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[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]

The given expression can be written in its simplest form by using the rule of exponents.

There are three components to the given expression, there is a negative base term -27, there is a base term with negative exponent x^-9, and both base terms have a fractional exponent 1/3.

Solving the term with negative exponent, the rule dictates that a term with a negative exponent can be written as its reciprocal. As x^-n=1/x^n,

x^-9=1/x^9

Hence, the expression becomes (-27/x^9)^1/3

The fractional exponent is applied to both the base terms. As (x^n)^m=x^nm,

(-27/x^9)^¹/₃=(-27)^1/3/(x^9*1/3)

Solving the negative term, the rule dictates that when there is a negative term with an odd number power, the negative sign can be extracted from the expression.

Hence,

(-27)^1/3=-(27^1/3)

Further simplifying the term, we know that 3^3=27,

-(27^1/3)=-(3^3*1/3)

Multiplying the powers for the entire expression,

-(3^3*1/3)/(x^9*1/3)=-3^1/x^3=-3/x^3

The simplest form of the expression (-27x^-9)^¹/₃ is -3/x^3

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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:

The numbers are 4 and 7

Step-by-step explanation:

To start, we can set up two equations.

x + y = 11 and x - y = 3

We now need to solve for one of these variables in terms of the other. I am choosing to solve for x, but either way will work. I'm using the second equation and solving for x by adding y to each side, which gives me

x = 3 + y

Now that I have a value for x, I can plug this into my first equation

3 + y + y = 11

Combining like terms gives me

3 + 2y = 11

Subtracting 3 from both sides leaves

2y = 8

And dividing by 2 to solve for y gets

y = 4

We now know one number, and to solve for the other we can plug our y value into either equation

x + 4 = 11

Subtracting 4 from both sides yields the x value

x = 7

So the two numbers are 4 and 7

The number representing a constant from the expression will be 9. Then the correct option is D.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The polynomial is given below.

⇒ 15x² + 2x + 9

If the power of the unknown is zero, then the term will be known as the constant term.

The polynomial can be written as,

⇒ 15x² + 2x + 9

⇒ 15x² + 2x + 9x⁰

The number representing a constant from the expression will be 9. Then the correct option is D.

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-12

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

3

After solving, the factors of equation 3x² = 18x-24 are:

So,

Given equation: 3x² = 18x-24

Then,

Factors are: (x-4) and (3x-6)

Therefore, after solving, the factors of equation 3x² = 18x-24 is:

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Answer:

if any number power of 0 is 1

so, (4)^0 =1

if any number power of -1 is equal to one divide this number.

like;

a^(-1) = 1/a

Therefore,

2^(-3) = 2^(-1) x 2^(-1) x 2^(-1)

= 1/2 x 1/2 x 1/2

Hence solution of 2^(-3). (4) ^0 is,

1/2 x 1/2 x 1/2 x 1

[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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Answer:115

Step-by-step explanation:

(4.25x) + 167= 117.35

If the inverse of f exists, it is represented by f⁻¹ and exists only if f is a bijective function.

The inverse of the function is f⁻¹ = - (x² - 3/2)

Domain is 3/2 to positive infinity

Range is 0 to positive infinity.

The inverse function of a function f is a function that reverses the operation of f. The inverse of f exists if and only if f is bijective, and it is denoted by f⁻¹ if it exists.

A function's inverse is not always a function. To ensure that the inverse function is also a function, the original function must be a one-to-one function. A one-to-one function is one in which each second element corresponds to exactly one first element.

Let the given function be f(x) = √-2x+3

y = √-2x+3

simplifying the value of x, we get

x = √-2x+3

x² = -2y + 3

simplifying the above equation, we get

x² - 3 = -2y

y = - (x² - 3/2)

Therefore, the inverse function be f⁻¹ = - (x² - 3/2)

Domain is 3/2 to positive infinity because a negative number cannot be square-rooted.

Range is 0 to positive infinity.

f⁻¹ = - (x² - 3/2)

The domain of the inverse is negative infinity to positive infinity, which is not a mirror image of the range of the original equation.

Anything squared is a positive number or zero.

The minimum value of the range is

f⁻¹ = - (x² - 3/2)

f⁻¹ = -(-3/2)

f⁻¹ = 3/2

The range of the inverse is 3/2 to positive infinity, a mirror of the domain of the original equation.

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Answer:

The missing number is 8

Step-by-step explanation:

[tex]10,360 \div 37 \div 35 = 8[/tex]

The similar polygons, use proportion to find the value of each variable.

x= 40, y = 18

[tex]\frac{JK}{NM}[/tex] = [tex]\frac{KL}{ML}[/tex] = [tex]\frac{LJ}{LN}[/tex]

[tex]\frac{40}{16}[/tex] = [tex]\frac{x}{16}[/tex] = [tex]\frac{45}{y}[/tex]

40*16 = 16*x

x= 40

40*y = 45*16

y = 18

In geometry, a polygon  may be a  plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or  the 2  together,  could also be  called a polygon.The segments of a polygonal circuit are called its edges or sides. The points where two edges meet are the polygon's vertices (singular: vertex) or corners.  the inside  of a solid polygon is sometimes called its body. An n-gon  may be a  polygon with n sides; for example, a triangle  may be a  3-gon.

A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains  of straightforward  polygons and they often define a polygon accordingly. A polygonal boundary  could also be  allowed to cross over itself, creating star polygons and other self-intersecting polygons.

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Without knowing what the dropdown list shows for reasons, it's hard to pinpoint exactly what is expected here.

Angle ACD is congruent to angle BCD because they are corresponding angles between the congruent triangles ∆ACD and ∆BCD.

The triangle congruency is due to angle-angle-side (AAS) similarity:

• angles A and B are congruent - this is given

• angles CDB and CDA are congruent right angles - this is implied by the given detail that CD and AB are perpendicular

• the leg CD is common to both triangles, and CD is of course congruent to itself (reflexive property)

So angles ACD and BCD are congruent, which means they have the same measure, so by definition of angle bisector, CD bisects angle ACB.

QED

The following inequality in slope-intercept form.

y≤-4x-15

Slope intercept form is y=mx+ c

what is a coordinate in geometry?

Coordinates are two numbers (Cartesian coordinates), or every so often a letter and a range of, that discover a particular point on a grid, called a coordinate aircraft. A coordinate aircraft has 4 quadrants and two axes: the x axis (horizontal) and y axis (vertical).

what is coordinate geometry instance?

In coordinate geometry,  lines are parallel if their slopes (m) are equal. for instance: the line y = ½ x - 1 is parallel to the line y = ½ x + 1 due to the fact their slopes are both the identical.

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The factoring of the expression 6 x²=5 x+6 is (2x-3) (3x+2)

By ordering the values, we get:

6 x² - 5x - 6

To solve this exercise, we have to follow the rules of factoring:

1. Factor 5 from 5x:

6 x² - 5x - 6

6 x² + (-9 + 4) x - 6

2. Apply the distributive property:

6 x² - 9x + 4x - 6

3. Groups the first two terms and the last two terms:

(6 x² - 9x) + 4x - 6

4. Factorize the greatest common denominator (GCM) of each group:

3x(2x - 3) + 2(2x - 3)

5. Simplify the common term (2x - 3) with the distributive property:

(2x-3) (3x+2)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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The value of y for which M is the mid-point of LN is equal to 3 and the numerical length of LN is 46 units.

The mid - point of a line is the point which divides it into two equal parts of same length.

Given in the question is a line segment LN such that M is its mid - point. From the question, we can write -

LM = 9y - 4

MN = 6y + 5

According to the question, M is the midpoint of LN, therefore -

LM = MN

9y - 4 = 6y + 5

9y - 6y = 9

3y = 9

y = 3

So, the length of LN will be -

LN = LN + MN = 9 x 3 - 4 + 6 x 3 + 5 = 23 + 23 = 46 units

Therefore, the value of y is equal to 3 and the numerical length of LN is 46 units.

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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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Answer:

12

Step-by-step explanation:

absolute value basically makes numbers positive

Answer:

A

Step-by-step explanation:

Answer:

A real number is a number that can take any value on the number line. They can be any of the rational and irrational numbers. Rational number is a number that can be expressed in the form of a fraction but with a non-zero denominator.

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:

32% of 200 is 64.

Step-by-step explanation:

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:

2.45

Step-by-step explanation:

11x-2=25

11x=25+2

11x=27

11x/11=27/11

x= 2.45.

To check:

11x-2=25

11 × 2.45 - 2 = 24.95.

Round 24.95 to nearest whole number and you will get 25.

Answer:

0.9

Step-by-step explanation:

4n = 3.60

n = 3.60 / 4

n = 0.9

Answer: n = 0.9

Step-by-step explanation:

1. isolate the variable by dividing 4 from both sides

2. 3.60/4 = 0.9

Answer:

mmmm

Step-by-step explanation:

!!!

Answer:

see explanation

Step-by-step explanation:

∠ CDF and 137° are a linear pair and sum to 180° , then

∠ CDF = 180° - 137° = 43°

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

the sum of the 3 angles in Δ CDF = 180° , then

∠ CFD + 43° + 32° = 180°

∠ CFD + 75° = 180° ( subtract 75° from both sides )

∠ CFD = 105°

then

∠ AFB = ∠ CFD = 105° ( vertically opposite angles are congruent )

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

∠ ABF= ∠ FCD = 32° ( alternate angles are congruent )

Answer:

The slope of the line is 12

(Sorry for the bad quality image)

Explanation:

To find the average rate of change, calculate the change in y over the change in x.

m = 12

Answer:

Rate of change = 12
y-intercept = (0, 20)

Step-by-step explanation:

Part 1) Rate of Change
The rate of change (or slope) is found using the formula [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
To use this formula, we must take the coordinates of two of the given points in the table and substitute them. For simplicity, I'll take the points (1, 32) and (4, 68).

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{68 - 32}{4 - 1} = \frac{36}3 = 12[/tex]

Therefore, the rate of change is 12.

Part 2) y-intercept
To find the y-intercept, we must find the value of the function where [tex]x = 0[/tex]. Since we have both the value of the function where [tex]x = 1[/tex] and we know that the rate of change is 12, we can simply subtract the rate of change from the y-value of the function at the point where [tex]x = 1[/tex].

The y-value of the function where [tex]x = 1[/tex] is 32, therefore, the y-value of the function at [tex]x = 0[/tex] is [tex]32 - 12 = 20[/tex]

The y-intercept is (0, 20).

The inequality that gat can be used to show the mobiles that are tolerable is w - 8 <= 0.3.

It should be noted that from the information, the

mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces.

Therefore, the mobiles are tolerable with an inequality will be:

w - 8 <= 0.3.

where w = weight of the mobiles.

In conclusion, the mobiles are tolerable with an inequality will be w - 8 <= 0.3.

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A particular mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces. The mobiles that are not within the tolerated weight must be recycled. Show which mobiles are tolerable with an inequality. ( W is the weight of the mobiles).