Solve the inequality and write the solution using:
the inequality

Answer:

3 or -3

Explanation:

Let's call the unknown number x. The square of this number is x². The product of 8 and the square of this number is 8x². Finally, it is decreased by 5, so 8x² - 5 and it is equal to 67, then the equation that represents the statement is:

8x² - 5 = 67

Now, we can solve the equation for x. Add 5 to both sides

8x² - 5 + 5 = 67 + 5

8x² = 72

Divide both sides by 8

8x²/8 = 72/8

x² = 9

Find the square root of both sides

x = √9

x = 3 or x = -3

Therefore, the number is 3 or -3

ANSWER:

24.63%

STEP-BY-STEP EXPLANATION:

The first thing is to mention that it is a profit because it was bought at a lower amount than it was sold, therefore

We take 100% as the lowest value, and thus we calculate the profit percentage

Then the difference between both percentages is the profit percentage

It is given that AB = CB from this information we conclude that <A=<C by reason :angles opposite equal sides.

<A+<B+<C=180°(Sum of angles in a triangle)

[tex](4x - 13) + (5x - 2) + (4x - 13) = 180 \\ 4x + 5x + 4x - 13 - 2 - 13 = 180 \\ 13x - 28 = 180 \\ 13x = 180 + 28 \\ 13x = 208 \\ \frac{13x}{13} = \frac{208}{13} \\ x = 16[/tex]

x=6°

ATTACHED IS THE SOLUTION

GOODLUCK

437,160 is read as four hundred thirty-seven thousand one hundred sixty and 43,716 is read as fourty-three thousand seven hundred sixteen.

The first number has hundreds of thousand and the second one only has tens of thousand. It means that the first number is greater than the second one.

Another way to know this is because of the number of figures before the decimal point. The first number has 6 figures before the decimal point and the second one only has 5.

That way, we know that 437,160 is greater than 43,716.

To Determine: How to determine a relation is function on a GRAPH

In other to achieve this, we will use the vertical test

If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function

Check the image below for a better clarification

With the use of the vertical line test, the graph in OPTION C and OPTION D are functions and the graph in OPTION A and B are not functions

In summary, you determine a relation is a function on a graph by using a vertical line test

EXPLANATION

There are two zeros in the product of 5x40 because multiplying the number 40 5 times give us the number 200 wich is a hundred type number.

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

STEP 2: Evaluate the expression

It can be seen that the result of the expression is 0.12

Hence, there are 2 digits after the decimal point for the product

Answer:

Step-by-step explanation:

you can view this,its similar just the numbers are switched.

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Answer:

35

Step-by-step explanation:

sorry if im wrong sorry

The expression (m⁻⁵n⁻³)⁻³ has an equivaent of m⁻¹⁵n⁹

From the question, the expression is represented as

(m−5n−3)−3

Rewrite the expression properly

This is done as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

This gives

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution is (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

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The given expression (m⁻⁵n⁻³)⁻³ has an equivalent to the m⁻¹⁵n⁹

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is represented as (m−5n−3)−3

Rewrite the expression as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets , we have

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products, we have;

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution will be; (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

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The given function is:

It is reflected across the x-axis to obtain a new function. This transformation follows the rule:

If we apply this rule, we obtain:

The answer is y=-|x|

Given:

Radius, r = 6

Let's find the chance of hitting the shaded area by finding the ratio.

Since the radius of the cirlce is 6, the length of one side of the square is the diameter:

s = 6 x 2 = 12

To find the ratio divide the area of the circle by area of the square. The area of the circle is the shaded area while the area of the square is the total possible area.

Thus,we have:

Therefore, the chance of hitting the shaded region is 78.54%

ANSWER:

78.54%

We will have the following:

Then:

So, the component form for the sum of the vectors will be:

Answer: .1$ so 10cents

Step-by-step explanation:

before we can dtermone whether it is a function, there must be a relationship between X and y i.e they must have a constannt of proportionality as shown:

From the table:

when x = 9, y = 1

when x = 7, y = 2

when x = 5, y = 2

when x = 3, y = 3

when x = 1, y = 4

let us determine the constant of proportionality from the given values as shown:

k = y2-y1/x2-x1

when x = 9, y = 1

when x = 7, y = 2

k = 2-1/7-9

k = 1/-2

k = -1/2

Also

when x = 5, y = 2

when x = 3, y = 3

k = 3-2/3-5

k = 1/-2

k = -1/2

Also;

when x = 5, y = 2

when x = 3, y = 3

k = 3-2/3-5

k = 1/-2

k = -1/2

Since all the constant of proportionality are the same;

Hence y = kx

y = -1/2 x

This shows that the tabke is a function and X is directly proportional to y. hence the answer is YES, it is function

hello

to determine if the sequence is arthimetic or a geometric progression, we check if a common difference or common ratio exists between the two sequence

the sequence is 36, 30, 24, 18,......

from careful observation, this is an arthimetic progression because a common difference exists between them

d = 30 - 36 = -6

or

d = 24 - 30 = -6

to find the 67th term, let's apply the formula

The measurement shows that the base of the triangle is approximately 7 cm

while the height is approximately 9cm

The area of the triangle is given by

Option D is the closest to the answer

Line t, segments AC, BC and BD are colinear, that is, all of them are in the same line. Then, the true statements are

A, B, and C

The limit of a function is the value that a function approaches as that function's inputs get closer and closer to some number.

