solve the equation -3 + 1/2n = 1/2 (-n + 14) in two different ways.

The piecewise function is:

f(x) = x + 1             if x < 2

f(x) = -7x + 42       if x > 5

On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).

On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).

That line passes through (-1, 0) and (0, 1), then the slope is:

a = (1 - 0)/(0 -(-1)) = 1

And the y-intercept is y = 1, then the equation of the line is:

y = x + 1

The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)

The slope is:

a = (0 - 7)/(6 -5) = -7

Then the line is something like:

y = -7*x + b

To find b, we use the point (6, 0)

0 = -7*6 + b

7*6 = 42 = b

Then this line is:

y = -7x + 42

Concluding, the piecewise function is:

f(x) = x + 1             if x < 2

f(x) = -7x + 42       if x > 5

The complete question is : Help please!! Express the function graphed on the axes below as a piecewise function.

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The distance between  the tent pole to the rope along the ground is 15 feet.

What is a cone?

A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.

Given that length of the tent pole is 8 feet.

The angle between the tent pole and the ground is 90°.

Thus the tent pole, the rope and the ground form a right angle triangle.

According too Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the legs.

Here the legs of the right angle triangle is the tent pole and the the distance the tent pole to the rope along the ground.

Assume that the distance the tent pole to the rope along the ground be x.

The length of the rope is 17 feet which is hypotenuse of the right angle triangle.

Therefore,

x² + 8² = 17²

x² + 64 = 289

x²  = 225

x = 15

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Answer: 15 feet

Step-by-step explanation:

first we grab 17 feet a square it

17^2 = 289

then we square 8 feet

8^2 = 64

subtract

289-64= 225

what squared equals 225?

15 does

Answer:

4

Step-by-step explanation:

Based on the given conditions, formulate:

16/6 ÷ 2/3

Divide a fraction by multiplying its reciprocal:

16/6 × 3/2

(16 × 3) ÷ (6 × 2)

48/12 = 4

Thus, Brett can make 4 smoothies with 2 4/6 cups of yogurt.

Answer:

23328

Step-by-step explanation:

since it is a geometrics sequence we will use the formula

[tex] {ar}^{n - 1} [/tex]

The first term(a) = 3

The second term = ar = 18

divide the first term and second term to find the common ratio

[tex] \frac{t2}{t1} = \frac{ar}{a} = \frac{18}{3} [/tex]

r = 6

Now lets find the sixth term

[tex]t6 = {ar}^{6 - 1} [/tex]

[tex]t6 = {ar}^{5} [/tex]

by substituting for the values

[tex]t6 = 3 \times {6}^{5} [/tex]

= 3 × 7776

= 23328

i hope this helped

Answer:

[tex]a_{6} = 23,328[/tex]

Step-by-step explanation:

⭐ Geometric Progression formula: [tex]a_{n} = a_1(b)^{n-1}[/tex]

We are given that [tex]a_{1}[/tex] = 3. Now, we need to find b.

b is the quotient of [tex]\frac{a__3}{a__2}[/tex].

Let's substitute the first term and common ratio into the formula.

[tex]a_n = 3(6)^{n-1}[/tex]

The problem wants us to solve for the 6th term, so we have to substitute 6 for n and solve.

[tex]a_6 = 3(6)^{6-1}\\a_6 = 3(6)^5\\a_6 = 3(7,776)\\a_6 = 23,328[/tex]

Step-by-step explanation:

this is a college question ? and you don't know how to do that ?

think back to elementary and middle school. and you had to use that all the way through high school as a very, VERY basic skill.

Focus !

g(3) just means that x = 3, and we need to replace every occurrence of x by 3. and then we calculate the result.

g(3) = 4×3 - 5 = 12 - 5 = 7

that's all to it.

Answer: 4 i think

Step-by-step explanation:

65=15y+5

65 - 5 = 15y +5 -5

60 = 15y

60/15 = 15y/15

4 = y

Answer: There are 95 tables in the middle group

Step-by-step explanation:

There are a total number of 250 tables.

There are three groups.

We know how many tables the left and right groups have

let x be the number of tables in the middle

75+80+x=250

155+x=250

x=95

a. The rational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 is 1/4.

b. The rational and irrational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 are 1/4 and ± √6.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A cubic polynomial function g(x) = 4x³ - x² - 24x + 6.

Therefore,

g(x) = 4x(x² - 6) - 1(x² - 6).

g(x) = (4x - 1)(x² - 6).

g(x) = (4x - 1)(x + √6)(x - √6).

Hence, x = 1/4, ± √6.

So, The roots of the polynomial are 1/4 and ± √6.

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The number from the expression is 22. 3

An algebraic expression can be defined as a mathematical expression that consists of variables, terms, constants, coefficients, and factors.

These expressions are also seen to be made up of mathematical or arithmetic operation, such as;

Some examples of algebraic expressions;

2x + 6

3x + 8

From the information given;

Let the number be x

Then'

3x - 17 = - 50

collect like terms

3x = 67

Make 'x' the subject

x = 22. 3

Hence, the value is 22. 3

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Answer:  12 row plans

The first seat has 2 possible options, the 2 directors. The second seat has another 2 options. With each director comes 2 options for the second seat, so 2 x 2=4 possible options for the 1st and 2nd seats. The third seat has 3 options. That means for each combination of the 1st and 2nd seat, there are 3 possible options. 4x3=12 combinations.

Step-by-step explanation:

The expression as a rounded decimal  is 1.23

From the question, we have the following parameters that can be used in our computation:

27/22

To start with, we evaluate the expression using a calculator

So, we have the following representation

27/22 = 1.22727272727

Next, we approximate to the nearest hundredth

So, we have the following representation

27/22 = 1.23

Hence, the approximated expression is 1.23

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The required number of new boys in a sports team is 62.

As mentioned in the question,  A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Given that the number of men is now 60% of the total members, how many of the 50 new members were women is to be determined,
Percentage of women, in the team = 100 - 60 = 40%
40% of total members are women = 35 + 50

Total members = 85 / 40%
Total member = 212
Number of new member that are boys = 212 - 85 - 65 = 62 boys

Thus, the required number of new boys in a sports team is 62.

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Answer:

Option 4

Step-by-step explanation:

The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).

hope this helps :)

Answer:

x=-2

y = 3× -2 + 4

y= -6 + 4

y = -2

A polygon is a plane shape with a minimum of three straight sides. Thus the appropriate answer are:

i. A and B Not Similar

ii. B and C Not Similar

iii. A and C Not Similar

Polygons are majorly plane shapes which have straight sides. They are named with respect to the number of their sides, and the minimum sides is three. Some common examples are: trigon (3 sides), octagon (8 sides), hexagon (6 sides), pentagon (5 sides) , etc.

Two or more shapes are said to be similar if and only if they have some common properties with respect to their sides or internal angles.

Considering the ratios of the sides of the given polygons, it can be deduced that:

i. A and B Not Similar

ii. B and C Not Similar

iii. A and C Not Similar

Thus none of the polygons are similar.

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The dimensions are 12 meter by 18 meter .

perimeter of rectangle = 2(length + width)

length and width of the  Luis plot by L and W, respectively.

We know that the perimeter, is 60 meters. So we can write:

2L + 2W = 60

Simplifying this equation, we can divide both sides by 2:

L + W = 30

now , area of the plot is 216 square meters:

L x W = 216

use substitution to solve for one of the variables. Let's solve for L in the first equation:

L = 30 - W

We can substitute this expression for L into the second equation:

(30 - W) x W = 216

[tex]W^2 - 30W + 216 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

W = [30 ± [tex]\sqrt{30^2 - 4 * 1 * 216}[/tex] / 2

Simplifying:

W = [30 ± 6] / 2

So  W = 18 or W = 12.

If W = 18, then L = 30 - 18 = 12.

If W = 12, then L = 30 - 12 = 18.

Therefore, the dimensions  are 18 meters by 12 meters or 12 meters by 18 meters.

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Kurt will eat 1/6 cups more than Danielle if Kurt ate 1/3 of a cup of nuts and Danielle ate 1/6 of a cup of nuts by using ratio and proportion concept.

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. For instance, if there is 1 boy and 3 girls, the ratio would be written as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.

A: b a/b is the ratio formula, which may be used to calculate any two values. A:b::c:da:b::c:da, on the other hand, is how the percentage formula is written. A ratio in mathematics displays the multiplicative relationship between two numbers.

Given,

A cup of nuts ate by Kurt=1/3

A cup of nuts ate by Danielle=1/6

(1/3)-(1/6)

=1/6

Therefore, Kurt will eat 1/6 cups more than Danielle.

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[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].

[tex]3/4x + 2/3y - 3/8x + 1/2y[/tex]

a) First, start by operating with the terms that contain the "x" variable.

[tex]3/4x- 3/8x\\ \\\frac{3}{4}x-\frac{3}{8}x\\ \\ \frac{3*2}{4*2}x-\frac{3}{8}x\\ \\\frac{6}{8}x-\frac{3}{8}x\\ \\x(\frac{6}{8} -\frac{3}{8} )\\ \\x(\frac{6-3}{8} )\\ \\x(\frac{3}{8} )\\ \\\frac{3}{8}x[/tex]

b) Start with terms containing "y".

[tex]2/3y+1/2y\\ \\\frac{2}{3}y +\frac{1}{2} y\\ \\\frac{2*2}{3*2}y +\frac{1*3}{2*3} y\\ \\\frac{4}{6}y +\frac{3}{6} y\\ \\y(\frac{4+3}{6})\\ \\y(\frac{7}{6})\\ \\\frac{7}{6} y[/tex]

[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].

The option that best describes the data is The data is band numerical

This kind of data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.

In this case the one variable is World History scores exam

Data that is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.

Numerical data, also known as quantitative data, is gathered in number form and differs from all other sorts of number data because it can be calculated mathematically and statistically.

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Kate and Miley sold 60 boxes of cookies in one hour.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b.

Given that,

Cookies sold by Kate in 45 minutes = 27 boxes.

Also,

Cookies sold by Miley in 30 minutes = 12 boxes.

To find the total boxes of cookies sold by girls in one hour,

Use ratio method,

Cookies sold by Kate in 3/4 hours = 27 boxes,

Cookies sold by Kate in 1 hour = 27 x (4/3) = 36

Cookies sold by Miley in 1/2 hours = 12 boxes,

Cookies sold by Miley in 1 hour = 12 x 2 = 24 boxes

Total cookies sold by Kate in Miley in one hour = 36 + 24 = 60

There are 60 boxes of cookies sold by the girls in one hour.

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This sample a simple random sample. It v a random sample.

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The measure of the other angle is 73°.

What are complementary angles?

Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.

How do you find a complementary angle?

Two angles are said to be complimentary if their sum is 90 degrees. So, to find the complement of an angle, subtract it from 90.

Here, we have

Given

Two angles are complementary. If one measures 17 degrees.

Complementary angles are two angles that add up to exactly 90 °.

∠A + ∠B = 90°

17 + ∠B = 90°

∠B = 90 - 17

∠B = 73°

Hence, the measure of the other angle is 73°.

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The correct answer is Option C. The proper decision, in this case, is  "Fail to reject H0. There is not enough evidence at the 1% level of significance to reject the claim."

The alternative hypothesis, in this case, is "μ1 ≠ μ2", as the claim being tested is that the two population means are equal.

To calculate the standardized test statistic, we can use the following formula:

Substituting in the values given in the problem, we get:

z = (18 - 20) / sqrt(((3.6^2) / 27) + ((1.4^2) / 26))

z = (-2) / sqrt((12.96 / 27) + (1.96 / 26))

z = (-2) / sqrt(0.481 + 0.075)

z = (-2) / sqrt(0.556)

z = (-2) / 0.746

z = -2.67

To calculate the P-value, we can use the standard normal table to look up the probability of getting a value of -2.67 or lower if the null hypothesis were true. The P-value in this case would be the probability of getting a value equal to -2.67 or lower, plus the probability of getting a value equal to 2.67 or higher.

Using the standard normal table, we find that the probability of getting a value equal to -2.67 or lower is 0.0039, and the probability of getting a value equal to 2.67 or higher is 0.9961. Therefore, the P-value is 0.0039 + 0.9961 = 1.0000.

Since the P-value is equal to 1.0000, which is greater than the level of significance α = 0.01, we fail to reject the null hypothesis.

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Answer:

< 1 = 64°

Step-by-step explanation:

First at all the sum of 2 angles should be 180°

< 3 + 116° = 180°

< 3 = 180 - 116

< 3 = 64°

Then, the sum of intern angles of a triangle must sum 180°, so:

< 1 + 52° + < 3 = 180°

< 1 +52 + 64 = 180

< 1 = 180 - 64 -52

< 1 = 64°

Answer: n = 15

Step-by-step explanation:

9 + n - 6 = 18

3 + n = 18

n = 15

Answer:

h(x) = (x-2)^2

Step-by-step explanation:

The side of the equilateral triangle is 2 ³/4 feet, having perimeter 8 ¹/₄  feet.

If all three of a triangle's sides are the same length, the triangle is said to be equilateral. Congruent sides refer to sides that have the same length, and they characterize an equilateral triangle.

Given that,

The perimeter of equilateral triangle = 8 ¹/₄  feet.

Simplify the rational term.

8 ¹/₄ = (32 + 1) / 4 = 33 /4.

Let each side of an equilateral triangle is a feet.

The perimeter of the equilateral triangle = 3a

Since, 3a = 33/4

a = 11/4

a = 2 ³/4

The required side of the equilateral triangle is 2 ³/4.

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The time required to grow $5000 to $8300, if the rate of interest is 7.5 %, is 7 years.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

The principal amount, p = $5000,

The amount, A = $8300

The rate of interest, r = 7.5 %,

Calculate the time as shown below,

[tex]A = p(1 + r / 400)^{4n}[/tex]

8300 = 5000 (1 + 7.5 / 400)⁴ⁿ

8300 / 5000 = (1 + 0.01875)⁴ⁿ

1.66  = (1.0188)⁴ⁿ

1.66 = (1.077)ⁿ

(1.077)⁷ = (1.077)ⁿ

n = 7

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The required, team 3, tower garden donation shows the proportional relationship between weeks and donation,

Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.

here,
From the table,
The ratio of a week to the donation of the individual team must be the same as the ratio of the preceding week and the donation of the respective team,
So,
Team 1,
1 / 1 =  2 / 3[1/4], false

Similarly, team 2 and team 4's relationship is also not proportional,
Now, team 3
1 / [2 1 / 3] = 2 / [4 2/3 ]
3 / 7 = 3/7

Thus, The necessary, team 3, tower garden gift illustrates the proportional relationship between weeks and donation.

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The equations have the same value of x are,

A) 5x + 4 = -54

B) 6(5/6x + 2/3) = -9(6)

C) 5x = -58

What is equation?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation

3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Consider the given equation

5/6 x + 2/3 = -9

Subtract 2/3 from both sides,

5/6x + 2/3 - 2/3 = -9 - 2/3

5/6x = -29/3

[tex]x = -\frac{29}{3}*\frac{6}{5}\\ x = -11.6[/tex]

The value of x is -11.6.

Hence, the equations have the same value of x are,

A) 5x + 4 = -54

B) 6(5/6x + 2/3) = -9(6)

C) 5x = -58

After solving above these equations we get the same value of x which is -11.6.

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Complete question:

Which equations have the same value of x as 5/6x + 2/3 = -9? Select three options. 6(5/6x + 2/3) = -9

6(5/6x + 2/3) = -9(6)

5 x + 4 = -54 5 x + 4 = -9

5 x = -13

5 x = negative 58