Jada is solving the equation shown below.

Negative one-half (x + 4) = 6

Which is a possible first step to begin to simplify the equation? Select two options.
Divide both sides of the equation by –2.
Subtract 4 from both sides of the equation.
Multiply both sides of the equation by –2.
Distribute –2 over (x + 4).
Distribute Negative one-half over (x + 4).

Answer: B

Step-by-step explanation:

The vertical asymptotes are at x=-4 and x=1, so the denominator needs to have factors of (x+4) and (x-1).

This eliminates everything except for B.

Answer:

a = 43 degrees

b = 137 degrees

Step-by-step explanation:

according to the alternate interior angle theorem, angle a equals angle theta, so angle a = 43 degrees

angle b is the supplement of angle a, so angle b = 180-angle a, or 137

The amount that the insurance company will pay is $1800.

It should be noted that the insurance company will pay John for the expenses of his injuries and repair of the car.

For the injury, he will get:

= $500 + ($1400 - $100)

= $500 + $2300

= $1800

Therefore, the amount is $1800.

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Based on the change in the company stock over the three weeks, the total increase in those three weeks is 1.38%.

assuming the stock has a value of $1, the value in the third week would be:
= 1 x (1 + 5/8%) x (1 + 1/2%) x (1 + 1/4%)

= $1.013809453125

the total increase is:
= (1.013809453125 - 1) / 1

= 1.38%

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The constant of proportionality is 6.

From the information given, the constant will be:

30 meals ÷ 5 days = 6

60 meals ÷ 10 days = 6

90 meals ÷ 15 days = 6

120 meals ÷ 20 days = 6

The constant of proportionality is 6. Therefore, the function will be:

y = kx

y = 6x

The value of y when x is 1 will be:

y = kx

y = 6 × 1 = 6

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Answer:

what they said

Step-by-step explanation:

30 Jagged rocks are the same 3 shiny rocks using the exchange rates provided(i.e. option D)

What is an exchange rate?

Exchange rate means the rate at which one item exchanges hands with another, for instance, in this case, 6 jagged rocks are equivalent to 2 smooth pebbles.

6 jagged rocks=2 smooth pebbles

divide both sides by 2

6/2 jagged rocks=2/2 smooth pebbles

3 jagged rocks=1 smooth pebble

We can rewrite as below:

1 jagged rock=1/3 smooth pebble

30jagged rocks=1/3*30 smooth pebbles

30 jagged rocks=10 smooth pebbles

Now we need to convert 10 smooth pebbles to shiny rock equivalence

3 smooth pebbles=1 shiny rock

1 smooth pebble=1/3 shiny rock

10 smooth pebbles=1/3*10 shiny rocks

10 smooth pebbles=3 shiny rocks( even though it is 3.33, but the final answer should be rounded to a whole number)

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Answer:

x = 2/7

x = -6

Step-by-step explanation:

You can solve the equation by setting each set of parentheses equal to 0 and simplifying.

7x - 2 = 0                                <----- First set of parentheses

7x = 2                                      <----- Add 2 to both sides

x = 2/7                                    <----- Divide both sides by 7

x + 6 = 0                                 <----- Second set of parentheses

x = -6                                      <----- Subtract 6 from both sides

The area of the square is given by the  quadratic expression:

[tex]A = 9x^2 - 6xy + y^2[/tex]

If we have a square whose side measures S, the area of said square is given by the equation:

[tex]A = S^2[/tex]

In this case, we know that the side length of our square is given by:

[tex]S = 3x - y[/tex]

Replacing that in the area equation we get:

[tex]A = (3x - y)^2[/tex]

Now we just need to expand that product, we will get:

[tex]A = (3x - y)^2 = (3x)*(3x) + (3x)*(-y) + (-y)*(3x) + (-y)*(-y) \\\\A = 9x^2 - 6xy + y^2[/tex]

Then we can see that the correct option is the last one.

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The interest is a) $7000

b) $17709.73

c) $18672.62

d) $18901.67

What is the formula for simple and compound interest?

Simple interest = (P× r× t)

Compound interest = P(1+r/n)^nt - P

We will find the interest as shown below:

P=$4,000

t=25 years

a) r=7%=0.07

Simple interest = (P× r× t)

= (4000×0.07×25)

= $7000

b) r=7%=0.07

Compound interest = P(1+r)^t - P

= 4000(1+0.07)^25-4000

= $17709.73056

rounding to nearest cents

= $17709.73

c) r=7%=0.07

n=4

Compound interest = P(1+r/n)^nt - P

= 4000(1+0.07/4)^(25*4)-4000

= $18672.62375

rounding to nearest cent

= $18672.62

d) r=7%=0.07

n=12

Compound interest = P(1+r/n)^nt - P

= 4000(1+0.07/12)^(25*12)-4000

= $18901.6728

rounding to nearest cent

= $18901.67

Hence, the interest is a) $7000

b) $17709.73

c) $18672.62

d) $18901.67

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ax² + bx + c = 0

discriminant = b² - 4ac

----> x² + 7x + 12

---> Discriminant of this equation = 7² - 12.1.4 = 49 - 48 = 1 (Positive discriminant)

x = (-7 + 1)/(2.1) = -6/2 = -3

or

x = (-7 - 1)/(2.1) = -8/2 = -4

Therefore, this equation has two real solutions and has a positive discriminant.

The correct answer is B

The graph that represents the inequality is:

Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.

The inequality is:

|2x - 6| < 4

Which means that the distance of 2x - 6 to the origin is less than 4, hence:

-4 < 2x - 6 < 4.

The solution is:

2x - 6 > -4

2x > 2

x > 1

2x - 6 < 4

2x < 10

x < 5

The solution has open circles at x = 1 and x = 5, as they are not part of the solution, and the shading is in the middle, as the solution is 1 < x < 5, hence the correct option is:

Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.

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Answer:

From least to most likely:

Event 4, Event 2, Event 3, Event 1

Step-by-step explanation:

Event 1 has a 100% chance because there are only red and orange marbles in the bag.

In event 2, there are 4 orange marbles in the bag, giving us a (4/20) chance. This is 20%

In event 3, there are 2 orange marbles of 8 total, giving us an (2/8) chance. This is 25%

Lastly, there are no purple marbles in either bag, giving us a 0% chance of this occurring.

The equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1

A line is the shortest distance between two points. The equation of a line in slope-intercept form is expressed as;

y = mx + b

m is the slope

b is the y-intercept

Given that m=1, b=-3, the required equation will be y = x - 3 or x - y = 3

For the parameter m=1, (-1,2)

y - 2 =1(x+1)

y - 2 = x+1

y =x + 3

Hence the equation of the line for the parameters m=1, (-1,2)  is y = x + 3

For the coordinates (-2,3),(-3,4)

Slope = 4-3/-3+2
Slope = -1

For the intercept;

4 =-1(-3) + b

b = 4 - 3

b = 1

Hence the equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1

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The equation of the line of best fit using the slope-intercept formula y=mx+b is y = x - 5

A line is the shortest distance between two points. The equation in point-slope form is expressed as:

y =. mx + b

m is the slope

b is the y intercept

Using the coordinate points (25, 20) and (60, 55)

Slope = 55-20/60-25
Slope = 35/35
Slope = 1

For the intercept

20 = 1(25) + b

b = 20 - 25

b = -5

Substitute

y = x + (-5)

y = x - 5

Hence the equation of the line of best fit using the slope-intercept formula y=mx+b is y = x - 5

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The surface area of this three-dimensional figure is equal to 536.6 square centimeters.

First of all, we would determine the total area of the three rectangles by using this formula:

Total area = 3 × Length × Width

Total area = 3 × 15 × 10

Total area = 450 cm².

Next, we would determine the total area of the two triangles by using this formula:

Total area = 2 × (1/2 × b × h)

Total area = b × h

Total area = 8.66 × 10

Total area = 86.6 cm².

Surface area = 450 + 86.6

Surface area = 536.6 cm².

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Answer: [tex]\frac{3}{c^2}[/tex]

Step-by-step explanation:

This uses the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex].

If Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that Mohal bought 20 chicken wings for $50.00 and spend $30.0.

We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

The price of one chicken wing is,

= $ 50 / 20

= $ 2.50

The number of chicken wings he can buy after spending $30.00,

= $30.00 / = $ 2.50

=12

Thus, Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.

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Answer:

x=1

Step-by-step explanation:

[tex] \sqrt{( - 3 - x) ^{2} + {( - 2 - 3)}^{2} } = \\ \sqrt{ {(4 - x)}^{2} + {(5 - 3)}^{2} } \\ \\ 9 + 6x + {x}^{2} + 25 = \\ 16 - 8x + {x}^{2} + 4 = = = > \\ 34 + 6x = 20 - 8x = > \\ 14 = 14x = = = > x = 1[/tex]

Done

The value of x that makes up the coordinate of B is -1

To find the value of x, we need to determine the coordinates of point B.

Since A to (B) = B to (C), the distance from point A to point B is equal to the distance from point B to point C. The distance between two points in a coordinate plane can be calculated using the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Let's calculate the distances:

Distance A to (B):

x₁ = -3 (x-coordinate of point A)

y₁ = -2 (y-coordinate of point A)

x₂ = x (x-coordinate of point B)

y₂ = 3 (y-coordinate of point B)

Distance A to (B) = √((x - (-3))² + (3 - (-2))²)

Distance A to (B) =√((x + 3)² + 5²)

Distance A to (B) = √(x² + 6x + 9 + 25)

Distance A to (B) = √(x² + 6x + 34)

Distance B to (C):

x₁ = x (x-coordinate of point B)

y₁ = 3 (y-coordinate of point B)

x₂ = 4 (x-coordinate of point C)

y₂ = 5 (y-coordinate of point C)

Distance B to (C) = √((4 - x)² + (5 - 3)²)

Distance B to (C) = √((4 - x)² + 2²)

Distance B to (C) = √((4 - x)² + 4)

Distance B to (C) = √(x² - 8x + 20)

Since A to (B) = B to (C):

√(x² + 6x + 34) = √(x² - 8x + 20)

Now, we can square both sides to get rid of the square root:

x² + 6x + 34 = x² - 8x + 20

Next, move all the x terms to one side of the equation:

x² - x² + 6x + 8x = 20 - 34

Combine like terms:

14x = -14

Finally, solve for x:

x = -14 / 14

x = -1

So the value of x is -1. Point B is located at (-1, 3).

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In the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.

A quadratic equation is a polynomial of degree 2, in a single variable x.

The standard form of a quadratic equation is ax² + bx + c = 0.

The quadratic formula is used to find the solution(s)/root(s) of this equation.

The quadratic formula is:

[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Thus, identifying the values of a, b, and c, is the first step in using the quadratic formula to find a solution(s)/root(s) to a quadratic equation.

In the question, we are asked to find the values of a, b, and c, in the given quadratic equation - 3x² - 5x + 9 = 0.

To find the values of a, b, and c, we compare the given equation, to the standard form of a quadratic equation, ax² + bx + c = 0.

On comparing, we get a is the coefficient of x², that is, a = -3.

On comparing, we get b is the coefficient of x, that is, b = -5.

On comparing, we get c is the constant term, that is, c = 9.

Thus, in the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.

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The provided question is incomplete.

The complete question is:

"Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.

What are the values a, b, and c in the following quadratic equation?

- 3x² - 5x + 9 = 0

Using the normal distribution, there is a 0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 2.5, \sigma = 0.5[/tex].

The probability that a randomly selected cyclist will take between 2.35 and 2.45 hours is the p-value of Z when X = 2.45 subtracted by the p-value of Z when X = 2.35, hence:

X = 2.45:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.45 - 2.5}{0.5}[/tex]

Z = -0.1

Z = -0.1 has a p-value of 0.4602.

X = 2.35:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.35 - 2.5}{0.5}[/tex]

Z = -0.3

Z = -0.3 has a p-value of 0.3821.

0.4602 - 0.3821 = 0.0781.

0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.

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The total cost needed to tile the training room with an area of 100 m² is R110.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let assume that the area of the trainig room is 100 m² and one box can complete 50 m², hence:

number of box needed = 100 m² / 50 m² = 2

Total  cost = R55 per box * 2 box = R110

The total cost needed to tile the training room with an area of 100 m² is R110.

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Answer:

2x-3/7x

Step-by-step explanation:

Answer:

The transformation being described is from g(x)=x2 g ( x ) = x 2 to f(x)=x2 f ( x ) = x 2 . The horizontal shift depends on the value of h . The horizontal shift is described as: f(x)=f(x+h) f ( x ) = f ( x + h ) - The graph is shifted to the left h units

The total bill after tax is $38.44.

The first step is to determine the total cost of 4 pizzas and 2 orders of breadsticks: (4 x $6.79) + (2 x 2.49) = $32.14

Now, determine the total cost after delivery fee has been added : $3 +  $32.14 =  $35.14

Now determine the total cost after tax : (1.094) x $35.14 = $38.44

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The total bill after tax of 9.4% is $38.44.

It worthy of note that the sales tax of 9.4% is a percentage of the total purchase bills prior to tax computation, it is the tax due on purchases which is an added percentage of the sales price

total cost of 4 pizzas= $6.79 *4

total cost of 4 pizzas=$27.16

total cost of 2 orders of breadsticks=$2.49*2

total cost of 2 orders of breadsticks=$4.98

total cost of purchase prior to adding delivery cost=$27.16+$4.98

total cost of purchase prior to adding delivery cost=$32.14

total cost of purchase after  delivery cost=$32.14+$3

total cost of purchase after  delivery cost=$35.14

total cost inclusive of 9.4% sales tax=$35.14*(1+9.4%)

total cost inclusive of 9.4% sales tax=$35.14*1.094

total cost inclusive of 9.4% sales tax=$38.44

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Answer:

The intersection of L and J or simply (L ∩ J)= ∅

or { }

Step-by-step explanation:

Hello!

The intersection operation is denoted by the symbol ∩. The set A ∩ B—read “A intersection B” or “the intersection of A and B”—is defined as the set composed of all elements that belong to both A and B.

Thus, at this situation there is no similar terms between the to set elements of L and J.

Answer:

Step-by-step explanation:

Given

Leg =  10

Leg = 6

hypotenuse = ?

equation

c^2 = a^2 + b^2

a = 10

b = 6

Solution

c^2 = 10^2 + 6^2                  Expand

c^2 = 100 + 36                     Combine

c^2 = 136                              Take the square root of both sides

√c^2 = √136

c = 11.66

answer

hypotenuse = 11.66

Answer:

D

Step-by-step explanation:

Sequence A is increasing using + 6

Sequence B is decreasing using - 6

Sequence C is decreasing using - 6

Sequence D is increasing using x 3

D is the odd one out