Solve. Check for extraneous solutions. 5-2 √x=3

The scientific notation has 3 significant digits.

A significant number is the the numbers that are in in the coefficient of an expression in scientific notation, 5, 9 and 8 are the significant numbers.

Scientific notation is used in expressing large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

For example, the number : 1 x 10² is equivalent to 100

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Using linear functions, it is found that:

a. The equations are given by: H(x) = 30 + 0.79x, R(x) = 75 + 0.55x.

b. The costs will be the same after 187.5 miles.

c. The estimate from the graph is reasonable, as it is the value of x for which both equations are equal.

A linear function is defined according to the following rule:

y = mx + b

In which:

For each function in the context of this problem, we have that:

Hence the equations for each company are given as follows:

The graph is given at the end of the answer, and from the intersection point, we have that the costs will be the same after 187.5 miles.

Numerically, this value is given as follows:

H(x) = R(x)

30 + 0.79x = 75 + 0.55x

0.24x = 45

x = 45/0.24

x = 187.5.

Hence the estimate from the graph is reasonable.

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Answer:

A

Step-by-step explanation:

Answer:

$459

Step-by-step explanation:

60x3=180

$299+180=$459

-12

----- = -4 that's the key to the operation so -4x 3

3

Answer:

P= (-12,0)

Q= (0,-8)

R= (-2,-16)

P'= (-17,0)

Q'= (-5,-8)

R'= (-7,-16)

Step-by-step explanation:

Assuming that each square is equal to one point, the shape is in quadrant 3, where all coordinates are negative.

Determine where each coordinate is for P, Q, and R; then move over each x coordinate by -5 (a.k.a. subtract 5).

This will give you your translation to P', Q', and R'.

Please let me know if I made any mistakes, and hope this helped!

The property illustrated by the statement where the equation is given as (7a * 2b) + 3c = 3c + (7a * 2b) is the Commutative Property of Addition

The equation is given as

(7a * 2b) + 3c = 3c + (7a * 2b)

The Commutative Property of Addition states that

a + b = b + a

In this case

a = (7a * 2b) and b = 3c

When the Commutative Property of Addition is applied using the above variables, we have

(7a * 2b) + 3c = 3c + (7a * 2b)

Hence, the property illustrated by the statement where the equation is given as (7a * 2b) + 3c = 3c + (7a * 2b) is the Commutative Property of Addition

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Answer:

well, best i can do for you : F

Step-by-step explanation:

Calculator soup

I forgot how to do this stuff, sorry

Answer: positive

Step-by-step explanation: That's just how it works. It's an algerbra rule. Hope that helped. Have a nice day.

Rule 1: The product of a negative integer and a positive integer is a negative integer. Rule 2: The product of two positive integers or two negative integers is a positive integer. That means if you multiply two OF the same sign numbers, the product is always positive.

Answer:115

Step-by-step explanation:

(4.25x) + 167= 117.35

Answer: D

Step-by-step explanation:

The mean of the combined group of classes is 69.35

Mean is given by by dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined. Mean is equal to (Sum of All Observations/Total Observations).

It is given that,

The mean of test scores of a class having 35 students = 73.1

And,

The mean of test scores of a class having 26 students = 65.6

We need to find,

The mean of the combined group of classes = mean of both classes

Mean of both classes = [tex]\frac{73.1 + 65.6}{2}[/tex]

= [tex]\frac{138.7}{2}[/tex]

= 69.35

Hence, 69.35 is the mean of the combined group of classes

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The percent of change when 40 is increased to 83 to the nearest tenth is: C. 107.5% increase.

In Mathematics, there are two main types of percentage and these include the following:

Mathematically, percentage increase can be calculated by using this formula:

Percentage increase = [Final value - Initial value]/Initial value × 100

Substituting the given parameters into the formula, we have;

Percentage increase = [83 - 40]/40 × 100

Percentage increase = 43/40 × 100

Percentage increase = 1.075 × 100

Percentage increase = 107.5%.

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96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25  is -1234

arithmetic sequence 1, -12, -25, .. .1,−12,−25

an arithmetic sequence can be written as

a , a + d , a + 2d , a + 3d , . . . . . a + (n-1)d

nth tern of an arithmetic sequence is

aₙ= a+ (n-1)d

a= first term of an arithmetic sequence

d = common difference of an arithmetic sequence

n = number of terms in an arithmetic sequence

So in the above arithmetic sequence

a= 1

d= -13

n= 96

a₉₆= 1+ (96-1)(-13)

    =  1- (95)13

    =  1- 1235

    = -1234

96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25  is -1234

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Answer: no

Step-by-step explanation:

A = 7, B = 13 and C = 6 then D = 11.1428571429. 3. A = 28, B = 34 and D =15 then C= 12.3529411765. 4. A = 13, B = 15, C = 2 and D = 33 then 13: 15

Answer:

slope 1/3

y = -2

x=1/3-2

Step-by-step explanation:

slope 1/3

y = -2

x=1/3-2

[Mathematical Situation]

Simplify the expression.

[tex]-1-\frac{2}{3} (\frac{6}{7}-\frac{3}{7}n)[/tex]

Solution:

[tex]-\frac{11}{7}+\frac{2n}{7}[/tex]

Hope this helps!

The simplified expression is -1 - 4/7 + (2/7)n.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

-1 - 2/3 (6/7 - (3/7)n)

Distributive operation.

= -1 - 2/3 x 6/7 + 2/3 x (3/7)n

= -1 - 4/7 + (2/7)n

Thus,

The simplified expression is -1 - 4/7 + (2/7)n.

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The equation has infinite solutions is the last option:

6(x - 1) = 2*(3x - 3)

Any equation in which we can remove the variable has infinite solutions (because it does not depend on the value of x) only if the equation is true.

Let's look at the fourth equation:

6(x - 1) = 2*(3x - 3)

If we expand both sides, we will get:

6x - 6 = 2*3x - 2*3

6x - 6 = 6x - 6

So we have the exact same thing in both sides, if we remove 6x - 6 in both sides we will get:

0 = 0

Then this equation has infinite solutions.

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Each logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 3.3}{log \\9}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression is,

[tex]log_9{3.3}[/tex]

as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]

therefore ,

[tex]log_9{3.3}[/tex] =  [tex]\frac{log \ 3.3}{log \ 9}[/tex]

Hence,  logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 3.3}{log \\9}[/tex]

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The solution of the given equation by rounding off it to the nearest ten-thousandth is 7.8295.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation: log₇3x = 3

We are given a logarithmic expression: log₇3x = 3        —- 1

We know that log₇3 = log 3 / log 7 and log (ab) = log a + log b

Using in equation 1, we have,

log₇3x = 3

log 3x / log 7 = 3

(log 3 + log x) / log 7 = 3

log 3 + log x = 3 × log 7

log 3 + log x = 2.535

log x = 2.535 - 0.4771

log x = 2.0579

x = 7.8295

Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 7.8295.

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It is an isosceles triangle.

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.

There are mainly three types of triangles:

Equilateral triangle

A triangle with three equal-length sides is said to be equilateral, matching what might also be referred as as a "regular" triangle. Because all three sides of an isosceles triangle are equal, an equilateral triangle is a particular case of an isosceles triangle. There are three equal sides to an equilateral triangle.

Isosceles triangle

A triangle with two equal sides is said to be isosceles.

Scalene triangle

A scalene triangle is a triangle wherein all 3 facets have distinct lengths. Also the angles of a scalene triangle have distinct measures. Some proper triangles may be a scalene triangle while the alternative angles or the legs aren't congruent.

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Answer:

Actual cost = 35.89 + 43.65 = 79.54  so it is some what lower than estimated cost.

Step-by-step explanation:

On the map, the separation between the two towns would be 5 cm.

Detailed explanation:

First, consider 2 cm and 30 miles as a ratio, which means that wherever you measure 2 cm with a ruler on a map, 30 miles will be scaled to that location.

Then, using some logic, we can state that if 2 cm = 30 mi, then 4 cm = 60 mi (double the 2 cm will result in doubling the 30 cm), and 1 cm = 15 mi (if you divide the 2cm by 2, 30mi will also be divided by 2). Because of this, 5cm (4cm + 4cm + 1cm) on the map equals 75mi (which is 30mi + 30mi + 15mi).

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The sum of the measures of all the angles in all of the triangles shown in the given diagram is 3,600°.

We need to find the sum of the measures of all the angles in all of the triangles shown in this diagram.

A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.

The sum of all the angles of the triangle is equal to 180°.

From the figure, by counting, we get there are 20 triangles.

As we know, the sum of all the interior angles of a triangle is 180°.

So, the sum of the measures of all the angles in all of the triangles = The number of triangles × 180°

= 20 × 180°

= 3,600°

Therefore, the sum of the measures of all the angles in all of the triangles shown in the given diagram is 3,600°.

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Answer:

i don't know what the question is but the total amount of comunity service she must do is 32 hours

Step-by-step explanation:

2 x 8 = 16 16 x 2 or 16 + 16 = 32 thus she must complete 32 hours of comunity service and she has already completed 16 hours of comunity service so she has 16 hours left to complete.

hope this helped = )

[tex]\displaystyle\\Answer:\ x=\frac{\pi }{4} \ \ \ \ \ x=\frac{7\pi }{4}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\secx=\sqrt{2} \ \ \ \ 0\leq x\leq 2\pi \\\\\frac{1}{cosx} =\sqrt{2} \\\\cosx=\frac{1}{\sqrt{2} } \\\\cosx=\frac{(1)(\sqrt{2)} }{(\sqrt{2})(\sqrt{2)} } \\\\cosx=\frac{\sqrt{2} }{2} \\\\x=\frac{\pi }{4} \\\\x=\frac{7\pi }{4}[/tex]

In the class of Mr. Kendrick's, Jonah is in Group B and Janeka is in Group A using the concept of Logical Reasoning.

As per the question statement, we are given that in Mr. Kendrick's class, students are divided into two groups for an activity. Students in group A must always tell the truth and correct info. Students in group B must always lie. Jonah and Janeka are in Mr. Kendrick's class. When asked if Jonah and Janeka are in group A or B, Jonah says, "We are both in Group B. "

By their statement and using the concept of Logical Reasoning, we can conclude that Jonah is in Group B and Janeka is in Group A.

As Jonah said, "We are both in Group B. " and as both the students can't be in same group so Jonah lied and hence he is in group B and Janeka is in group A.

This is a classic example of  Logical Reasoning.

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