Factorise 8x + 12
Thankssssss

Using the greatest common factor, it is found that the greatest possible number of footballs that each could have received is of 6.

In this problem, the amounts of footballs are of 42 and 54, hence:

42 - 54|2

21 - 27|3

7 - 9

Then, gcf(42, 54) = 2 x 3 = 6, which means that the greatest possible number of footballs that each could have received is of 6.

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Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

The quadrilateral QRST is a trapezoid and not an isosceles trapezoid.

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.

Given that, a quadrilateral QRST has vertices Q(−1,0), R(2,2), S(5,0), T(−1,−4).  

We need tof verify that it is a trapezoid or not, we will find slopes of each side,

Slope = y₂-y₁ / x₂-x₁

Slope QR = 2-0 / 2+1 = 2/3

Slope RS = 0-2 / 5-2 = -2/3

Slope ST = -4-0 / -1-5 = 2/3

Slope QT = -4/0 = not defined

QR ║ ST

Since, two slope are equal therefore, the quadrilateral QRST is a trapezoid

Finding the distance between QS and TR

QS = √(5+1)²+(0-0)² = 6 units

TR = √(-1-2)²+(-4-2)² = √9+36 = √45 = 6.70

Since, QS ≠ TR, it is not an isosceles trapezoid.

Hence, the quadrilateral QRST is a trapezoid and not an isosceles trapezoid.

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The expression of a function is
(a) {"++", "+-", "-+", "--"}

(b) {"000", "001", "010", "011", "100", "101", "110", "111"}

(a) Roster notation is used to express a set of elements in a compact form. In this case, A is the set {+, -}, and A^2 is the set of all possible ordered pairs of elements from A. This set can be expressed using roster notation as {"++", "+-", "-+", "--"}. The double symbols indicate the two elements of each ordered pair.

(b) Here, A is the set {0, 1}, and A^3 is the set of all possible ordered triplets of elements from A. This set can be expressed using roster notation as {"000", "001", "010", "011", "100", "101", "110", "111"}. The triple symbols indicate the three elements of each ordered triplet.

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Answer:

Option 3

Step-by-step explanation:

\(\left(x+3\right)^{\frac{1}{3}}+3\)

Answer:

option 4 on edg

Step-by-step explanation:

y=3(x+3) +3

The required value of h, representing the height of the three-dimensional rectangle, is 12.

The diagonal of a three-dimensional rectangle is defined by the equation d² = x² + y² + h². To solve for h, we can rearrange the equation as follows:

h² = d² - x² - y²

Given the values d = 13, x = 3, and y = 4, we can substitute them into the equation:

h² = 13² - 3² - 4²

h² = 169 - 9 - 16

h² = 144

Taking the square root of both sides, we find:

h = 12

Therefore, the value of h, representing the height of the three-dimensional rectangle, is 12.

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The solution is

a) The number is 6

b) The equation of the parabola is y = x² + 4x + 96 with vertex ( -2 , 92 ) and the y intercept is ( 0 , 96 ) and the axis of symmetry is x = -2

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

a)

Let the equation be represented as A

Now , the value of A is

Let the number be = n

A = Two-fifth of the sum of a number and 24 is equal to 5 times the number decreased by 18

Substituting the values in the equation , we get

2/5 ( n + 24 ) = 5n - 18

On simplifying the equation , we get

Multiply by 5 on both sides of the equation , we get

2 ( n + 24 ) = 25n - 90

2n + 48 = 25n - 90

Subtracting 2n on both sides of the equation , we get

23n - 90 = 48

Adding 90 on both sides of the equation , we get

23n = 138

Divide by 23 on both sides of the equation , we get

n = 6

Therefore , the number is 6

b)

The equation of parabola is given as

y = x² + 4x + 96

Now , the equation can be simplified as

y = (x + 2)² + 92

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

Substituting the values in the equation , we get

The vertex of the parabola is P ( -2 , 92 )

The y intercept of the parabola is ( 0 , 96 )

The axis of symmetry of parabola is x = -2

Hence , the equation of parabola is y = (x + 2)² + 92

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Based on the intersecting secants theorem:

a. CG*CE = CH*CD

b. length of DH = 10 in.

