Solve for x: −7 < x − 1 < 8

[tex]\huge{\boxed{(x-2, y+4)}}[/tex]

[tex]x_1 \bf{-2} =x_2[/tex]

[tex]y_1 \bf{+4} =y_2[/tex]

This means that the answer is the subtract [tex]2[/tex] from the [tex]x[/tex] and add [tex]4[/tex] to the [tex]y[/tex], which is represented as [tex]\boxed{(x-2, y+4)}[/tex]

Also, thank you for posting your first question, and welcome to the community! If you have any questions, don’t hesitate to reach out to me!

The translation that maps (3,-4) to its image (1,0) is given by:

(x, y) ⇒ (x - 2, y + 4)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Translation is the movement of a point either up, down, left or right.

If a point A(x, y) is moved a units left and b units up, the new point is at A'(x - a, y + b).

The translation that maps (3,-4) to its image (1,0) is given by:

(x, y) ⇒ (x - 2, y + 4)

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Answer:

Quotient: x^4+7x^3-2x^2-9x-3

Remainder: -10

Step-by-step explanation:

x5 + 15x+ + 54x3 – 25x2– 75x – 34 by x + 8.

Since the exponents are arranged in descending order so, 15x^4

x^5 + 15x^4+ + 54x^3 – 25x^2– 75x – 34 by x + 8

The division is shown in figure attached.

Quotient: x^4+7x^3-2x^2-9x-3

Remainder: -10

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+3y+2z=8&(1)\\3x+y+3z=-10&(2)\\-2x-2y-z=10&(3)\end{array}\right\qquad\text{subtract both sides of the equations (1) from (2)}\\\\\underline{-\left\{\begin{array}{ccc}3x+y+3z=-10\\x+3y+2z=8\end{array}\right }\\.\qquad2x-2y+z=-18\qquad(4)\qquad\text{add both sides of the equations (3) and (4)}\\\\\underline{+\left\{\begin{array}{ccc}-2x-2y-z=10\\2x-2y+z=-18\end{array}\right}\\.\qquad-4y=-8\qquad\text{divide both sides by (-4)}\\.\qquad\qquad y=2\qquad\text{put the value of y to (1) and (3)}[/tex]

[tex]\left\{\begin{array}{ccc}x+3(2)+2z=8\\-2x-2(2)-z=10\end{array}\right\\\left\{\begin{array}{ccc}x+6+2z=8&\text{subtract 6 from both sides}\\-2x-4-z=10&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+2z=2&\text{multiply both sides by 2}\\-2x-z=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+4z=4\\-2x-z=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad3z=18\qquad\text{divide both sides by 3}\\.\qquad\qquad z=6\qquad\text{put the value of z to the first equation}[/tex]

[tex]x+2(6)=2\\x+12=2\qquad\text{subtract 10 from both sides}\\x=-10[/tex]

Answer:

c = 13.1

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

# ∠A is opposite to side a

# ∠B is opposite to side b

# ∠C is opposite to side c

- The sine rule is:

# [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

* Lets solve the problem

- In Δ ABC

∵ m∠A = 57°

∵ m∠B = 37°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 57° + 37° + m∠C = 180°

∴ 94° + m∠C = 180° ⇒ subtract 94° from both sides

∴ m∠C = 86°

- Lets use the sine rule to find c

∵ a = 11 and m∠A = 57°

∵ m∠C = 86°

∵ [tex]\frac{sin(57)}{11}=\frac{sin(86)}{c}[/tex]

- By using cross multiplication

∴ c sin(57) = 11 sin(86) ⇒ divide both sides by sin(57)

∴ [tex]c=\frac{11(sin86)}{sin57}=13.1[/tex]

* c = 13.1

Answer:

reciprocal

Step-by-step explanation:

Final answer:

To divide two fractions, rewrite the operation as the first fraction multiplied by the reciprocal of the second. Multiplication of fractions involves simply multiplying the numerators and denominators, then simplifying by any common factors.

Explanation:

To divide two fractions, first rewrite the problem as the dividend times the reciprocal of the divisor. When dividing by a fraction, it is equivalent to multiplying by the reciprocal of that fraction. For example, dividing by ⅓ is the same as multiplying by 3 (the reciprocal of ⅓). Similarly, multiplying by ½ is the same as dividing by 2 because ½ is the reciprocal of 2. To multiply fractions, simply multiply the numerators together and the denominators together, simplifying by any common factors as necessary.

Demonstrating this concept through an example, let’s consider the division of 4 by ⅓. First, we find the reciprocal of ⅓, which is 3, and then we multiply 4 by 3 to get 12. Through the multiplication of fractions, if we have ⅛ multiplied by ⅓, we would multiply the numerators (2 and 1) and the denominators (8 and 3), and then simplify the resulting fraction by canceling out any common factors.

