-2x = 16–8y
x+4y= 25
Solve by substitution

Answer:

B. y = tan x  and  C. y = cot x

Step-by-step explanation:

Range:

range is defined as the set of values that any given function y=f(x), can take for which the x values are defined. It is the value that y can take for the values of x.

Given:

From the given options

the range of tanx and cotx are all real numbers

as the period of tanx and cotx are π

where as range of secx is all real numbers except π/2 + n*π i.e.

(-∞ , -1] U [1 , + ∞)

And range of cscx is all real numbers except n*π i.e.

(-∞ , -1] U [1 , + ∞)

So from the given option:

option B and C are correct while A and D are not !

The answer is:  The correct options are B. Tan(x) and C. Cot(x)

The range is the output of a function when we evaluate the function with inputs (domain), not all functions have a range of all real numbers, however it's more common to find functions without range or domain restrictions.

Both options B. Tan(x) and C. Cot(x) have a range of all real numbers while the functions Sec(x) and Csc (x) have a restricted range.

Sec(x) and Csc(x):

Domain, all real numbers.

Range, from -1 to 1 or  [-1,1]

Tan(x) and Cot(x):

Domain, all real numbers except [tex]\frac{\pi }{2}+-n\pi[/tex]

Range, all real numbers.

Hence, the correct options are B. Tan(x) and C. Cot(x)

Have a nice day!

Answer:

Step-by-step explanation:

[tex]\text{The zeros is for}\ f(x)=0.\\\\f(x)=3x^3-3x^2-6x\\\\f(x)=0\iff3x^3-3x^2-6x=0\qquad\text{divide both sides by 3}\\\\x^3-x^2-2x=0\qquad\text{distributive}\\\\x(x^2-x-2)=0\\\\x(x^2+x-2x-2)=0\\\\x\bigg(x(x+1)-2(x+1)\bigg)=0\\\\x(x+1)(x-2)=0\\\\\text{The product is equal to 0, when one of the factors is equal to 0.}\\\text{Therefore:}[/tex]

[tex]x(x+1)(x-2)=0\iff x=0\ \vee\ x+1=0\ \vee\ x-2=0\\\\x=0\ \vee\ x=-1\ \vee\ x=2[/tex]

Answer:

0.8

Step-by-step explanation:

You are given the equation

[tex]\left(\dfrac{1}{64}\right)^{0.5x-3}=8^{9x-2}[/tex]

First note that

[tex]\dfrac{1}{64}=\dfrac{1}{2^6}=2^{-6}\\ \\\left(\dfrac{1}{64}\right)^{0.5x-3}=(2^{-6})^{0.5x-3}=2^{-6\cdot (0.5x-3)}=2^{-3x+18}\\ \\8=2^3\\ \\8^{9x-2}=(2^3)^{9x-2}=2^{3\cdot (9x-2)}=2^{27x-6}[/tex]

Now

[tex]2^{-3x+18}=2^{27x-6}\\ \\-3x+18=27x-6\\ \\-3x-27x=-6-18\\ \\-30x=-24\\ \\x=\dfrac{24}{30}=\dfrac{8}{10}=0.8[/tex]

Final answer:

To solve the given equation, we convert both sides to a common base and equate the exponents. After simplifying, we find that the solution is x = 8/11.

Explanation:

We are asked to solve the equation (1/64)^0.5x-3 = 8^9x-2. To begin, we will express both sides of the equation with the same base since 64 is 2^6 and 8 is 2^3. This transformation will allow us to use the property of exponents that states when the bases are equal, the exponents must also be equal.

First, let's rewrite the equation using base 2:

Now, since the bases are the same, we can equate the exponents:

The solution to the equation is x = 8/11. Always remember to check for extraneous solutions when dealing with exponents and roots.

[tex]\bf \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\[1em] [\log(3)-\log(4)]-\log(2)\implies \log\left( \cfrac{3}{4} \right)-\log(2)\implies \log\left( \cfrac{\frac{3}{4}}{~~2~~} \right) \\\\\\ \log\left( \cfrac{\frac{3}{4}}{~~\frac{2}{1}~~} \right)\implies \log\left( \cfrac{3}{4}\cdot \cfrac{1}{2} \right)\implies \log\left( \cfrac{3}{8} \right)[/tex]

To write the expression as a single logarithm, we'll use the properties of logarithms to combine them. The given expression is:
(log3 - log4) - log2
We start by combining the first two logarithms inside the parenthesis using the difference of logarithms property:
log(a) - log(b) = log(a/b)
Applying this property to (log3 - log4), we get:
log(3/4)
Now, our expression looks like this:
log(3/4) - log2
We can use the same property to combine this with the remaining logarithm:
log(a) - log(b) = log(a/b)
So we apply it with a = 3/4 and b = 2:
log((3/4)/2)
When dividing by 2, we are effectively multiplying by 1/2, so we have:
log(3/4 * 1/2)
Now we perform the multiplication inside the logarithm:
log(3/8)
And that is the expression written as a single logarithm:
log(3/8)

Answer:

the answer is the green bin

Step-by-step explanation:

12•5•4 is 240

10•6•5 is 300

so, the answer is the green bin

hope this helps!

have a blessed day!

please give brainliest!

The terminal side of an angle measuring -7x/6 radians lies in the second quadrant, considering the angle implies a clockwise rotation from the positive x-axis and one complete rotation is 2π radians.

One complete revolution is equal to 2π radians, which is approximately 6.28 radians. Negative angles imply a clockwise rotation from the positive x-axis. The given angle, -7x/6 radians, would place the terminal side in a clockwise rotation from the positive x-axis.

Angles that measure between 0 to -π/2 radians lie in the fourth quadrant, while angles between -π/2 to -π radians lie in the third quadrant, angles between -π to -3π/2 radians lie in the second quadrant, and angles between -3π/2 to -2π radians lie in the first quadrant.

Assuming the variable x represents any positive real number, the angle -7x/6 would likely be between -π and -3π/2 (or -1.57 and -4.71), and therefore, the terminal side of this angle would lie in the second quadrant.

Answer:

i think its 4

Step-by-step explanation:

Answer:

2.45

Step-by-step explanation:

The expected value is the sum of the points times the probability.

The expected number of points from a touchdown is:

E = 7×0.35 + 0×0.65

E = 2.45

Answer:

The length of NO is [tex]14\ ft[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

The Kite  has two pairs of equal-length adjacent (next to each other) sides.

so

The perimeter is equal to

[tex]P=2[MN+NO][/tex]

[tex]P=80\ ft[/tex]

so

[tex]80=2[MN+NO][/tex]

[tex]40=[MN+NO][/tex]

substitute the values and solve for x

[tex]40=[(3x+5)+(x-7)][/tex]

[tex]40=[4x-2][/tex]

[tex]4x=42[/tex]

[tex]x=21\ ft[/tex]

step 2

Find the length of NO

[tex]NO=(21-7)=14\ ft[/tex]

Answer:

b. closed circles on 1 and 4 with arrows pointing outward

Step-by-step explanation:

Which of the following describes the graph of {x | x < = 1} u {x | x > = 4},

We have been given the following set;

x < = 1

This set comprises of real numbers that are less than or equal to 1;

(1, 0, -1, -2, -3, -4, .......... -∞)

On the other hand, the set x > = 4 comprises of real numbers that are greater than or equal to 4;

(4, 5, 6, 7, 8, 9, ........∞)

The symbol ∪ means a union of sets. That is the set of numbers that belong in either or both sets;

{x | x < = 1} u {x | x > = 4} is same as writing;

(1, 0, -1, -2, -3, -4, .......... -∞) ∪ (4, 5, 6, 7, 8, 9, ........∞)

Therefore, the solution set will be closed circles on 1 and 4 with arrows pointing outward

Answer:

Closed circles on 1 and 4 with arrows pointing outward ⇒ answer b

Step-by-step explanation:

* Lets study the meaning of the inequality

- If a < x < b, that means the value of x is between a and b

- If a ≤ x ≤ b, that means the value of x is from a to b

- If x < a and x > b, that means the value of x is smaller than a and

 grater than b

- If x ≤ a and x ≥ b, that means the value of x is smaller than or equal a and

 grater than or equal b

* Now lets solve the problem

∵ {x I x ≤ 1}

∴ x is smaller than or equal 1

∵ {x I x ≥ 4}

∴ x is greater than or equal 4

∵ {x I x ≤1} ∪ {x I x ≥ 4}

- The meaning of ∪ is all numbers smaller than or equal 1 and all

  the numbers greater than or equal 4

∴ {x I x ≤ 1} ∪ {x I x ≥ 4} = (-∞ , 1] ∪ [4 , ∞)

- This solution represented graphically by closed circles on 1 and

 4 with arrows pointing outward

Select the equations of the lines that are parallel to the line whose equation is y = 3x + 5

Answer:

6x+2y=12

and

3y=9x

Answer:

It is 2, 4, & 5.

Step-by-step explanation:

just got it right on edge.

Answer:

Step-by-step explanation:

We know that the diagonals of the parallelogram intersect in half.

Therefore we hawe the equation:

x - 30 = -9 - 6x              add 30 to both sides

x = 21 - 6x              add 6x to both sides

7x = 21            divide both sides by 7

x = 3

X=3 hope this helps sorry if I’m wrong

1. 1/3 to get a red ball.

2. 4/13 to get a blue ball.

3. 3/7 to get a green ball.

Hope this helps!

Answer:

115°

Step-by-step explanation:

A triangle always has 3 angles, and thew sum of the angles is always 180°. Therefore,

38° + 27° + x° = 180°

65° + x° = 180°

x° = 115°

Answer:

x(x)=1/4(30+60+x)

Step-by-step explanation:

minutes spent on math homework= x

minutes spent on history homework= 30 min

minutes spent on English homework= 60 min

Total minutes spent on homework = x+30 +60

Also

x= 1/4(x+30 +60)

x= x/4 + 90/4

x-x/4= 90/4

(4x-x)/4=90/4

3x=90

x=30

Hence time spent on maths=30 min

total time spent= 30+60+30

                          = 120 min

1/4 of 120 min= 30 mins!

Answer:

A. 1/4(x + 30 + 60) = x

Step-by-step explanation:

Answer:

The length of the rectangular pen is [tex]40\ ft[/tex]

The width of the rectangular pen is [tex]20\ ft[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangular pen

y----> the width of the rectangular pen

we know that

The perimeter of the rectangular pen in this problem is equal to

[tex]P=x+2y[/tex] ---> remember that one side of the rectangle won’t need a fence

[tex]P=80\ ft[/tex]

so

[tex]80=x+2y[/tex]

[tex]y=(80-x)/2[/tex] -----> equation A

The area of the rectangular pen is equal to

[tex]A=xy[/tex] -----> equation B

Substitute equation A in equation B

[tex]A=x*(80-x)/2\\ \\A=-0.5x^{2}+40x[/tex]

The quadratic equation is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex is the length of the rectangular pen that maximize the area of the pen

The y-coordinate of the vertex is the maximum area of the pen

using a graphing tool

The vertex is the point (40,800)

see the attached figure

so

[tex]x=40\ ft[/tex]

Find the value of y

[tex]y=(80-x)/2[/tex] ----> [tex]y=(80-40)/2=20\ ft[/tex]

therefore

The length of the rectangular pen is [tex]40\ ft[/tex]

The width of the rectangular pen is [tex]20\ ft[/tex]

Answer:

length is 40

Width is 20

Step-by-Step explanation:

Answer:

easy, it traveled/swam 75.6 miles

Step-by-step explanation:

16.8 x 4.5= 75.6

hope this helps

Answer:

Step-by-step explanation:

Box 1: contains 4 items, two of which are pens. the probability of choosing a pen is 2/4

Box 2: contains 7 crayons and 3 colored pencils for a total of 10. The probability of choosing 1 crayon out of that box is 7/10

Event Probability = 2/4 * 7/10 = 14/40   = 7 / 20

there are 36 possible outcomes

Answer:

c. the empty set

Step-by-step explanation:

set of {x | x < - 5} n {x | x > 5}

The set x < - 5 comprises of real numbers that are less than -5;

(-6, -7, -8, -9, -10, -11, ......)

On the other hand, the set x > 5 comprises of real numbers greater than 5;

(6, 7, 8, 9, 10, 11, ......)

Clearly, the intersection of the above sets is empty, in that the intersection has no elements.

Therefore, {x | x < - 5} n {x | x > 5} is an empty or null set

Answer:

The solution set empty set or null set ⇒ answer c

Step-by-step explanation:

* Lets study the meaning of the inequality

- If a < x < b, that means the value of x is between a and b

- If a ≤ x ≤ b, that means the value of x is from a to b

- If x < a and x > b, that means the value of x is smaller than a and

 grater than b

- If x ≤ a and x ≥ b, that means the value of x is smaller than or equal a and

 grater than or equal b

* Now lets solve the problem

∵ {x I x < -5}

∴ x is smaller than -5

∵ {x I x > 5}

∴ x is greater than 5

∵ {x I x < -5} ∩ {x I x > 5}

- The meaning of ∩ is the common numbers between the

 two sets, but there is no common numbers between the

 two sets

∴ {x I x < -5} ∩ {x I x > 5} = { }

∴ The solution set empty set or null set

Answer:

D

Step-by-step explanation:

add -3m + 1m = -2m

add 5 -11= -6

combine like terms

ANSWER

[tex]a_n=7n - 22[/tex]

EXPLANATION

The recursive rule for the sequence is

[tex]a_n=a_{n-1}+7[/tex]

In general the recursive rule is written as:

[tex]a_n=a_{n-1}+d[/tex]

This implies that, d=7

The first term of the sequence is

[tex]a_1= - 15[/tex]

The explicit rule is given by:

[tex]a_n=a_1 + d(n - 1)[/tex]

We substitute to get;

[tex]a_n= - 15 + 7(n - 1)[/tex]

[tex]a_n= - 15 + 7n - 7[/tex]

[tex]a_n=7n - 22[/tex]

Answer:

Step-by-step explanation:

Put x = -3 to the equation of the function h(x) = x² - 2:

h(-3) = (-3)² - 2 = 9 - 2 = 7

The answer is:

The second option: 2

[tex]\sqrt[4]{81}=3[/tex]

We can solve the problem and find the simplified expression using the following root property:

[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]

We are given the expression:

[tex]\sqrt[4]{81}[/tex]

Which can be rewrite like this:

[tex]\sqrt[4]{81}=\sqrt[4]{3^{4}}[/tex]

Now, simplifying we have:

[tex]\sqrt[4]{3^{4}}=3^{\frac{4}{4} }=3[/tex]

Hence, the answer is the second option:

[tex]\sqrt[4]{81}=3[/tex]

Have a nice day!

Answer:

The correct answer is second option

3

Step-by-step explanation:

From the attached question we can see that,

⁴√81

To find the correct option

We know that 3⁴ = 81

⁴√81 can be written as,

⁴√81 = ⁴√(3 * 3 * 3 * 3)      

 = ⁴√(3)⁴

 = 3

Therefore the answer is 3

The correct option is  second option.  3

.140 I think it's that

Answer:

Step-by-step explanation:

Total number of marbles = 6 + 3 + 5 = 14

You want to draw out 3 marbles -- all of them red. In solving this, you have to assume that none are put back.

