solve the equation. justify each step
2(-x - 5) = 12

The terms of the algebraic equation 3+6ab+c are (d) 3, 6ab  and c

The algebraic equation is given as

3 + 6ab + c

Consider an equation represented as

x + y

The terms of the equation are x and y

Also, for an equation represented as

x + y + z;

The terms are x, y and z

Using the above as a guide, the terms of 3 + 6ab + c are 3, 6ab  and c

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Answer:

x = 1/4p

y = 3/2p

Step-by-step explanation:

2x + 3y =5p__________________equ 1

y = 2x + p____________________equ 2

sub equ 2 for y in equ 1

2x + 3(2x + p) = 5p_______________open brackets

8x = 2p______________________divide both sides by 8

x = 1/4p

sub 1/4p for x in equ 2

y = 2(1/4p) + p___________________open brackets

y = 3/2p

The probability of favorable  outcomes  P(E) = 37/256

What is probability in math?

Given,

      8 coins are faced simultaneously .

total outcomes = 2 * 2 * 2* 2 * 2 * 2 * 2 * 2

                             = 2⁸

                             = 256

favorable outcomes = 6 heads + 7 heads + 8 heads

                      = ⁸C₆ + ⁸C₇  + ⁸C₈

                       = 28 + 8 + 1   = 37

the probability of favorable  outcomes =            

              P(E) = 37/256

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Answer:

see explanation

Step-by-step explanation:

(a)

AB = 4 + x

(b)

the area (A) of rectangle ABCD is calculated as

A = length × breadth

   = AB × AD

   = (4 + x)(6 + x) ← expand using FOIL

   = 24 + 10x + x²

given A = 28 , then

x² + 10x + 24 = 28 ( subtract 24 from both sides )

x² + 10x = 4 ← in the form x² + ax = b

with a = 10 and b = 4

The linear functions representing the systems of equations in each case are given as follows:

8. (D) 6x − y = 8 3x + 2y = 9

9. (C) a + o = 72 a = o + 8.

10. (C) 4x + 3y = −12 2x − 5y = 10.

The slope-intercept representation of a linear function is presented by the rule as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

For the line m, we have that when x increases by 6, y increases by 36, hence the slope is:

m = 36/6 = 6.

Considering the positive slope of 6, at x = 0, the numeric value is 12 less than the numeric value at x = 2, hence the intercept is:

b = 4 - 2 x 6 = -8.

Hence the equation is:

y = 6x - 8.

6x - y - 8.

Thus option d is correct.

For item 9, we use the variables a and o. The total is of 72, hence:

a + o = 72.

Suppose that a crate has 8 more apples than oranges, hence:

a = o + 8.

Thus option c is correct.

For line r in item 10, when x increases by 3, y decays by 4, hence the slope is:

m = -4/3.

When x = 0, y = -4, hence the intercept is:

b = -4.

Thus the equation is:

y = -4x/3 - 4

3y = -4x - 4.

4x + 3y = -12.

Meaning that option c is correct.

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The fraction 7/2a+4/a*a can be written as (7 + 8a) / 2a

What is a fraction?

In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are in spoken common English. In other words, a fraction indicates the components of a whole or group of items.

Solution Explained:

First, we simplify the equation

=  [tex]\frac{7}{2a} + \frac{4}{a} X a[/tex]

=  [tex]\frac{7}{2a} + 4[/tex]

= [tex]\frac{7 + 8a}{2a}[/tex]

Therefore, the equation can be written as (7 + 8a) / 2a

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Step-by-step explanation:

ratios are special fractions and follow therefore all the fraction rules.

e.g. they follow the rule that for transformations the same multiplications or divisions have to happen for the denominator and the numerator when bringing them to the same denominator.

and they follow the same division and multiplication rules.

2/3 : 1/6 : 5/2 = (2/3)×(2/2) : 1/6 : (5/2)×(3/3) =

4/6 : 1/6 : 15/6 = 4 : 1 : 15

Answer:

a = 1

Step-by-step explanation:

Given equation,

→ 7(5a - 4) - 1 = 14 - 8

Now the value of a will be,

→ 7(5a - 4) - 1 = 14 - 8

→ 35a - 28 - 1 = 6

→ 35a - 29 = 6

→ 35a = 6 + 29

→ a = 35/35

→ [ a = 1 ]

Hence, the value of a is 1.

The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

y = [tex]a(x-h)^2[/tex] + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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Answer:

$3.70

Step-by-step explanation:

12 dimes, and dimes are ten cents each. So we will multiply 10*12=120. Which is $1.20.

10 quarters, and quarters are twenty-five cents each. So we will multiply 10*25=250. Which is $2.50

Now we take our two totals and add them together. 1.20+2.50=3.70.

So we have $3.70.

I hope this helps!!!

Step-by-step explanation:

4a)

that means all 4 events happen in combination as one event.

so, we have to multiply the probabilities of all 4 events.

that means

0.63⁴ = 0.15752961... ≈ 0.16

so, there is a 16% chance that all 4 children get sick.

in other words, the probabilty for that is about 0.16.

b)

the probabilty of at least 1 kids getting sick is the opposite of the probability of no kids is getting sick.

the probability of getting sick is 0.63, so the probability of not getting sick is 1 - 0.63 = 0.37.

the probability of no kids getting sick is similar to a)

0.37⁴ = 0.01874161 ≈ 0.02

the probabilty of at least one kid getting sick is the opposite of that :

1 - 0.01874161... = 0.98125839 ≈ 0.98

5)

A u B is the sample space. so, any possible event is either part of A or B or both.

that means

P(A') = 0.35 = 1 - P(A)

P(A) = 1 - 0.35 = 0.65

P(A and B') = P(of every A that is not B) = 0.25.

because P(A) = 0.65

that means that

P(A and B) = P(every A that is also B) =

= 0.65 - 0.25 = 0.4

P(B) = P(A') + P(A and B) = 0.35 + 0.4 = 0.75

FYI

we could have gotten this directly from

P(A and B') = P(of every A that is not B = everything that is only A) = 0.25.

because

P(A and B')' = P(of everything that is not "only A" = everything that is B) = P(B) = 1 - 0.25 = 0.75

The rectangle has its dimensions to be 8.8 units by 12.4 units

From the question, the equation is given as

2x(x + 8) = 110

This equation represents the area of the rectangle

So, we have

2x(x + 8) = 110

Divide by 2

x(x + 8) = 55

Open the brackets

This gives

x² + 8x = 55

Rewrite as

x² + 8x - 55 = 0

Using a graphing calculator, we have the solutions to be

x = -12.4 and x = 4.4

The variable x cannot be negative

So, we have

x = 4.4

In 2x(x + 8) = 110, we have

Length = 2x

Width = x + 8

So, we have

Length = 2 x 4.4

Width = 4.4 + 8

Evaluate

Length = 8.8

Width = 12.4

Hence, the dimensions of the rectangle are 8.8 units by 12.4 units

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The expression that makes v the subject of the formula, W=5+v/v-3 is v= (5 + 3W)/ (W-1).

The concept is the concept of finding the subject of the formula in an expression.

To know the subject of the formula, we will need to perform some simplification:

W=5+v/v-3

then this can be expressed as:

W(v-3) = 5+v

Wv - 3W = 5+v

then we can rearrange the expression as:

Wv - v = 5 + 3W

then we can factorize  the expression as :

v(W-1) = (5 + 3W)

v= (5 + 3W)/ (W-1)

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The explicit formula is a_n = 3+4n

From the question, we have

a1 = 7

We know that,

a_n = a_1 +(n-1)d

a_n = 7 +(n-1)4

a_n = 7+4n-4

a_n = 3+4n

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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The equation for the vertical line that goes through point M(−2, 6) is x = -2.

Answer:

The equation of a straight line is:

y = mx + b;

y, x are variables, m is the slope of the line and b is the y intercept.

The slope of a vertical is undefined. Since the line passes through the point M(−2, 6), hence the equation of the vertical line is:

x = -2

The model which properly represent the information in given axioms is Cross geometry (+).

In the given question we have following information,

by using the above axioms we draw a geometry of Cross sign Geometry as seen above .

We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .

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Yes, a baseball fit in box A.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m³, cm³, in³, etc.

Volume is simply the amount of space a three-dimensional solid takes up. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.

Given:

The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches.

So, the maximum value of Circumference

2πr = 9.5

r= 9.5/ 2 x 3.14

r = 1.472 inch

So, Volume of ball = 4/3 πr³

Volume of ball = 4/3 x 3.14 x (1.472)³

Volume of ball = 13.36 inch³ < 64 inch³

Hence, it will fit inside the box.

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Answer:

<ABD = 67.17

Step-by-step explanation:

Comment

This requires 2 steps.

Finding <A

<A is found by taking the inverse tangent of the ratio 8/19.

<A = tan-1*(8/19)

<A = 22.83 degrees. We'll round it later.

Finding <ABD

You have to use 2 facts here.

All triangle angles add up to 180 degrees.

You find the third angle by subtracting the other 2.

<A = 22.83                                       Found above

<ADB = 90 degrees                        Given

<ABD = ?

Equation

< A + <ADB + <ABD = 180

Solution

22,83 + 90 + <ABD = 180                 Combine the left

112.83 + <ABD = 180                         Subtract 112.83 from both sides.

112.83-112.83 +<ABD = 180 - 112.83  Combine

<ABD = 67.17

The answer to the nearest degree is 67.

11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.

Given that,

35 percent of the 80 kids in the group are girls. 9 of the female students selected volleyball as their preferred sport.

We have to find what percentage of the female students chose volleyball.

The total children's are 80.

The 35% are girls.

9 have selected the volleyball

So,

9/80

0.1125

The percent is

11.25%

Therefore, 11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.

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A system of inequality to represent the maximum amount of flooring needed is c + h ≥ 2000.

A system of inequality to represent the maximum amount of money wants to spend is 4.50c + 8.25h ≥ 10,000.

In order to solve this word problem, we would assign variables to the number of square feet of carpet and the number of square feet of hardwood for the given flooring area, and then translate the word problem into an algebraic inequality as follows:

For the maximum amount of flooring needed, we have:

c + h ≥ 2000

For the maximum amount of money, we have:

4.50c + 8.25h ≥ 10,000.

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The answer is not a linear function, and the evaluation of the partial derivatives was done to a point. Thus, options (a) and (c) are correct. The correct equation for the tangent plane is  z = 3x - 108y - z + 241 = 0.

In a given point (x₀, y, z₀) the equation of the tangent plane to a surface given by the function S = f(x, y)can be obtained by

z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀) ... (i)

where  f ₓ (x₀, y₀, z₀) and fᵧ (x₀, y₀, z₀) (y - y₀) are the partial derivatives of f(x, y) with respect to x and y respectively. These two derivatives are evaluated at the point (x₀, y₀, z₀) .

Thus, we need to find two missing inputs, the z₀ coordinate and the two partial derivatives, in our problem in order to use equation (i).

In the case of z₀, evaluation of the given function gives us z = -80.

The partial derivatives are thus-

δf(x,y) / δx = fₓ (x, y) = 3x²

fₓ (x₀, y₀) = fₓ (1, 3) = 3

δf(x,y)/δxy= fᵧ (x, y) = -4y³

fᵧ (x₀, y₀) = fᵧ (1, 3) = -108

Now, arranging these values in equation (i) we obtain:

z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀)

z +80 = 3x² (x -1) - 4y³ (y - 3)

z = -80 +3x² (x -1) - 4y³ (y - 3)

Now, we will substitute the values of the partial derivatives at the given point:

z = -80 + 3x² (x -1) - 4y³ (y - 3)

z = 3x² (x -1) - 108 (y - 3)

z = 241 + 3x -108y

i.e., 3x - 108y - z + 241

Thus, the correct equation is 3x - 108y - z + 241.

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The complete question is-

A student was asked to find the equation of the tangent plane to the surface z = x³−y⁴ at the point (x, y) = (1, 3). The student's answer was z = −80 + 3x²(x−1)−(4y³)(y−3).

(a) At a glance, how do you know this is wrong? What mistakes did the student make? Select all that apply. A. The (x - 1) and (y - 3) should be x and y. B. The -80 should not be in the answer. C. The partial derivatives were not evaluated at this point. D. The correct answer is not a linear function. E. All of the above.

(b) What is the correct equation for the tangent plane? z=

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The change in the amount of seed in the feeder after 7 days is 78.75 ounces.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.

For example, if you ran 80 meters in 10 seconds, you ran on average 8 meters in 1 second

To find the rate at which the amount of seed decreases.

11 1/4 ounces = 5 days

Dividing both sides of the equation by 5.

11 1/4 ounces = 1 day

Multiplying 7 on both sides to get the number for 7 days

7 x 11.25 ounces = 7 days

78.75 ounces  = 7 days

If the amount of seed in a bird feeder decreases by 11 1/4 ounces in 5 days, the amount of seed decreases by 78.75 ounces.

The change in the amount of seed in the feeder in 7 days is 78.75 ounces.

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The number of donuts that can be purchased for $10 is 20.

The total cost of Mrs. Goodwin's donut purchase varies directly with the number of donuts purchased. The total cost of 15 donuts was $7.5. We need to find out the number of donuts that can be purchased for $10.

Let the number of donuts, price, and constant of proportionality be represented by the variables "n", "p", and "k", respectively.

The price is directly proportional to the number of donuts purchased.

p ∝ n

We will remove the proportionality sign.

p = k*n

7.5 = k*15

k = 1/2

The equation is p = (1/2)n. We will now calculate the number of donuts that can be purchased for $10.

p = (1/2)n

10 = (1/2)n

n = 10*2

n = 20

Hence, the number of donuts that can be purchased for $10 is 20.

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The equation representing the elevation of the loon and the time of the dive is 3x-2y = 0, and the Loon has been diving for 14.67 seconds.

The red throated loon dived down to a distance of 12 feet under the water in 8 seconds.

We can assume that the loon is diving at a constant rate.

The relation between the elevation wise of the loan after 1 second into the dive can be represented by the linear equation which has the slope,

Slope = 12/8

Slope = 3/2

Now as we have the slope of the equation we can write the equation by using the point slope form, with the point, (8,12)

(y - 12)/(x - 8) = 3/2

2y - 24 = 3x - 24

3x - 2y = 0

This is the equation that represent the elevation y of the loan after x seconds.

When the elevation of The Loon is 22 feet,

We can put y = 22,

3x = 2(22)

x = 14.67 seconds.

So, the loon has been diving for 14.67 seconds.

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The inequality of the graph represented in the figure is y ≥ 1/2x

The graph represents the given parameter

On the graph, we have the following points

(x, y) = (0, 0) and (2, 1)

This can be re-expressed as

(x, y) = (2, 1)

The slope is then calculated as

Slope = y/x

This gives

Slope = 1/2

The equation is then calculated as

y = Slope * x

So, we have

y = 1/2x

On the graph, we can see that the upper part of the graph is shaded and the line is a thick line

This means that the inequality expression is ≥

So, we have

y ≥ 1/2x

Hence, the inequality of the graph is y ≥ 1/2x

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The monthly budget for rent is $1,627.33 ≤ m ≤ $2,441.00

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

Let m represent the monthly rent of the shop.

The average yearly revenue is $195,280. Hence:

Monthly revenue = $195,280 / 12 = $16273.33

If the monthly budget for rent is 10%, hence:

m = 10% of $16273.33 = 0.1 * $16273.33 = $1627.33

If the monthly budget for rent is 15%, hence:

m = 15% of $16273.33 = 0.15 * $16273.33 = $2441.00

$1,627.33 ≤ m ≤ $2,441.00

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The residual of a theatre performance with a revenue of $700 and 70 seats occupied is 45.

From the information illustrated, the theater director recorded the number of seats occupied at past performances and the total revenue per performance.

The equation is given as:

y = -325 + 14x

y = actual performance for 70 seats occupied

For x = 70

y = -325 + 14x

= 325 + 14(70)

= -325 + 980

= 655

Therefore, the residual will be:

= 700 - 655

= 45

The residual is 45.

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Ty has  2 5/6 pounds of coffee left after giving 5/6 pounds of coffee to his grandma

Fraction is a numerical quantity that is not a whole number

From the question,

Ty bought 3 4/6 pounds of coffee

converting 3 4/6 to improper fraction

we have 22/6

Ty gave his friend 5/6 pound of coffee to his grandma

To estimate how much coffee Ty has left

We substract Coffee given to his grandma from Coffee bought

That is,

22/6 - 5/6

= 17/6

= 2 5/6 pounds of coffee left

Ty has 2 5/6 pounds of toffee left. He gave 5/6 of what he bought to his grandma.

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The solution of the system of equation by substitution is x = 3 and y = -1.

System of equation can be solved using different techniques such as substitution method, elimination method and graphical method.

Let's solve the system of equation by substitution method

Therefore,

3x + 2y = 7

x = 3y + 6

Substitute equation(ii) in equation(i)

3(3y + 6) + 2y = 7

9y + 18 + 2y = 7

9y + 2y + 18 = 7

11y = 7 - 18

11y = -11

y = -11 / 11

y = -1

Hence, let's find x

x = 3(-1) + 6

x = -3 + 6

x = 3

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