Select all the correct answers.

Which three equations are equivalent to 1 +3|x-21 = 16?

O

X-2 = -5 or x - 2 = 5

X=-3 or x = 7

O

|x+2) = 5

0

x+2 = -5 or x+ 2 = 5

0

O

x=3 or x= -7

O

| x-2= 5

Answer:

\(x = \frac{60}{5} = 12\)

..........................................

The length of the third side is 2√34 + 6.

We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let x be the length of the third side. Then we have:

2√34 + 6 > x

Subtracting 6 from both sides, we get:

2√34 > x - 6

Adding 6 to both sides, we get:

x < 2√34 + 6

Therefore, the length of the third side must be less than 2√34 + 6.

To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:

2√34 + 6 = x

If this is true, then the given sides can form a triangle.

Simplifying the equation, we get:

x = 2√34 + 6

The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.

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Answer:

25.5 miles per hour

Step-by-step explanation:

If you take the number of miles traveled, and divide it by the amount of hours that have past, you will get the speed. So if 34 minutes past, you need that in hours. To get 34 minutes in hours, you divide it by the amount on minutes in 1 hour. 34 minutes / 60 minutes in one hour, you get 0.5666666... hours. Now if you have traveled 45 minutes in that amount of time, divide 45/0.5666666... and you get 25.5 miles PER one hour that passes.

The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

Answer:

43

Step-by-step explanation:

Order of Operations first

30 - 9 / 3 + 8 x 2

30 - 3 + 16

27+16

43

Answer:

metaphor

Step-by-step explanation:

Answer:

Metaphor!

Step-by-step explanation:

Kites are described as "colorful fishes swimming in the sky".

Metaphors don't use like or as but still compare.

The range of the data is the difference between the highest and lowest values, which is 8 inches. Adding another plant with a height of 14 inches would not change the range, so the range would remain 8 inches.

Data is a collection of facts, figures, or information that can be processed and used to draw conclusions or make decisions. It can be stored in a variety of formats, including numerical, text, images, audio, and video. Data can be collected from a variety of sources, such as surveys, observations, experiments, or transactions. It can be used to inform decisions in areas such as business, health care, education, and research. Data can be analyzed to gain insight, develop strategies, identify trends, and make predictions. Data is a valuable resource and is increasingly important in today's digital age.

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Answer:

27

Step-by-step explanation:

9³÷3³=729÷27

         = 27

Answer:

the answer is 3

Step-by-step explanation:

Answer: y=-1/8x-2

Step-by-step explanation:

Given the slope, we can start to fill out the slot-intercept form equation.

y=-1/8x+b

We don't know the value of b, but we can plug in the given point to solve for b.

-3=-1/8(8)+b

-3=-1+b

b=-2

Now that we know b, we can finish our slope-intercept equation.

y=-1/8x-2

The regression line equation is given as

a.

When the truck has driven 100.000 miles, it means x = 100.000

Substitute x = 100.000 into the regression line equation

y = 38.257 - 0.1629(100.000)

y=38.257 - 16290

y= $21967

The price of the truck after driving 100.000 miles is $21967

b.Interprete the slope:

This can be interpreted as the the price for driving just 1 mile

Hence, the slope is the price that will cost to drive 1 mile

C. The y-intercept of the line

The y-intercept is where the line x = 0

This means the price of the Ford when mile covered is zero.

The is interpreted as the initial price of the Ford before it begins to cover any mile.

Step-by-step explanation:

- x^2 -15x + 54 = 0

x^2 + 15x - 54 = 0

the two solutions will add up to  - b/a  =  - 15

Or you can factor it

( -x^2 -15x+54) = 0

(x+18)(-x+3) = 0     shows x = -18 or 3     sum = - 15

Answer:

-------------------

Given quadratic equation:

Write it in standard form of ax² + bx + c = 0:

According to Vieta's theorem, sum of the two roots is - b/a, that is:

Answer:

m = 1/2 and b = 1.

Step-by-step explanation:

The y intercept (b)  is at y = 1 so we have

y = mx + 1  so b = 1

The m is the slope of the line.

The graph passes through the point (4, 2)

From the graph, the slope  = 2/4 = 1/2.

So it is y = 1/2x + 1.

The value of f(x) is a 4 at x = -4

and the value of f(4) = -2

let f(x) = y

since f(x) = 4, y = 4

we find the value of x when y is 4

We trace the x and y axis:

When y =4, x = -4

The value of f(4) means x would be replaced by 4

So we check on the graph for the value of f(4) or the value of y when x = 4

At x =4, y = -2

The value of f(x) is a 4 at x = -4

and the value of f(4) = -2

Answer:

point D

Step-by-step explanation:

(5;-2)

the first number(5) is always the x-values ( horizontal line ) and the second number ( -2) is always the y-value ( verticle line )

Answer:

6 7/30

Step-by-step explanation:

Answer:

m∠F = 45°

Step-by-step explanation:

Notice the lengths of the given sides and the right angle. This is enough information to prove that this is a 45-45-90 triangle, or just basically a square cut diagonally.

Regardless if even just one side is given for a 45-45-90 triangle, all 45-45-90 triangles have one thing in common. The sides that form the right angle are equivalent and the hypotenuse is equal to one of the sides that form the right angle times the square root of two. I'm aware that it sounded confusing, as I'm awful at explaining, so just look at the picture I've attached instead of trying to understand my explanation that seemed like trying to learn a second language.

Look at the picture. See that FD = x times that square root of 2 and that DE = x. Now look back at your picture. It's connecting, now isn't it?

Now that we know that this is indeed a 45-45-90 triangle, we can confirm that m∠F = 45°

The distances from the point (x,y) are given as follows:

Suppose that we have two points with coordinates given by \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates of the focus of the parabola are given as follows:

(-3,2).

Hence the distance of the point (x,y) to the focus of the parabola is given as follows:

√(x+3)²+(y-2)².

The equation that defines the directrix is given as follows:

y = 4.

The y-coordinate of the point is of:

y.

Hence the distance is of:

|y - 4|.

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The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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Answer:

see attached

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{3}{5} +\frac{1}{4} +\frac{3}{8} =\) Distance Janie walked

First add \(\frac{1}{4} and\frac{3}{8}\) canvert 1/4 by multiplying by 2/2 to get a commmon denominator.

\(\frac{1}{4} *\frac{2}{2} =\frac{2}{8}\)

\(\frac{2}{8} +\frac{3}{8} =\frac{5}{8}\)

Now find a common denominator for 3/5 and 5/8 by multiplying 3/5 by 8/8  and 5/8 by 5/5.

\(\frac{3}{5}*\frac{8}{8}=\frac{24}{40}\)

\(\frac{5}{8}*\frac{5}{5}=\frac{25}{40}\)

Now add them.

\(\frac{24}{40}+\frac{25}{40}=\frac{49}{40}=1\frac{9}{40}\)miles

You can also convert all to decimals and add.

3/5 = .6

1/4 = .25

3/8 = .375

.6 + .25 + .375 = 1.225

Also 1 \(\frac{9}{40}\) = 1.225

Answer:

D

Step-by-step explanation:

For simplify the work we can start to factorise all the possibles expressions:

2x + 8.

8 is multiple of 2, so it can became

2(x+4)

x^2 - 16 this is a difference of two squares, so it can be rewritten as:

(x+4)(x-4)

x^2 + 8x + 16

we have to find two numbers whose sum is 8 and whose product is 16

the two number are 4 and 4

it becames:

(x+4)(x+4)

x+ 4 can‘t be simplified

if we look at the expression, we can find that x-4 appears at the numerator so

x^2 - 16 must be at numerator

but the second factor (x+4) doesn’t appear, so has been simplified. This situation can be possible only in the D option

in fact

(x+4)(x-4)/2(x+4) * (x+4)/(x+4)(x+4)

it became

(x+4)(x-4)/2 * 1/(x+4)(x+4)

(x-4)/2(x+4)

Answer:

Step-by-step explanation:

I got 100% on the test

The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.

Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.

Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)

At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.

Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)

Combining (1) and (2), we get:

∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,

∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.

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Answer:

Step-by-step explanation:

3438

Answer:

Actually, it's 98.66, not 3438.

Step-by-step explanation:

It's the right answer.

The best way to find Arianna's errors is to attempt to work out the problem on our own.

We are given the expression

Her first step was correct, we should rewrite our radical as a fractional exponent.

However, in the next step, she should not have written the expression as two natural logs as a fraction. Instead, we have to apply the quotient property:

Instead, we will have

Arianna correctly rewrote the exponent of "a" as a coefficient, but not for "e". Before we get there, let's expand the second part of the expression using the product property:

So, we will have

Applying the product property, Arianna should have moved the 4 to be a coefficient of ln(e):

The rest of her work is fine, so let's just finish the expression from here. The identity property of natural states

so now we can have

And finally, we will distribute the negative:

Part 2 a) Arianna had these two mistakes: First, she should have written the division as a subtraction. Second, she should have written the exponent 4 as a coefficient in front of ln(e) rather than ln(4e).

Part 2 b) the final expression should really be

Answer:

it’s c

Step-by-step explanation:

i’m smart

The problem of scheduling exams for the high school students can be solved by using graph theory. We can represent the overlap of students in the form of a graph where each teacher is a node and the edges represent the students who belong to both the teachers classes.

To ensure that no student has to take more than one exam each day, we need to find a coloring of the graph such that no two adjacent nodes have the same color. This is equivalent to scheduling exams such that no two exams on the same day have any common students.

Using a greedy approach, we may overcome this issue by starting with any node and assigning it a color.. We then recursively color the neighbors of the node with a different color and so on. This algorithm will always produce a valid coloring since we are guaranteed to find a valid color for every node, given that we have not run out of colors.

In this case, we have seven teachers so we need at least seven colors. However we can find a valid coloring with fewer colors, depending on the structure of the graph. This problem can also be extended to more general situations, where we have more than one exam per day or where we have more complex constraints on the scheduling of exams.

The answer is general as no additional data is given.

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Answer:

169,344

Step-by-step explanation:

Data provided in the question

Different fruits = 8

Different vegetables = 9

There is only room for 6 items

Based on the above information, the number of ways for an equal number of fruits & veggies is

For the number of combinations of fruit is

\(= 8\times7\times6\)

For the number of combinations of vegetables is

\(= 9\times8\times7\)

So, the total combinations are

\(= 9\times8\times8\times7\times7\times6\)

= 169,344