The answer is

P(Red) = 6/14 * 5/13 * 4/12

P(Red) = 3/7 + 5/13 + 1/3

numerator = 3*5*1 = 15

denominator = 7 * 13 * 3

denominator = 273

P(red) = 15 / 273

P(red) = 0.0549

Answer:

The two consecutive integers are -119 and -120

Step-by-step explanation:

As we know that these two integers are consecutive, that means that they will have a difference of 1. This means that we can find the two integers by adding 1 to the sum of -239 and then dividing it by two

[tex]1-239=-238\\\frac{-238}{2} =-119\\-119-1=-120[/tex]

When needing to determine two consecutive integers with a given sum, they can be represented as 'x' and 'x+1'. The equation x + (x + 1) = -239 gives us the solution of the two integers as -120 and -119.

In the given question, since we are dealing with consecutive integers, we can represent the integers as 'x' and 'x+1'. As per the information in the question, we know that the sum of these two consecutive integers is -239. Therefore, we can create the equation:

x + (x + 1) = -239

Solving this equation gives us:

2x + 1 = -239

Therefore,

2x = -240

So, x = -120

This indicates that our first integer is -120. Because we are dealing with consecutive integers, the next integer would be -120 + 1 = -119. Thus, the two consecutive integers are -120 and -119.

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Answer:

-3

Step-by-step explanation:

Expression: |-4| - |7|

1. Absolute value (positive distance from zero; found by removing negative sign unless positive): 4 - 7

2. Subtract: -3

The simplified expression is given by -3.

The absolute value of a number is the positive value of that number. The number, if it is negative, will become positive and a positive number will remain positive.

It is given that the expression is: |-4|-|+7|​

We can now simplify the expression.

The expression can be simplified as follows:

|-4|-|+7|​ = 4 - 7

= -3

The given expression was simplified.

The simplified value of the given expression |-4|-|+7|​ is found to be -3.

Therefore, we have found that the simplified expression is given by -3.

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For this case we must indicate an algebraic expression corresponding to the following:

"6 to the square root of 3"

Then, we must indicate an expression of the form:

[tex]a ^ n[/tex]

Where:

[tex]a = 6\\n = \sqrt {3}[/tex]

Thus, the expression is:

[tex]6 ^ {\sqrt {3}}[/tex]

ANswer:

[tex]6 ^ {\sqrt {3}}[/tex]

Answer:

x = 2  is the axis of symmetry

Step-by-step explanation:

y - 4x = 7 – x2?

y =  -x²+4x +7

y = - ((x²- 4x+4)-4)+7

y = - (x-2)²+11 ..... is the the parabola's equation  when : x = 2  is the axis of symmetry

The axis of symmetry for the graph of y - 4x = 7 – x² is x= 2.

The axis of symmetry is a hypothetical straight line that divides a shape into two identical sections, resulting in one component being the mirror image of the other. When folded along the axis of the symmetry, the two portions get overlaid. The straight line is also known as the line of symmetry/mirror line.

The axis of symmetry is a straight line that makes an object's shape symmetrical. The axis of symmetry produces identical reflections on all four sides. It might be horizontal, vertical, or lateral in orientation.

We have the Equation:

y - 4x = 7 – x²

Now, arranging the equation as

y =  -x²+4x +7

y = - ((x²- 4x+4)-4)+7

Now, using the algebraic Identity

(a -b)² = a² - 2ab + b²

So, the equation can be written as

y = - (x-2)²+11

This is in the parabola's equation.

Thus, the axis of symmetry is x= 2.

Learn more about Axis of Symmetry here:

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Answer:

465.3 = 16.5x

Step-by-step explanation:

We can determine the miles per gallon  by taking the number of miles driven and dividing by the gallons

465.3 /16.5 =x

Rewriting by multiplying each side by 16.5

465.3 = 16.5x

Answer:

A

Step-by-step explanation: