be found using the Pythagorean theorem:

a^2 + b^2 = c^2

where a = b = 11.5/2 = 5.75 (half the length of a diagonal of the square base) and c is the slant height. Solving for c, we get:

c = sqrt(a^2 + b^2) = sqrt(2*(5.75)^2) = 8.121 inches (rounded to 3 decimal places)

The area of each triangular face can be found using the formula:

Area of triangle = (1/2) * base * height

where the base is 11.5 inches and the height is 8.121 inches.

Area of each triangular face = (1/2) * 11.5 * 8.121 = 46.876 square inches (rounded to 3 decimal places)

So, the total surface area of the square pyramid is:

Total surface area = Area of base + 4 * Area of each triangular face

Total surface area = 132.25 + 4 * 46.876 = 330.124 square inches (rounded to 3 decimal places)

Therefore, the total surface area of the square pyramid is approximately 330.124 square inches.

The cost of each notebook the customer purchased is $1.19

From the question, we are to determine how much each notebook the customer purchased cost.

Let's assume the price of each notebook is "x" dollars. Then, we can set up the following equation to solve for "x":

12x = 48 - 33.72

We can simplify the right side of the equation:

12x = 14.28

Then, we can solve for "x" by dividing both sides by 12:

12x/12 = 14.28/12

x = 1.19

The value of x is 1.19

Hence, each notebook costs $1.19.

Here is the correct question:

A customer purchased 12 notebooks at the same price each. The customer had $48 before purchasing the notebooks and was left with $33.72 after purchasing them. How much did each notebook cost?

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The product of 4/6-2a x 3-a/2 is equal to 2a-1. To calculate this, the fractions must first be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Next, the two terms should be multiplied together, resulting in 2a-1.

The product of 4/6-2a x 3-a/2 can be found by expanding the terms and then solving the equation. First, the fractions must be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Once the fractions are simplified, the two terms should be multiplied together, resulting in 2a-1. Now that the two terms have been multiplied, the equation can be expanded by using the Distributive Property. The equation should be written as (2/3-2a) x (3-a/2). This can be simplified by distributing the 2/3 and 3 across the parentheses. This results in (2-6a+2a^2) x (3-1/2a). Finally, the equation should be simplified by combining like terms. This results in 2-6a+2a^2+3-1/2a, which simplifies to 2a-1. Therefore, the product of 4/6-2a x 3-a/2 is equal to 2a-1.

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Answer:

The inequality that would represent the possible values for the number of hours lifeguarding, l, and the number of hours walking dogs, d, that Katherine can work in a given week is:

l + d ≤ 14

This is because the sum of the hours worked in both jobs should not exceed 14 hours.

Answer:

Elizabeth gave away 216 marbles out of a total of 360 marbles.

To find the percentage of marbles that Elizabeth gave away, we can use the formula:

percentage = (part/whole) x 100%

where "part" is the number of marbles Elizabeth gave away, and "whole" is the total number of marbles.

So, plugging in the values we have:

percentage = (216/360) x 100%

percentage = 0.6 x 100%

percentage = 60%

Therefore, Elizabeth gave away 60% of the marbles.

The measure of the central angle in the "Punk" section is 72 degrees.

The measure of the central angle in the "Punk" section can be determined by calculating the percentage of punk songs sold in relation to the total number of songs sold, and then converting that percentage to degrees.

To calculate the percentage of punk songs sold, divide the number of punk songs sold by the total number of songs sold, and multiply by 100.

For example, if 200 punk songs were sold and the total number of songs sold was 1000, the percentage of punk songs sold would be:

200/1000 * 100 = 20%

To convert this percentage to degrees, multiply the percentage by 360 (the total number of degrees in a circle).

20% * 360 = 72 degrees

Therefore, the measure of the central angle in the "Punk" section is 72 degrees.

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Answer:

$0.40

Step-by-step explanation:

Latte 5.65

Muffin 3.95

Add both 5.65 +3.95 = 9.60

Deduct it from $10

You have 0.40

Answer:

We can express 25 pens out of 51 in ratio form as:

25:51

8×4=32

11-8=3

4×3=12

12÷2=6

32+6=38

=38inch^2

it might b wrong tho?

The solution for u is 36.

To solve for u using the multiplicative property of equality, we need to isolate u on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction that is attached to u. The reciprocal of (5/6) is (6/5), so we can multiply both sides of the equation by (6/5) to get:

(6/5) * 30 = (6/5) * (5/6) * u

Simplifying the right side of the equation gives us:

(6/5) * 30 = u

Multiplying the fraction and the whole number gives us:

(180/5) = u

Simplifying the fraction gives us:

36 = u

Therefore, the solution for u is 36.