The question asks us to estimate from the table:

To find the limit of g(x) as x tends to -2, we need to check the trend of the function as we head towards -2 from both negative and positive infinity.

From negative infinity, the closest value we can get to before -2 is -2.001 according to the values given in the table. The value of g(x) from the table is:

From positive infinity, the closest value we can get to before -2 is -1.999 according to the values given in the table. The value of g(x) from the table is:

From the options, the closest estimate for the limit is 8.03.

The correct option is the SECOND OPTION.

Given,

The expression is,

Required:

The graph of the line.

The interval notation is [-3, infinity).

The line of the inequality is,

Hence, the graph of the line is obtained.

Given rectangle A'B'C'D', you know that it was obtained after translating rectangle ABCD using this rule:

That indicates that each point of rectangle ABCD was translating 4 units to the left and 3 units up, in order to obtain rectangle A'B'C'D'.

Notice that the coordinates of the vertices of rectangle A'B'C'D' are:

Therefore, in order to find the coordinates of ABCD, you can add 4 units to the x-coordinate of each point and subtract 3 units to each y-coordinate of each point. You get:

Hence, the answers are:

- First option.

- Second option.

- Fourth option.

- Fifth option.

The expression given is,

Subtract 3 from both sides

Divide both sides by 5

Apply absolute rule:

Add 3 to both sides

Therefore, the answer has the form:

Hence, the solution using interval notation is

a. Given that:

- The mean age of the 36 respondents is 40 years.

- The standard deviation of ages is 10 years.

You need to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected.

Then, you need to use this formula:

Where "x" is the sample mean, "z" is the confidence level value, "n" is the sample size, and σ is the standard deviation.

In this case:

Therefore, by substituting values into the formula:

You get these two values:

b. If you assume that:

You get the following values by substituting them into the formula:

Hence, the answers are:

a.

b.

Given:

Given the equation

Required: Solve for y.

Explanation:

Subtract 2x on both sides.

Multiply both sides by -4.

Final Answer: y = 4(2x - 1)

Determine the volume of each rectangular or triangular prism round to the nearest tenth if necessary ​

____________________

volume = base (B)* height (H)

_____________________

Base area

Triangle

B = b*h/2

Rectangle

B= L1*L2

__________________

volume = base (B)* height (H)

H= 15

Triangle case

B = 4.8 *9.6 /2

B = 46.08 / 2

B= 23.04

V= 23. 04* 15

V= 345.6 in ^3

The composite functions are evaluated and simplified as:

(f o g)(x) = 9x² + 5

(g o f)(x) = 3x² + 15

To evaluate a composite function, the inner function is evaluated first using the given input. After then, the output of the inner function is used as the input to evaluate the outer function.

Given the following:

Therefore:

a. (f o g)(x) = f(g(x))

Substitute g(x) for x into f(x) = x² + 5

f(g(x)) = (3x)² + 5

Simplify the function

f(g(x)) = 9x² + 5

b. (g o f)(x) = g(f(x))

Substitute f(x) for x into g(x) = 3x:

g(f(x)) = 3(x² + 5)

Simplify the function

g(f(x)) = 3x² + 15

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Answers:

2a. The arena will fit on the rug

b. Width = 36 in

c. Standing room: 4 in

3. 144 in²

Explanation:

2. Part a.

First, we need to convert the measures of the rug to inches, so taking into account that 1 ft = 12 in, we get

Length = 6 ft x 12 in/ 1ft = 72 in

Width = 4 ft x 12 in/ 1 ft = 48 in

Then, the area of the rug will be

Area = Length x Width

Area = 72 in x 48 in

Area = 3456 in²

Therefore, the area of the arena, which is 2160 in² is lower than the area of the rug. It means that the area will fit on the rug.

Part b.

The area of the arena is equal to

Area = Length x Width

To find the width of the area, we need to solve the equation for the width, so

Width = Area/Length

So, replacing Area = 2160 in² and Length = 60 in, we get

Width = 2160 in² / 60 in

Width = 36 in

Therefore, the width of the area is 36 in.

Part c.

The measures that we get from parts a and b can be represented as

Therefore, the missing length can be calculated as:

(48 in - 36 in)/2 = 12 in/ 2 = 6 in

Therefore, a drive will have 6 in of standing room.

3.

Finally, to know how much space each robot take up, we need to divide the area of the arena by 15, so

2160 in²/ 15 = 144 in²

Therefore, each robot take 144 in²

The rectangle has a width of 7 yards and a length of 42 yards.

For a rectangle of length L and width W, the perimeter is:

P  = 2*(L + W)

Here we know that:

L = 6*W

P = 98yd =  2*(L + W)

Then we have the system of equations:

L = 6*W

98yd =  2*(L + W)

If we substitute the first equation into the second one, we get:

98yd = 2*(6*W + W)

98yd = 14*W

98yd/14 = W = 7yd

So the width is 7 yards, and the length is 6 times that, so:

L = 6*7yd = 42yd

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Data:

Domingo: D

Jennifer: J

Initial number of cards:

D=250

J=82

After each meeting(m):

D=250-12m

J=82+12m

After the first meeting: m=1

You increase in 1 the m after each meeting and get the next table: