the first step in determining the solution to the system of equations, y=-x² - 4x-3 and y= 2x + 5, algebraically isthe two equations equal as -x² - 4x - 3= 2x + 5. What is the next step?et y = 0 in y=-x2 - 4x-3.actor each side of the equation.se substitution to create a one-variable equation.ombine like terms onto one side of the equation.

Notice that [tex](x,y,-z)[/tex] is a gradient field:

[tex]\nabla f(x,y,z) = (x,y,-z) \implies \begin{cases} f_x = x \\ f_y = y \\ f_z = -z \end{cases}[/tex]

That is, there exists a scalar function [tex]f(x,y,z)[/tex] whose gradient is the given vector field. Solve for [tex]f[/tex].

[tex]\displaystyle \int f_x \, dx = \int x \, dx \implies f(x,y,z) = \frac12 x^2 + g(y,z)[/tex]

[tex]f_y = g_y = y \implies \displaystyle \int g_y \, dy = \int y \, dy \implies g(y,z) = \frac12 y^2 + h(z)[/tex]

[tex]f_z = h_z = -z \implies \displaystyle \int h_z \, dz = - \int z \, dz \implies h(z) = -\frac12 z^2 + C[/tex]

[tex]\implies f(x,y,z) = \dfrac{x^2+y^2-z^2}2 + C[/tex]

By the gradient theorem, it follows that

[tex]\displaystyle \int_{(1,0,-3)}^{(6,4,8)} x \, dx + y \, dy - z \, dz = f(6,4,8) - f(1,0,-3) = \boxed{-2}[/tex]

The point-slope form of a line is given by:

y - k = m ( x - h)

Where m is the slope of the line and (h, k) is a point through which the line passes.

We are given the values of m = 1/4 and the point (0, -1).

Substituting:

The average cost per minute which the shop runs is $1.50

To find the shop's cost per minute, we can write down equations and proceed to solve.

In the given question, 3 cupcakes cost $6.75 and 5 cupcakes cost $9.75.

But we were not given the average cost per cupcake.

To do that, let's write an equation for this.

[tex]y = mx + c[/tex]

Let's find the slope to this equation which determines the average cost per minute.

[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{9.75 - 6.75}{5 - 3} \\m = 1.50[/tex]

The shop's cost per minute was calculated to be $1.50.

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Jenna bought a coat on sale for $120

The price of the coat is the 2/3of the original price

Let the original price is $x

So, the equation will be :

2/3 of x =120

So, The original price of the coat is $180

Answer:

11

Step-by-step explanation:

A = lw

l = A/w

l = 77/7

l = 11

Hope that helps

The total number associated to barre class is 207 + 196 = 403

Therefore, the probability that a attendee does not attend a barre class is given by 403/2153 = 0.1872

The coat of the dress based on the percentage is $66.

From the information, it was stated that Tonya spends 55% of her savings on a new dress and that she saved $120.

Let the cost of the dress be represented as x

Therefore, the appropriate information given I'll be expressed as:

= 55% × 120 = x

0.55 × 120 = x

Multiply

x = 66

The amount spent is $66.

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SOLUTION

A coin was flipped.

A = probability of it landing on a head

B = probability of it landing on a tail.

We are asked P(A and B), that means probability of landing on a head and on a tail.

A coin can only land on a head or it can land on a tail. It can't land on a head and a tail at the same time.

Therefore the probability of landing on a head and a tail is 0.

Hence, the answer is 0.

The various algebraic properties used for each of the given expressions are;

1) Symmetric property of equality.

2) Distributive property of equality.

3) Addition property of equality.

4) Division property of equality.

5) Addition property of equality.

6) Transitive property of equality.

7) Associative property of equality.

8) Multiplication property of equality

9) Commutative property of equality.

There are different properties of equality or algebra such as;

1)  If AB=CD, then CD=AB; Property used here is Symmetric property of equality because it suits the definition.

2) 5(x-4) = 5x-20; Property used here is Distributive property of equality because it suits the definition.

3) 3x - 17 = 8, then 3x = 25; Property used here is Addition property of equality because it suits the definition.

4) 22m=440, then m=20; Property used here is Division property of equality because it suits the definition.

5) :(2a+3a)-4a=7a+55, then (5a)-4a=7a+55; Property used here is Addition property of equality because it suits the definition.

6) If GH=2x+17, and 2x+17=JK, then GH=JK; Property used here is Transitive property of equality because it suits the definition.

7) 2b+(b-7)=17, then (2b+b)-7=17; Property used here is Associative property of equality because it suits the definition.

8) (x+7)/3=13, then x+7=39.; Property used here is Multiplication property of equality because it suits the definition.

9) m 10:4+x=13, then x+4=13; Property used here is Commutative property of equality because it suits the definition.

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The expresion for the correlation coefficient is :

summation of x = 5 + 7 + 10 + 15 + 19

Summation of x = 56

Summation of y = 19 + 17 + 16 + 12 + 7

Summation of y = 71

Summation of prodcut xy

Summation of x^2 = 25 + 49 + 100 + 225 + 361

Summation of x^2 = 760

Summation of y^2 = 361 + 289 + 256 + 144 + 49

Summation of y^2 = 1099

Substitute tha value in the expression of correlation coefficient

Answer: A) Correlation coefficient is 0.985

Given

the age of the winner for best actor was 38 and the age of the winner for best actress was 51.

For all best​ actors, the mean age is 46.8 years and the standard deviation is 5.7 years.

For all best​ actresses, the mean age is 31.9 years and the standard deviation is 10.8 years.​

Find

who had the more extreme age when winning the​ award, the actor or the​ actress

Explanation

the Z- score is given by

Best Actor

X = 38

mean = 46.8 years

standard deviation = 5.7 years.

so ,

Best Actress

X = 51

mean = 31.9 years

standard deviation = 10.8 years.

so ,

the best actress's age is farther from the mean so he has the more extreme age when the winning the award.

Final Answer

Hence , the z- score for best actor is -1.54 and for best actress = 1.77

Actress has more extreme age

The first step to this problem is finding the amount of butterfat there are in the 385 gallons milk with 5% of butterfat in it. To do that we need to multiply the percentage by the total amount of milk. This is done below:

There are 19.25 gallons of butterfat on the final mixture, the amount of butterfat from each of the milks we are going to mix need to be equal to that. The first milk contains 8% of butterfat, while the second milk contains 1%. So we have:

Where "x" is the number of gallons from the first milk and "y" is the number of gallons from the second milk. The number of gallons of each milk, when added, should be equal to the number of gallons on the final milk, so we have:

The same is valid for the amount of butterfat.

We have now created a system of equations as shown below:

To solve this system we will multiply the first equation by "-0.01":

Now we need to add both equations.

To find the value of "y" we will use the first equation:

We need 220 gallons from the 8% butterfat milk and 165 gallons from the 1% butterfat milk.

The general form of a quadratic equation is given by the expression:

A quadratic equation having a maximum value or point is one that has its value of a to be lesser than zero

(a < 0). Such a graph opens downwards

Therefore, any quadratic equation that has the a-value to be lesser than zero has a maximum point

Mathematically expressed as:

ANSWER :

EXPLANATION :

Answer:

x-intercept: (-0.5,0)

y-intercept: (0,1)

Slope: 2

Domain: All real values

Range: All real values

Step-by-step explanation:

x-intercept:

The x-intercept is the value of x when y = 0. In this graphic, we have that when y = 0, x = -0.5. So the x-intercept is given by: (-0.5,0)

y-intercept:

The y-intercept is the value of y when x = 0. In this graphic, we have that when x = 0, y = 1. So the y-intercept is given by: (0,1).

Slope:

To find the slope, we select two points. The slope is given by the division of the change in y by the change in x.

Two points: (-0.5, 0) and (0,1)

Change in y: 1 - 0 = 1

Change in x: 0 - (-0.5) = 0 + 0.5 = 0.5

Slope: 1/0.5 = 2

Domain and range:

In a line, the domain is all real values, the same for the range.

Let's simplify the following equation

A)

If the dress costs x and the pair of pants cost $25 dollars less, the cost of the pants will be:

B)

We know that the dress costs x and the pants cost x-25. Molly bought 2 dresses and 3 pairs of pants, with the total amount of $675. Thus:

If x is the dress cost, so the dress will cost $150. And the pants:

The pants will cost $125.

Answer:

L x W =   8.5 x 24    or     12 x 17

Step-by-step explanation:

x  (41 -2x) =204

-2x^2 + 41x -204 = 0      Use Quadratic Formula to find x = 8.5 or 12

(x-8.5)(x-12) = 0

         two sides = 8.5       and river/third side =  24

      or  two sides 12     and river/thirdside = 17

In order to simplify an equation we want to add all the terms with the same unkowns.

In the equation

4 - 2y + (-8y) + 7.3

we can see that there are terms with y and numbers alone.

We combine like terms:

Terms with y: -2y,

Given data:

First squaring both sides we get,

Therefore, the value for the solution which satisfies the above equation are

Thus, the ans is (a) , (b) , (d) , (e)

If Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years

The interest rate = 4.6%

The final amount = $1610

The time period = 15 years

The compound interest

A = [tex]P(1+\frac{r}{100})^{t}[/tex]

Where A is the final amount

P is the principal amount

r = interest rate

t is the time period

Substitute the values in the equation

1610 = [tex]P(1+\frac{4.6}{100})^{15}[/tex]

1610 = P×1.96

P = 1610/1.96

P = $820.06

Hence, if Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years

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y= 2x+4

Slope-intercept form

y=mx+b

Where:

m= slope

b= y-intercept

y=2x+4

Slope = m= 2

Perpendicular lines have negative reciprocal slopes.

So, the slope of the new line = -1/2

New equation:

y= -1/2x+b

Replace x,y by the point (4,2) and solve for b:

2 = -1/2(4)+b

2= -2 + b

2+2 = b

4 = b

New line equation:

y= -1/2x+4

Answer: The number is 4,000.

Step-by-step explanation:

        First, we will turn 0.2% into a decimal.

0.2% / 100 = 0.002

        Next, we will set up an equation. Let x be equal to "what number:"

0.2% of what number is 8 ➜ 0.002x = 8

        Lastly, we will solve by dividing both sides by 0.02.

0.002x = 8

x = 4,000

        If we wish to, we can check our answer.

4,000 * 0.002 = 8

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Top left: Yes, each input corresponds to only one output.

Top right: Yes, each input corresponds to only one output.

Bottom left: Yes, each input corresponds to only one output.

Bottom right: No, the input of -1 corresponds to three different outputs.

The graph of the linear function and it's inverse is given at the end of the answer.

The inverse function is: [tex]h^{-1}(x) = -6x + 55[/tex]

To find the inverse function, we exchange x and y in the original function, then isolate y.

In the context of this problem, first we have to find the function h(x), which is a linear function going through points (1,9) and (3,2), hence the slope is given by:

m = (2 - 1)/(3 - 9) = -1/6.

Then:

y = -x/6 + b.

When x = 1, y = 9, hence we can find the intercept b as follows:

9 = -1/6 + b

b = 54/6 + 1/6

b = 55/6.

Then the equation is:

h(x) = -x/6 + 55/6

Then:

y =  -x/6 + 55/6

6y = -x + 55

6x = -y + 55

y = -6x + 55.

Hence the inverse function is:

[tex]h^{-1}(x) = -6x + 55[/tex]

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Using the Fundamental Counting Theorem, the number of possible plates is given as follows:

1,000,000.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is given according to the following rule:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this question, the plate is composed by six independent digits, hence the parameters are given as follows:

[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = 10[/tex]

(as there are 10 possible digits, from 0 to 9).

Hence the number of possible plates is calculated as follows:

N = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10^6 = 1,000,000.

This problem is incomplete, hence we suppose that it asks for how many plates can be built.

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The measure of the fourth angle that is x and the value is 133°

A regular octagon will have all its sides equal in length. Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080°.

Let the 8 interior angles of the octagon be:

x-12, x-8, x-4, x, x+4, x+8, x+12, x+16.

Their sum = 8x+16 = 1080, or

this implies 8x = 1080–16 = 1064  

thus on further solving we get x = 133

Hence the sixth angle = x+8 =141 degrees.

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Using the Fundamental Counting Theorem, the number of length-n sequences that have at least one pair of adjacent LEDs that light up with the same color is:

[tex]N = 4 - 4 \times 3^{n - 1}[/tex]

It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In the context of this problem, there are n LEDs, each with 4 possible colors, hence he total number of sequences is:

[tex]T = 4^n[/tex]

For sequences with no repeating LEDs, we have that:

Hence the number is:

[tex]T_n = 4 \times 3^{n-1}[/tex]

(n - 1) as the first LED is not included on those with 3 possibilities.

Having at least one repeating and no repeating are complementary events, hence the number of sequences is:

[tex]N = 4 - 4 \times 3^{n - 1}[/tex]

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Formula for the trigonometry is y = b sin ( πx/2 - π/2) + 4

y = A sin( ωx + δ) + b

period: t = 4

ω = 2π/t = 2π/4 = π/2

A = 10 -(-2)/ 2

  = 6

b = (10-2)/2

  = 4

y = b sin (πx/2 + δ) + 4

x = 0, y = bsinδ + 4 = -2

sinδ = -1   => δ = -π/2

y = b sin( πx/2 - π/2) + 4

Therefore the formula for the trigonometry function is y = b sin(πx/2 - π/2) + 4.

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