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a) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 is 0.00153. b) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 comes out as 0.00153 percent

To find the monthly payment needed to repay a $40,000 loan over 20 years with a 0.5% interest rate per month, we can use the following formula: Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^-Number of payments)

Plugging in the given values: Monthly payment = ($40,000 * 0.005) / (1 - (1 + 0.005)^-240) Monthly payment = $200 / (1 - 0.334) Monthly payment = $200 / 0.666, Monthly payment = $300.30

Therefore, the monthly payment needed to repay the $40,000 loan over 20 years with a 0.5% interest rate per month is $300.30.To find the monthly interest rate for a $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53, we can use the same formula and rearrange it to solve for the monthly interest rate:

Monthly interest rate = (Monthly payment * (1 - (1 + Monthly interest rate)^-Number of payments)) / Loan amount. Plugging in the given values:

0.005 = ($544.53 * (1 - (1 + 0.005)^-240)) / $40,000

0.005 * $40,000 = $544.53 * (1 - (1 + 0.005)^-240)

$200 = $544.53 * (1 - (1 + 0.005)^-240)

$200 / $544.53 = 1 - (1 + 0.005)^-240

0.367 = 1 - (1 + 0.005)^-240

(1 + 0.005)^-240 = 0.633

1 + 0.005 = 0.633^-240

0.005 = 0.633^-240 - 1

0.005 = -0.367

Monthly interest rate = -0.367 / -240

Monthly interest rate = 0.00153

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so since 45000 split on a 7:10:13 ratio, so let's simply divide 45000 by (7+10+13) and distribute accordingly to each daughter.

[tex]\stackrel{Ana}{7}~~ : ~~\stackrel{Betty}{10}~~ : ~~\stackrel{Chandra}{13} \\\\\\ \stackrel{Ana}{7\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Betty}{10\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Chandra}{13\cdot \frac{45000}{7+10+13}} \\\\\\ \stackrel{Ana}{7\cdot 1500}~~ : ~~\stackrel{Betty}{10\cdot 1500}~~ : ~~\stackrel{Chandra}{13\cdot 1500} ~~ \implies~\hfill \stackrel{Ana}{10500}~~ : ~~\stackrel{Betty}{15000}~~ : ~~\stackrel{Chandra}{19500}[/tex]

To simplify the complex fraction ((1)/(f^(3))-(1)/(a^(3)))/((1)/(f^(2))-(1)/(a^(2))), we can use the common denominator method.

Step 1: Find the common denominator for the numerator and denominator of the complex fraction. The common denominator for the numerator is (f^(3))(a^(3)) and the common denominator for the denominator is (f^(2))(a^(2)).

Step 2: Multiply each term in the numerator and denominator by the common denominator to get rid of the fractions.

Numerator: ((1)(a^(3))-(1)(f^(3)))/(f^(3))(a^(3))

Denominator: ((1)(a^(2))-(1)(f^(2)))/(f^(2))(a^(2))

Step 3: Simplify the numerator and denominator by combining like terms.

Numerator: (a^(3)-f^(3))/(f^(3))(a^(3))

Denominator: (a^(2)-f^(2))/(f^(2))(a^(2))

Step 4: Divide the numerator and denominator by the common factor (f^(2))(a^(2)).

Simplified fraction: (a-f)/(f^(1))(a^(1))

Step 5: Simplify the final fraction by canceling out the common factors.

Final answer: (a-f)/(fa)

Therefore, the simplified complex fraction is (a-f)/(fa).

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The greatest common factor of these three expressions, 28w, 8w⁵, and 20w⁴, is 4w.

The greatest common factor (GCF) of three univariate monomials is the largest factor that divides all three expressions. To find the GCF of 28w, 8w⁵, and 20w⁴, we need to find the largest factor that is common to all three expressions.

First, we need to find the GCF of the coefficients of the three expressions. The GCF of 28, 8, and 20 is 4.

Next, we need to find the GCF of the variables of the three expressions. The GCF of w, w⁵, and w⁴ is w, since it is the lowest power of w that is common to all three expressions.

Therefore, the GCF of 28w, 8w⁵, and 20w⁴ is 4w.

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The answer in simplest form is 9/2

The division involving a whole number and a fraction can be simplified by multiplying the whole number by the reciprocal of the fraction.

The reciprocal of a fraction is obtained by flipping the numerator and denominator.

In this case, the division is 3 ÷ (2/3). The reciprocal of (2/3) is (3/2).

So, we can multiply 3 by (3/2) to simplify the division:

3 × (3/2) = (3/1) × (3/2) = (3 × 3) / (1 × 2) = 9/2

Therefore, the answer in simplest form is 9/2.

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The equations are y = 5x and y = 3 + x, and the table of values are

x   4    1    0    3    6    2    5   -1    7

y  20  5   0    15   18   10  25   -5  30

x   4    1    0    3    6    2    5   -1    7

y  7    4    3    6     9   5    8   2    10

When A = 20 and C = 0

Here, we have

A = 20 and C = 0

This means that we have the points (4, 20) and (0, 0).

Assuming the table is a linear table, we first need to find the slope of the table using

m = (y2 - y1) / (x2 - x1)

Using the points (4, 20) and (0, 0), we get:

m = (0 - 20) / (0 - 4) = 20/4 = 5

The equation is  then calculated as

y = mx + c

Calculating c, we have

20 = 5 * 4 + c

Evaluate

c = 0

So, the equation is

y = 5x

When the table is completed using the above equation, we have the following table of values

x   4    1    0    3    6    2    5   -1    7

y  20  5   0    15   18   10  25   -5  30

When A = 7 and F = 5

Here, we have

(4, 7) and (2, 5).

In the above, we can see that y is 3 more than x

So, the equation is

y = 3 + x

When the table is completed using the above equation, we have the following table of values

x   4    1    0    3    6    2    5   -1    7

y  7    4    3    6     9   5    8   2    10

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