Calculate the average rate of change over the interval 2

The vertices of a triangle are also called the points. Every triangle has 3 vertices. In this case, they are given.

A(-4,4)

B(-4,8)

C(0,4)

I graphed these points for you :)

The approximate probability that both you and your friend will choose chocolate ice cream from seven different flavors is 1/49, or approximately 0.020408.

We are looking to find the probability that both you and your friend choose chocolate ice cream from a selection of 7 different flavors. Since the choice of ice cream is independent for each person, we can calculate the probability of both events occurring by multiplying the probability of each event occurring individually.

The probability that one person chooses chocolate ice cream is 1 out of 7, or approximately 0.142857. To find the probability that both you and your friend choose chocolate ice cream, we multiply the individual probabilities:

Probability of you choosing chocolate: 1/7

Probability of your friend choosing chocolate: 1/7

Combined probability: 1/7 x 1/7 = 1/49

Therefore, the approximate probability that both you and your friend choose chocolate ice cream is 1/49, or approximately 0.020408.

ANSWER

The correct answer is C

EXPLANATION

The given inequality is:

[tex]2x - 8 \: < \: 7[/tex]

Group the constant terms on the right hand side to get;

[tex]2x \: < \: 7 + 8[/tex]

Simplify the right hand side

[tex]2x \: < \: 15[/tex]

Divide both sides by 2

[tex]x \: < \: \frac{15}{2} [/tex]

{x|x<15/2}

The correct answer is C

Answer:

[tex]\large\boxed{\left\{x\ |\ x<\dfrac{15}{2}\right\}}[/tex]

Step-by-step explanation:

[tex]2x-8<7\qquad\text{add 8 to both sides}\\\\2x-8+8<7+8\\\\2x<15\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}<\dfrac{15}{2}\\\\x<\dfrac{15}{2}[/tex]

Answer:

Step-by-step explanation:

[tex]V_p=4\\\\\text{Calculate the volume of a cube:}\\\\V_{c}=\left(\dfrac{1}{3}\right)^3=\dfrac{1}{27}\\\\\text{Calculate how many times the volume of the prism is greater}\\\text{than the volume of the cube:}\\\\\dfrac{V_p}{V_c}=\dfrac{4}{\frac{1}{27}}=4\cdot27=108[/tex]

Answer:

[tex]\large\boxed{\dfrac{1}{x^2}+x^2=23}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{1}{x}+x\right)^2=25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\\left(\dfrac{1}{x}\right)^2+2(x\!\!\!\!\diagup)\left(\dfrac{1}{x\!\!\!\!\diagup}\right)+x^2=25\\\\\dfrac{1}{x^2}+2+x^2=25\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{x^2}+x^2=23[/tex]

The value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] is equal to 23 by using the algebraic identity which has the relationship between [tex](\frac{1}{x } +x)^2[/tex] and [tex]\frac{1}{x^{2} } +x^{2}[/tex]  is [tex](a+b)^2 = a^2 +b^2 +2ab[/tex].

Given that if [tex](\frac{1}{x } +x)^2[/tex] = 25 then find the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] .

To find the  value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] by using the algebraic identity and follow the steps:

Apply the algebraic identity to the given equation, that is :

 [tex](a+b)^2 = a^2 +b^2 +2ab[/tex]

Given that :

[tex](\frac{1}{x } +x)^2=25[/tex]

Expand the LHS by using mentioned algebraic identity:

[tex]\frac{1}{x^2 } +x^2+2x\times\frac{1}{x} =25[/tex]

On cancelation of the variable x in third term of the LHS gives:

[tex]\frac{1}{x^2 } +x^2+2=25[/tex]

Subtract by 2 on both sides, gives:

[tex]\frac{1}{x^2 } +x^2=23[/tex]

Therefore, the value of [tex]\frac{1}{x^{2} } +x^{2}[/tex] is equal to 23 by using the algebraic identity which has the relationship between [tex](\frac{1}{x } +x)^2[/tex] and [tex]\frac{1}{x^{2} } +x^{2}[/tex]  is

[tex](a+b)^2 = a^2 +b^2 +2ab[/tex]

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The sum of the measures of the interior angles of a triangle is 180˚. Example 3: In NMQ. ∆.

For this case, we have given an ABC triangle with internal angles α,β,γ. By definition, the sum of the internal angles must be 180 degrees.

That is to say:

α+β+γ=180

This can be demonstrated according to the fifth postulate of Euclid. From there we have to draw a parallel to one of the sides, by the vertex opposite him, the interior angles of the left side add two right angles.

Answer:

180 degrees

Answer: B.

Length x width x height

Whenever you're finding the volume of a quadrilateral, you multiply the base x width x height of the shape. In this case, you have all three of those elements.

First I substituted those numbers into their spots in the expression (it doesn't matter which you multiply first, since multiplying is commutative).

8 x 12 x 5 = 480

Your answer is 480 square inches.

Answer:

is the fourth one

Step-by-step explanation:

just replace x with the numbers given

and then work it out.

y=x-5

y=1-5=-4

y=2-5=-3

and so on

hope this helps

For this case we have a function of the form [tex]y = f (x)[/tex]where:

[tex]f (x) = x-5[/tex]

We must find the values of "y" when [tex]x = 1,2,3,4[/tex]

Then, keeping in mind that different signs are subtracted and the sign of the major is placed:

Answer:

Option D

Answer:

Mitch bought 5 buckets of wings

Step-by-step explanation:

y=# of wings

X= # of pizza

X+Y=13

X = 13 - Y

11.75X + 19.95Y = 193.75

11.75(13 - Y) + 19.95Y = 193.75

152.75 - 11.75Y + 19.95Y = 193.75

152.75 + 8.2Y = 193.75

8.2Y = 41

Y = 5

Mitch bought 5 buckets of wings

Mitch bought 5 buckets of wings for his Super Bowl party, which was determined by solving a system of equations using the given information about the total number of items purchased and the total cost.

To determine how many buckets of wings Mitch bought for his Super Bowl party, let's define a system of equations based on the information given:

Let's say p represents the number of pizzas, and w represents the number of buckets of wings. We are told that Mitch bought a total of 13 items, which gives us the equation:
p + w = 13.

We are also told that he spent a total of $193.75, with pizzas costing $11.75 each and buckets of wings costing $19.95 each. This gives us the second equation:
11.75p + 19.95w = 193.75.

To solve the system of equations, we can use substitution or elimination. One way is to solve the first equation for p (p = 13 - w) and substitute that into the second equation, leading to:
11.75(13 - w) + 19.95w = 193.75.

Simplifying the equation will allow us to find the value for w. The simplified equation is:
152.75 + 8.2w = 193.75

Subtracting 152.75 from both sides gives us
8.2w = 41,
and dividing both sides by 8.2 yields
w = 5.

Therefore, Mitch bought 5 buckets of wings for the party.

The answer is -9

Answer:

The missing value is -9

Step-by-step explanation:

-9+6 is -3.

Answer: First option.

Step-by-step explanation:

 To simplify the polynomial [tex]2x^2y + 8x^3 - xy^2 - 2x^3 + 3xy^2 + 6y^3[/tex] you need to add the like terms, then you get:

[tex]=2x^2y+6x^3+2xy^2+6y^3[/tex]

Now, you know that Raj put this polynomial in standard form with the last term being 6y³, this means that he ordered it in descending order of "x" power and in ascending order of "y" power:

[tex]=6x^3+2x^2y+2xy^2+6y^3[/tex]

You can observe that the first term of the polynomial  that Raj ended up with, is:

[tex]6x^3[/tex]

Answer:

The answer would b A

Answer:

Step-by-step explanation:

Step 1: Additive inverse

Step 2: Additive identity

Step 3: Addition property of equality

22 is D

Answer:

[tex]x^{15}.y^{9}[/tex]

Step-by-step explanation:

[tex]\frac{x^{19} . y^{21}}{(x^2. y^6)^2} \\\\Here\,\, exponent\,\, rules\,\, will\,\, be\,\, used.\\First\,\, multiply\,\, power\,\, of \,\,2\,\, with\,\, denominator \,\,exponents\\\\\frac{x^{19} . y^{21}}{x^4. y^{12}}\\If \,\, same\,\, bases\,\, are\,\, divided\,\, then\,\, their\,\, exponents\,\, are \,\,subtracted\,\,\\\\x^{19-4}.y^{21-12}\\\\x^{15}.y^{9}[/tex]

Convert the tax rate from a percent to a decimal number by moving the decimal point 2 places to the left.

8.8% = 0.088

Now multiply the price of the item by the tax rate:

63 x 0.088 = 5.544

Now round that to the nearest cent = $5.54

Answer:

$5.54

Step-by-step explanation:

Answer:

x = - 7, x = 5

Step-by-step explanation:

To find the zeros equate f(x) to zero, that is

x² + 2x - 35 = 0

To factorise the quadratic

Consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (+ 2)

The factors are + 7 and - 5, since

7 × - 5 = 35 and 7 - 5 = + 2, hence

(x + 7)(x - 5) = 0

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 5 = 0 ⇒ x = 5

ANSWER

[tex]x = - 7 \: or \: x = 5[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 2x - 35[/tex]

To find the zeros, we equate the function to zero.

[tex] {x}^{2} + 2x - 35 = 0[/tex]

Split the middle term to obtain,

[tex]{x}^{2} + 7x - 5x- 35 = 0[/tex]

Factor by grouping:

[tex]{x}(x + 7) - 5(x + 7)= 0[/tex]

[tex](x + 7)(x - 5) = 0[/tex]

[tex](x + 7) = 0 \: or \: (x - 5) = 0[/tex]

.

[tex]x = - 7 \: or \: x = 5[/tex]

Answer:

7x2-1 = 0

Step-by-step explanation:

Add  1  to both sides of the equation :

                     7x2 = 1

Divide both sides of the equation by 7:

                    x2 = 1/7 = 0.143

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 1/7  

Answer:

Step-by-step explanation:

Rewrite 7x^2 + 1 = 0 as 7x^2 = - 1, and then as x^2 = -1/7.

Taking the square root of both sides, and remembering that the square root of a negative number is imaginary, we get:

                        i√7

x = ±i(1/7) = ± ----------

                          7

Answer:

12

Step-by-step explanation:

1/3 (12) +8

4+8= 12

Answer:

12

Step-by-step explanation:

we can use PEMDAS to find the solution to the expression, PEMDAS stands for:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

we look at the expression and we see parentheses, so we solve whats inside of the parentheses

(4 x 3) = 12

1/3 (12) + 2³

now, we solve for the exponents in the expression

2³ = 2 x 2 x 2 = 8

1/3 (12) + 8

now we multiply the terms in the expression that need to be multiplied.

1/3 x 12 = 4

4 + 8

we have no division in the expression, so we skip that step and move onto addition, which will be our last step as there is no subtraction in the expression either

4 + 8 = 12

our answer to the expression is 12

This may be what you're looking for:

The center-radius form of the circle equation is in the format

(x – h)²+ (y – k)² = r²

with the center being at the point (h, k) and the radius being "r"

So, just plug in the (-5,3) and you get:

(x+5)²+(y-3)²=16

Answer:

24

Step-by-step explanation:

4x6 = 24

-2 and 2 are 4 apart

2 and -4 are 6 apart

Answer:

24 square units

Step-by-step explanation:

STEP 1: Convert interest rate of 2% per 6 months into rate per year.

rate per year = rate per 6 month⋅2=2%⋅2=4%

STEP 2: Convert 9 months into years.

 9 months =

9

12

 years=0.75 years

STEP 3: Find principal by using the formula

I=P⋅i⋅t

, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

In this example I = $15, i = 4% and t = 0.75 years, so

I

P

P

P

=P⋅i⋅t

=

I

i⋅t

=

15

0.04⋅0.75

=500

Final answer:

To calculate the amount at 6% simple interest on Rs 1200 for 9 months, apply the simple interest formula. Convert time to years, calculate the interest, then add it to the principal to find the total amount due, which is Rs 1254.

Explanation:

To find the amount at 6% simple interest on Rs 1200 due in 9 months, you can use the simple interest formula:

Simple Interest =  Principal × Rate × Time

We have the Principal (P) as Rs 1200, the Rate (R) as 6% per annum (or 0.06 when expressed as a decimal), and the Time (T) as 9 months. The rate is given per annum but we have in months so, we need to convert the time to years. There are 12 months in a year, so 9 months is ⅓ or 0.75 years.

Now, let's calculate the simple interest (SI):

SI = 1200 × 0.06 × 0.75 = Rs 54

Total Amount = Principal + Simple Interest

Total Amount = 1200 + 54 = Rs 1254

Therefore, the total amount due at the end of 9 months would be Rs 1254.

Answer:

a. equivalent

b. not equivalent

c. equivalent

d. equivalent

Step-by-step explanation:

a. 3x +7x = (3+7)x = 10x . . . equivalent to 10x

__

b. 5x -10x = (5 -10)x = -5x . . . not equivalent to 5x

__

c. 4(1 +2x) -3x = 4·1 +4·2x -3x = 4 +(8 -3)x = 4 +5x = 5x +4 . . . equivalent to 5x +4

__

d. 5 -3(2 -4x) = 5 -3·2 -3(-4x) = 5 -6 +12x = -1 +12x . . . equivalent to -1 +12x

The side length of the triangle are as follows:

a = 11.71 and b = 15.56

The side of a triangle can be found using sine rule or cosine rule depending on the sides and angles given in a triangle.

Therefore, the sides a and b can be found in the triangle using sine rule as follows:

a / sin A = b / sin B = c / sin C

b / sin 110 = 7 / sin 25°

cross multiply

b sin 25 = 7 sin 110°

b = 7 sin 110° / sin 25

b = 6.5778483455 / 0.42261826174

b = 15.5625174507

b = 15.56 units

Let's find a as follows:

a / sin 45 = 7 / sin 25

a sin 25 = 7 sin 45

a = 7 sin 45 / sin 25

a = 4.94974746831 / 0.42261826174

a = 11.7108376716

a = 11.71 units

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Answer:

1 + 1.58i , 1 - 1.58i

Step-by-step explanation:

2x^2=4x-7

2x^2 - 4x + 7 = 0

x = [-(-4) +/- sqrt((-4)^2 - 4 * 2 * 7 )] / 2*2

= [ 4 +/- sqrt (16 - 56)] / 4

= [4 +/- sqrt (-40) ] / 4

= 1 +/- 6.32i / 4

= 1 + 1.58i  and 1 - 1.58i  (answer).

Answer:

[tex]\boxed{x = 1 \pm i\sqrt{\frac{5}{ 2}} }\\[/tex]

Step-by-step explanation:

2x² = 4x - 7

2x² - 4x + 7 =0

a = 2; b = -4; c = 7

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

[tex]=\frac{4\pm\sqrt{(-2)^2-4\times2\times7}}{2\times2}\\[/tex]

[tex]= 1 \pm\frac{\sqrt{16-56}}{4}\\[/tex]

[tex]= 1 \pm\frac{\sqrt{-40}}{4}\\[/tex]

[tex]= 1 \pm\frac{2i\sqrt{10}}{4}\\[/tex]

[tex]= 1 \pm\frac{i\sqrt{10}}{2}\\[/tex]

[tex]= 1 \pm i\sqrt{\frac{10}{4}}\\[/tex]

[tex]\boxed{= 1 \pm i\sqrt{\frac{5}{ 2}} }\\[/tex]

The graph of y = 2x² - 4x + 7 has a minimum at (1, 5). It never touches the x-axis, so both roots are imaginary.

What you did in the graph was correct. Essentially, all you have to do to achieve a negative slope is either make the rise negative or the run negative (make sure not to do both, as the negatives would cancel out and make a normal line)

Answer:

The cosine function that models this reaction is:

[tex]y=-70cos(\frac{1}{4}\pi x) +90[/tex]

Step-by-step explanation:

The general cosine function has the following form

[tex]y = Acos(bx) + k[/tex]

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.

[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

The maximum temperature is 160 and the minimum is 20. Then the amplitude A is:

[tex]A =\frac{160-20}{2}\\\\A= 70[/tex]

The reaction completes a cycle in 8 hours

Then the period is 8 hours.

Thus:

[tex]\frac{2\pi}{b}=8\\\\ b=\frac{2\pi}{8}\\\\ b=\frac{1}{4}\pi[/tex]

The function is:

[tex]y = 70cos(\frac{1}{4}\pi x)+k[/tex]

when [tex]t=0[/tex] y is minumum therefore [tex]y=-cos(x)[/tex]

So

[tex]y = -70cos(\frac{1}{4}\pi x)+k[/tex]

Now we substitute [tex]t = 0[/tex] in the function and solve for k

[tex]20 = -70cos(0)+k\\\\k=20+70\\\\k=90[/tex]

Finally

[tex]y=-70cos(\frac{1}{4}\pi x) +90[/tex]

Answer:

The answer would be B $6.99.  With this problem you would need to divide the total cost by 8 to get the price for a single steak.  

Step-by-step explanation:

Answer:

The height of the cone is 97 in

Step-by-step explanation:

Equate the formulas for the volume of a cylinder and that of a cone:

Vol-Cyl              Vol-Cone

πr²h         =        (1/3)πr²h

Now cancel out items that are the same on both sides (π):

r²h             =         (1/3)r²h

Now substitute the given values for both solids:

(12 in)²(8 in)  =  (1/3)(6 in)²(h-cone)

                                 1152 in³

Then (h-cone) = --------------------  =  97 in

                                   12 in²

The height of the cone is 97 in

Answer:

96 in

Step-by-step explanation:

The most efficient way is the 1st option

because all you have to do is add -3y on both sides to isolate x

If you used any other variables, you would have to use division which are extra steps

Answer:

Hence, the correct option is A) The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.

Step-by-step explanation:

Consider the provided system of equation.

x - 3y = 1  and  7x + 2y = 7

Let first solve the second equation.

[tex]7x + 2y = 7[/tex]

Step 1:

Divide both the sides by 7.

[tex]x + \frac{2y}{7} = 1[/tex]

Step 2:

[tex]x = 1- \frac{2y}{7} [/tex]

It took 2 steps to isolate the the variable x.

Now again consider the system of equation.

But this time we will solve the first equation.

[tex]x - 3y = 1[/tex]

Step 1:

[tex]x = 1 + 3y[/tex]

it took only 1 step to isolate the variable as the variable x in the first equation has a coefficient of one.

Hence, the correct option is A) The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.

Answer:

Frequency is the number of times that roll occurred.

Ex: 7 occurred 5 times...... 5 goes in the frequency column.