Perform the indicated operation.
f(x) = −3x² + 3x; _g(x) = 2x+5
(ƒ + g)(3)

The solutions to the equation [tex]15z^2 +6z -8 =4z[/tex] are z = 2/3 or z = -4/5.

To solve the quadratic equation [tex]15z^2 +6z -8 =4z[/tex], we first need to rearrange it into standard form:

[tex]15z^2 + 2z - 8 = 0[/tex]

Now we can apply the quadratic formula:

z = (-b ± √(b² - 4ac)) / 2a

where a = 15, b = 2, and c = -8.

Plugging in these values, we get:

z = (-2 ± √(2² - 4(15)(-8))) / (2(15))

z = (-2 ± √(4 + 480)) / 30

z = (-2 ± √484) / 30

z = (-2 ± 22) / 30

So z equals either (-2 + 22)/30 = 2/3 or (-2 - 22)/30 = -4/5.

Therefore, the solutions to the equation 15z² +6z -8 =4z are z = 2/3 or z = -4/5.

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He needs an additional $0.23 to buy the football with the coupon after the discount coupon.

A discount is a reduction in the price of a product or service. It is often used as a marketing tool to attract customers and increase sales. Discounts can be expressed as a percentage or a dollar amount.

The discounted price is the price of a product or service after a discount has been applied. The discount is usually expressed as a percentage or a dollar amount and is subtracted from the original price.

In the given question,

The discount Justin can get is 12% of the original price, which is:

0.12 x 22.99 = 2.76

So the discounted price of the football is:

22.99 - 2.76 = 20.23

Since Justin has exactly $20, he doesn't have enough money to buy the football with the coupon. He needs:

20.23 - 20 = 0.23

So he needs an additional $0.23 to buy the football with the coupon.

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Answer: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.

Step-by-step explanation:

The graph shows two pieces of the function, with one increasing from the point (0, 0) through the point (12, 18) to the endpoint (24, 36) and the other increasing from the point (24, 36) through the point (48, 60) to the right.

This means that the first 24 cupcakes cost $1.50 each and all cupcakes after that cost $1 each, as shown by the first piece of the function. The second piece of the function shows that the price per cupcake does not increase after 36 cupcakes, so option 3 and option 4 can be eliminated.

Therefore, the correct answer is: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.

The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8

The slope-intercept form of a line is given by

                   y = mx + c

Where 'm' is slope and c in y-intercept

Here we have

The coordinate of points (0, -8) and slope (m) = 3/2

As we know the formula for slope intercept form is  y = mx + c

Where 'm' is the slope

=> y = (3/2)x + c

=> -8 = 3/2(0) + c

=> c = - 8

Hence, Equation of the line is y = 3/2(x) + (-8)

=> y = 3x/2 - 8

The equation can be rewritten using function notation as follows

=> f(x) = 3x/2 - 8

Therefore,

The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8

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The total number of eggs is 1542.

To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:

35/100 = 540/x

where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:

35x = 54000

x = 54000/35

x = 1542.86

Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.

To find the number of eggs that are not sold, we can subtract the number of eggs sold from the total number of eggs:

1542 - 540 = 1002

Find out more about The total number of eggs is 1542.

To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:

35/100 = 540/x

where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:

35x = 54000

x = 54000/35

x = 1542.86

Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.

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Answer:4x + 3x + 2x - 4 - 3

Step-by-step explanation:Hope this helps

Answer: A - addition property of equality

Explanation: because -8x - 42 = -22

+42 +42

____________

-8x = 20

__ __

-8 -8

x = -2.5

Answer:

Step-by-step explanation:

Answer:

5 seconds

Step-by-step explanation:

when the phone hits the ground then y = 0 , that is

- 16t² + 400 = 0 ( subtract 400 from both sides )

- 16t² = - 400 ( divide both sides by - 16 )

t² = 25 ( take square root of both sides )

t = [tex]\sqrt{25}[/tex] = 5

the phone hits the ground after 5 seconds

Answer:

5 seconds

Step-by-step explanation:

y = [tex]-16t^{2} + 400 \\[/tex]

Make t the subject:

[tex]16t^{2} = -400\\t^{2} = \frac{400}{16} = 25\\ t = \sqrt{25} = 5[/tex]

Therefore the answer is 5 seconds

Check the picture below.

[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]

The value of x is 4.5 rounded to the nearest tenth.

Tangent of a circle is defined as the line which passes through exactly one point on the circle.

Secant of a circle is the line which passes through two points on the circle.

Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.

Using the theorem, we can say here that,

(8 + 2) 2 = x²

x² = 10 × 2

x² = 20

x = √20

x = 4.472 ≈ 4.5

Hence the value of x is 4.5.

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The sides of 15mm, 28mm and 11mm are the sides of a triangle.

To determine if three given lengths can form a triangle, we can apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

If we add the two shorter sides together, we get [tex]15 + 11 = 26[/tex]  . This sum is greater than the longest side, which is [tex]28[/tex] . Similarly, if we add the two smaller sides to the longest side, we get  [tex]11 + 28 = 39[/tex] and  [tex]15 + 28 = 43[/tex] , which are both greater than the remaining side.

Therefore, the three given lengths satisfy the Triangle Inequality Theorem and can form a triangle.

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Answer: I'm pretty bad at math, but I made it more simple for you :)

Step-by-step explanation:

The answer is y = 4 + 5x/4

I hope it helped a bit sorryy

The simplified form of the expression the sum of 6. 6 and 3. 2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6 is -0.3267

To simplify this expression, we'll work from the inside out, using the order of arithmetic operation

First, we'll evaluate the expression inside the parentheses:

(2 - 5 + 6) = 3

Next, we'll calculate the squared difference of 2 and 5:

(2 - 5)^2 = (-3)^2 = 9

Then, we'll subtract the result from step 2 from the result of step 1:

3 - 9 = -6

Next, we'll calculate the sum of 6.6 and 3.2:

6.6 + 3.2 = 9.8

Finally, we'll divide the result from step 4 by 5 times the result from step 3:

9.8 / (5 × -6) = 9.8 / -30

= -0.3267 (rounded to four decimal places)

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1) Birth order among siblings in a family: Nominal level of measurement

2) Volume of water used by a household in a day: Ratio level of measurement

3) Highest degree conferred (high school, bachelor's, and so on): Ordinal level of measurement

4) Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years: Interval level of measurement

1) Birth order among siblings in a family: This variable is measured at the nominal level of measurement, as there is no inherent order or ranking to the categories

2) Volume of water used by a household in a day: This variable is measured at the ratio level of measurement, as it has a true zero point (i.e., no water usage) and the values can be compared in terms of ratios

3) Highest degree conferred (high school, bachelor's, and so on): This variable is measured at the ordinal level of measurement, as the categories have an inherent order or ranking (e.g., a bachelor's degree is higher than a high school diploma, but it does not necessarily indicate that someone with a bachelor's degree is "twice as educated" as someone with a high school diploma).

4) Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years: This variable is measured at the interval level of measurement, as the values have a meaningful order and distance between them (i.e., the difference between 4 years and 5 years is the same as the difference between 7 years and 8 years). However, there is no true zero point, as "zero years old" is not a meaningful category in this context.

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Answer:

The lines that go through all 3 sides of the triangle mean the angles are all equal. Since a triangle is 180 degrees, to find a single angle, we must divide by 3.

180 degrees / 3 = 60 degrees

Solve for X

60 = (2x + 10)  

-10 from both sides:

50 = (2x)

x = 25

Solve for Y

60 = (3y + 3)

-3 from both sides:

57 = (3y)

y = 19

Hope that helps

Cullumber Beauty Corporation's break-even point in sales dollars for the year 2022 is $1,200,000.

What is the break-even point?

The break-even point is defined as the point at which a company's overall costs are equal to its total revenue. The company neither makes a profit nor incurs a loss at this point. The break-even point in dollar amount is calculated by dividing the fixed costs by the contribution margin ratio.The given information is:Net sales revenue = $3,500,000Commission expense = 21% of sales = 0.21 * $3,500,000 = $735,000Net sales revenue − Variable costs = Contribution marginContribution margin − Fixed costs = Operating incomeBreak-even point is the level of sales revenue required to cover all of a company's costs. At this point, the operating income is zero. The fixed expenses are divided by the contribution margin ratio to find the break-even point in dollars.

Fixed expenses = [tex]$900,000[/tex]Net sales revenue − Variable costs = Contribution marginContribution margin − Fixed expenses = Operating income0 = Net sales revenue − Variable costs − Fixed expenses0 = [tex]$3,500,000 − (0.75 × $3,500,000) − $900,0000.25 × $3,500,000 = $900,000$875,000 = $900,000[/tex] − Commission expense[tex]$3,500,000 − $875,000 = $2,625,000[/tex]

Break-even point = $900,000 ÷ (0.75 × $3,500,000)Break-even point = $900,000 ÷ $2,625,000Break-even point = 0.34 ≈ 34%Break-even point in sales dollars = 34% × $3,500,000Break-even point in sales dollars = $1,190,000 ≈ $1,200,000Therefore, Cullumber Beauty Corporation's break-even point in sales dollars for the year 2022 is $1,200,000.

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If at a school of 550 children 80% walk to school, the 110 children come to school by other means.

If 80% of the children walk to school, then the remaining 20% of children must arrive at school by other means (such as being driven by a parent, taking public transportation, etc.).

To find out how many children come to school by other means, we can use the following formula:

Number of children who come to school by other means = Total number of children x Percentage who don't walk to school

In this case, we have:

Number of children who come to school by other means = 550 x 20% = 110

Therefore, 110 children come to school by other means.

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The given question is incomplete, the complete question is:

At a school of 550 children 80% walk to school, how many comes in other way ?

The minimum number of moves required to complete the Tower of Hanoi game is related to the number of disks, and can be described by the equation m = [tex]2^n - 1[/tex].

Let n be the number of disks and m be the minimum number of moves required to complete the Tower of Hanoi game. Renae's observations suggest that the equation m = [tex]2^n - 1[/tex] describes this pattern.

When n=1, the minimum number of moves required to complete the game is m=1. Plugging this value into the equation m=[tex]2^n-1[/tex]gives m=[tex]2^1-1[/tex]=1. Therefore, the equation holds true for n=1.

Assume that the equation holds true for n=k. That is, m=[tex]2^k-1[/tex] is the minimum number of moves required to complete the game with k disks.

Now, consider the case where n=k+1. This requires a minimum of m=[tex]2^k-1[/tex] moves, according to the equation. Then, the largest disk can be moved to the ending peg in one move. Finally, the k disks that were moved to the spare peg must be moved to the ending peg, which requires another minimum of m=[tex]2^k-1[/tex] moves.

Thus, the total minimum number of moves required to complete the game with k+1 disks is:

m = [tex]2(2^k-1) + 1[/tex]

m = [tex]2^(k+1) - 2 + 1[/tex]

m = [tex]2^(k+1) - 1[/tex]

This is the same as the equation we started with, but with k+1 in place of n. Therefore, the equation holds true for all positive integers n by mathematical induction.

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Answer:

all you gotta do is mirror that half u and make it a full u

and since the points it intersects at is (1,-1) plot the other half on (1,1)

The missing value is approximately 64.12 degrees, which is closest to option D: 21.25 using inverse cos.

The inverse cosine (or arccosine) of both sides of the equation must be taken in order to locate the missing value in the equation cos = 7/18 to the closest tenth. We will then be able to convert the value of to degrees and round it to the closest hundredth using the value of the radian that is produced.

cos θ = 7/18

= arccos(7, 18, 7)

A 1.1181 radian angle

We can use the conversion factor /180 to convert radians to degrees.

θ = 1.1181 × 180/π

64.12 degrees.

As a result, the figure that is lacking is roughly 64.12 degrees, which is closest to choice D: 21.25.

Due to the periodic nature of the cosine function, there are often two solutions when determining the inverse cosine of a value. But, since the problem states that we should round to the closest hundredth, which suggests a single answer, we can disregard the second option in this instance. By reinserting the value we discovered into the original equation and making sure it equals 7/18, we can further confirm that the result is accurate.

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The correlation coefficient that reflects the strongest relationship is +0.25, the correct option is b.

EXPLANATION:

The correlation coefficient ranges from -1 to +1.

The magnitude (absolute value) of the correlation coefficient indicates the strength of the relationship, with values closer to -1 or +1 indicating a stronger relationship.

Therefore, the correlation coefficient that reflects the strongest relationship is +1.23.

However, since this value is greater than +1, which is not possible, it seems to be an invalid value.

Among the given options,

The correlation coefficient that reflects the strongest relationship is b) +0.25.

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The equation of the line that contains the point (-6, 5) and is parallel to x + 2y = 14 in slope-intercept form is y = (-1/2)x + 2.

Due to their similar slopes, parallel lines move in the x direction with the same rate of change. If we know the slope of a line, we can use that slope to determine the slope of any line that is parallel to it. The point-slope form of a line can be used to get the equation of a line that is parallel to a given line and passes through a specified point.

The given equation of the line is:

x + 2y = 14

Rewriting the equation in standard form we have:

y = (-1/2)x + 7

where, -1/2 is the slope of the line.

The slope of two parallel lines are equal. Thus the slope of new line is m = -1/2.

Now, using the point slope form:

y - y1 = m(x - x1)

Substitute the values:

y - 5 = (-1/2)(x - (-6))

y - 5 = (-1/2)x - 3

y = (-1/2)x + 2

Hence, the equation of the line that contains the point (-6, 5) and is parallel to x + 2y = 14 in slope-intercept form is y = (-1/2)x + 2.

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The true statements are:

a) P(3) = 4/52 or 1/13

b) P(black number cards) = 18/26 or 9/13

c) P(red ace) = 2/52 or 1/26

d) P(face card) = 12/52 or 3/13

Probability deals with the study of random events and their likelihood of occurrence. It is computed by dividing the proportion of positive results by the total number of possibilities that could occur.

As we know that the standard deck card has 52 cards, in which 26 red cards (13 are diamonds, 13 are hearts) 26 black cards (13 are clubs, 13 are spades). Where 12 cards are face cards, 36 cards are number cards.

a) P(3) = 4/52 or 1/13: This is true. There are four 3s in a standard deck of 52 cards, so the probability is 4/52 or 1/13.

b) P(black number cards) = 18/26 or 9/13: This is a true. There are 26 black cards, out of those there are 9+9=18 black number cards (2 through 10), so the probability of drawing a black number card is 18/26 or 9/13.

c) P(red ace) = 2/52 or 1/26: This is true. There are two red aces in a standard deck of 52 cards, so the probability of drawing a red ace is 2/52 or 1/26.

d) P(face card) = 12/52 or 3/13: This is a true. There are twelve face cards in a standard deck of 52 cards, so the probability of drawing a face card is 12/52 or 3/13.

e) P(even number card) < P(odd number card): This is a false. There are 5×4=20 even number cards (2, 4, 6, 8, and 10 of each suit) and 4×4=16 odd number cards (3, 5, 7, 9 of each suit) in a standard deck of 52 cards. Therefore, the probability of drawing an even number card, (20/52 or 5/13) is greater than the probability of drawing an odd number card, (16/52 or 4/13).

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Complete question-

The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small.

What does the "x is small" approximation mean? The x is small approximation does not mean that x is zero. If that were the case, the reactant and product concentrations wouldn't change from their initial values. The x is small approximation just means that when x is added or subtracted to another number, it doesn't change that number by very much. When does the "x is small" approximation work? The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small. What is the <5% rule? The x is small approximation must satisfy the <5% rule, whereby the x approximation divided by the number it was subtracted from is less than 5% (or 0.05). What is the method of successive approximation? The method of successive approximation is solving for x as if it were small, and then substituting the value obtained back into the equation (where x was initially neglected) to solve for x again. This can be repeated until the calculated value of x stops changing with each iteration, an indication that we have arrived at an acceptable value for x.

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The answer is one intersection.

What is a function?

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

The graph of the function f(x) = 0.8x is a straight line with slope 0.8 passing through the origin (0, 0). The graph of the function g(x) = ⌊x⌋ is the collection of all points (x, y) where y is the greatest integer less than or equal to x. This function is not continuous and has a discontinuity at each integer.

To find the intersections between the two graphs, we need to determine where the values of f(x) and g(x) are equal.

we need to find the integer values of x where 0.8x and x are equal.

0.8x = x

0.2x = 0

x = 0

Thus, the two graphs intersect at the point (0, 0). There are no other intersections between the two graphs, since they have different slopes and one is continuous while the other is not. Therefore, the answer is one intersection.

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Answer:

11.6 sq. inches

Step-by-step explanation:

The lateral area of a cone can be found using the formula:

L = πrℓ

where r is the radius of the circular base and ℓ is the slant height.

Substituting in the given values, we have:

L = 3.14 x 2.6 x 1.5

L ≈ 11.6

Rounding to the nearest tenth, the approximate lateral area of the cone is 11.6 square inches.