When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.

a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:

CG*CE = CH*CD

b. Given the following lengths:

CG = 3 in, CH = 2 in, and GE = 5 in

CE = CG + GE = 3 + 5 = 8 in.

CD = CH + DH = 2 + DH

Substitute into CG*CE = CH*CD:

3*8 = 2*(2 + DH)

24 = 4 + 2DH

24 - 4 = 2DH

20 = 2DH

20/2 = DH

DH = 10 in.

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Answer:

(a) Yes, E and F are independent events.

(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4

Answer:

Step-by-step explanation:

C I took the test

The equation of Finley's annual salary represents 57,000(1.04n – 1) during the nth year.

The percentage is defined as ratio expressed as a fraction of 100.

Finley was paid an annual salary of $57,000

with a 4% raise for each following year

Finley's annual salary, during the 2th year

⇒ 4% of 57,000 + 57,000

⇒ (0.04)57,000 + 57,000

⇒ 2280 + 57,000

⇒ 59280

Finley's annual salary, during the 2th year

Determine the difference between year 2 and year 1 salary.

Rate of change = 4% of 57,000 - 57,000

Rate of change = (0.04)57,000 - 57,000

Rate of change = 57,000(0.04 - 1)

Finley's annual salary, during the 5th year

Determine the difference between year 5 and year 4 salary

⇒ 57,000(0.04(5) - 1)

That's the constant.

Finley's annual salary, during the nth year

So, f (n) = 57,000(1.04n – 1)

Hence, the equation of Finley's annual salary represents 57,000(1.04n – 1) during the nth year.

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Answer:

1.5x = 30 - 1.5

Step-by-step explanation:

30 grams minus the weight of the bag 1.5

1.5x x is the number of marbles and the bag so take 1 out and you have an answer which is 28.5 19 marbles

The best interpretation for the expression 85h + 75 is;

The charge for each hour worked is $85

The initial charge before commencement of work per hour is $75

The general formula of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, the slope may also be called the rate of change of the output with the input while the y-intercept represents the initial value or the value of the output when the input is zero.

Now, we are given the equation for total bill as;

T = 85h + 75

where h is number of hours worked

Thus;

The charge for each hour worked is $85

The initial charge will be $75 before commencement of work per hour.

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The given scenario, where a sample of teen drivers at a high school is surveyed about their engagement in the illegal activity of texting while driving, is an example of Selection bias. Option C

Selection bias occurs when the process of selecting participants for a study or survey is not random or representative of the entire population.

In this case, the sample consists only of teen drivers at a high school, which may not accurately represent all teen drivers in the broader population. The sample is limited to a specific group, which can introduce bias and affect the generalizability of the results to the wider population of teen drivers.

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Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

If the null hypothesis is correct, the probability that the test will result in a type 1 mistake is what is known as the alpha level for a hypothesis test. In other words, even in the absence of a treatment effect, the alpha level impacts the likelihood of collecting sample data in the critical zone.

The alpha level establishes the boundaries for identifying the key area that results in "extremely unlikely" or significant results that deviate from the null hypothesis. The likelihood of making a Type I error is one in twenty, according to researchers who use an alpha value or level of significance of.05.

The chance of rejecting the null hypothesis when it is true is known as the significance level, which is alternatively written as alpha or. For instance, a significance level of 0.05 represents a 5% probability of assuming the existence of a difference when none actually exists.

Hence we get the required answer.

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Without knowing the total number of coins or the ratio between one dollar and two dollar coins in the jar, we cannot accurately determine the number of two dollar coins.

Amadi has a jar with both one dollar and two dollar coins. The question is asking how many of the coins in the jar are two dollar coins.
To determine the number of two dollar coins, we need more information. The question does not provide any details about the total number of coins or the ratio between one dollar and two dollar coins in the jar. Without this information, it is not possible to give an accurate answer.
If we assume that the jar contains a total of 100 coins, we can use algebra to solve for the number of two dollar coins.

Let's say the number of two dollar coins is x. Then, the number of one dollar coins would be 100 - x.
Since the value of the two dollar coins is double the value of the one dollar coins, we can set up the equation 2x + 1(100 - x) = total value of coins.
Simplifying the equation, we get 2x + 100 - x = total value of coins.
Combining like terms, we have x + 100 = total value of coins.
Since we don't know the total value of coins, we cannot solve for x. Therefore, we cannot determine the number of two dollar coins without additional information.

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Answer:

the answer is y=3 I hope I helped

Answer:

\(x = 3\)

Step-by-step explanation:

\(y + 3 = - y + 9\)

\(y + y = 9 - 3\)

\(2y = 6\)

\( \frac{2y}{2} = \frac{6}{2} \)

\(x = 3\)

By placing the given value in equation , we get u + v - 4u = (-20, 13)

A physical quantity that has both directions and magnitude is referred to as a vector quantity.

A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.

To evaluate u + v - 4u, we first need to find the vector 4u, which is obtained by multiplying the vector u by the scalar 4:

4u = 4(5,-2) = (20,-8)

Now, we can add u and v, and subtract 4u from the result:

u + v - 4u = (5,-2) + (-5,7) - (20,-8)

= (5 - 5 - 20, -2 + 7 + 8)

= (-20, 13)

Therefore, u + v - 4u = (-20, 13).

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Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Step-by-step explanation:

here is the answer to your question

A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

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Answer:b

Step-by-step explanation:mark brainliest

Answer:

f(1) = -6

f(2) = -4

f(n) = f(n - 2) + f(n - 1)

=> f(3) =  f(2) + f(1) = -6 + (-4) = -10

Hope this helps!

:)

Answer:

f(3)=-10

Step-by-step explanation:

Khan

Answer:

put your first point at 7 in y axis that point go down 3 to the rights side 1 and your point should be at (1,4) then connect the dots and that's how you graph it

Step-by-step explanation:

The equation of the line y = - 3x + 7 is drawn below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

The equation of the line is given below.

y = -3x + 7

Convert the line into intercepts form, then we have

y = - 3x + 7

3x + y = 7

x / (7/3) + y / 7 = 1

The equation of the line is drawn below.

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For the given function, the value of h(t)=\t+2\+3 is for f(6) = 7

A function is a means to explain what takes place with an input variable to produce an output result. We may find a set of output values if we consider a straightforward function, like multiply by three. Algebra can be used in place of Function = multiply by 3.

Before the t and after the 2, I'm going to presume that's an absolute value sign.

Absolute value brackets are treated similarly to parentheses, with the exception that the negative sign is removed once the contents have been thoroughly simplified. (If you still have variables, don't do that.)

In this instance, t equals 6 plus 2 equals 8. 8 has an absolute value of 8. Add 3 is 11.

so,

h(6) = 11.

2 + -6 equals -4. 4 is -4's absolute value. Add 3 is 7.

so,

h(-6) is 7.

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Probability = # of desired options / # of total options

Our desired option is blue and there are 9 blue marbles in the bag.

There are 32 total marbles (options) in the bag.

P(blue) = 9 / 32 = 0.28125 = 28.125%

Hope this helps!

The given assertion states that the length of BD in its simplest radical version is 7/√2.

A triangle is indeed a 3-sided shape that is occasionally (though not frequently) referred to as the trigon. There are three edges and three angles in every triangle, some of which could be the same.

Since BD is an altitude of the right triangle ABC, we can use the Pythagorean Theorem to find the length of BD. First, let's determine the size of AC:

AC² = AD * DC = 7 * 5 = 35

When we square the two edges, we obtain:

AC = √35

Now, we can use the fact that BD is an altitude to write:

BD = (AC * AD) / hypotenuse

where hypotenuse is the length of BC.

Using the Pythagorean Theorem, we can find the length of BC:

BC² = AC² + AB²

Since triangle ABC is a right triangle, we have AB = BC, so we can write:

BC² = AC² + BC²

Simplifying, we get:

BC² / AC² = 2

When we square the two edges, we obtain:

BC / AC = √2

Multiplying both sides by AC, we get:

BC = AC * √2 = √35 * √2 = √70

Now, we can substitute the values of AC, AD, and BC into the formula for BD:

BD = (AC * AD) / BC = (√35 * 7) / √70 = 7 / √2

Therefore, the length of BD in simplest radical form is 7 / √2.

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