Answer:

Option D. x=15°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

see the attached figure to better understand the problem

∠x=(1/2)[arc AB-arc CD]

arc AB=40°

Remember that the diameter divide the circle into two equal parts

arc CD=180°-(130+40)°=10°

substitute

∠x=(1/2)[40°-10°]=15°

Answer:

x = 15!

Step-by-step explanation:

I got it right on my in class exercise!

Answer:

Assuming you have [tex]f(n)=0.4f(n-1)+12[/tex] with [tex]f(1)=4[/tex], the answer is f(2)=13.6.

Step-by-step explanation:

I think that says [tex]f(n)=0.4f(n-1)+12[/tex] with [tex]f(1)=4[/tex].

Now we want to find [tex]f(2)[/tex] so replace n with 2:

This gives you:

[tex]f(2)=0.4f(2-1)+12[/tex]

[tex]f(2)=0.4f(1)+12[/tex]

[tex]f(2)=0.4(4)+12[/tex]

[tex]f(2)=1.6+12[/tex]

[tex]f(2)=13.6[/tex]

Answer:

13.6 (Answer C)

Step-by-step explanation:

I think you meant  f(n) = 0.4 * f(n-1) + 12, where * represents multiplication.

Then f(2) = 0.4 * (4) + 12, or 1.6 + 12, or 13.6.

Answer:

[tex]x=\frac{1+\sqrt{35}i}{-6}\,\, and\,\, x=\frac{1-\sqrt{35}i}{-6}\\[/tex]

Step-by-step explanation:

the quadratic formula is:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a= -2, b = -1 and c =-3

Putting values in the formula

[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(-3)(-3)}}{2(-3)}\\x=\frac{1\pm\sqrt{-35}}{-6}\\x=\frac{1+\sqrt{-35}}{-6}\,\, and\,\, x=\frac{1-\sqrt{-35}}{-6}\\We\,\, know \,\,that \,\,\sqrt{-1} = i  \\x=\frac{1+\sqrt{35}i}{-6}\,\, and\,\, x=\frac{1-\sqrt{35}i}{-6}\\[/tex]

So, [tex]x=\frac{1+\sqrt{35}i}{-6}\,\, and\,\, x=\frac{1-\sqrt{35}i}{-6}\\[/tex]

Answer:

Using quadratic formula, the solution to this equation is  the roots of the equations given are ;   x = 1+√35i /  -6   or                x = 1-√35i /  -6

Step-by-step explanation:

-3x²  -  x   - 3=0

To solve this using quadratic formula, we will first of all write down the quadratic formula

x = -b ±√b²- 4ac   /   2a

From the above question;

a = -3    b = -1  and c=-3

So we can now proceed to plug-in our variable

x = -(-1) ± √(-1)² - 4(-3)(-3)    /      2(-3)

x=  1±√1-36   /   -6

x = 1 ±√-35    /  -6

x=1 ± √35  ·  √-1    /-6

x = 1±√35 i    /     -6

Note the square root of negative 1 is i

Either x = 1+√35i /  -6   or   x = 1-√35i /  -6

Therefore the roots of the equations given are ;   x = 1+√35i / -6   or   x = 1-√35i /  -6

Intersection of two sets E and F is set G which contains elements x that are common to set E and set F.

[tex]G=E\cap F=\{x; x\in E\wedge x\in F\}[/tex]

Here G is,

[tex]G=\{-2,6\}[/tex]

Union of two sets E and F is a set H which contains all elements x that occur in set E or set F.

[tex]H=E\cup F=\{x; x\in E\vee x\in F\}[/tex]

Hence,

[tex]H=\{-2,-1,2,3,5,6,7\}[/tex]

Hope this helps.

r3t40

The intersection of sets E and F: E ∩ F = {-2, 6}

The union of sets E and F: E U F = {-2, -1, 2, 3, 5, 6, 7}

The correct rule that describes the composition of transformations mapping AABC to AA"B"C" is:

- Ro. 900 ◦ T-6, -2(x, y)

Here's a step-by-step explanation:

1. "Ro. 900" stands for a 900 degrees counterclockwise rotation.

2. "T-6, -2" represents a translation of 6 units to the left and 2 units down.

3. When these transformations are applied in sequence to the original figure AABC, you first rotate it 900 degrees counterclockwise and then translate it 6 units to the left and 2 units down, resulting in the figure AA"B"C".

This rule combines rotation and translation to map AABC to AA"B"C". This composition of transformations is what leads to the desired outcome.

The complete question is : Which rule describes composition of transformations that maps ABC to A"B"C"?

Answer: 40% or 2/5

Step-by-step explanation:

10 total marbles

6 yellow

4 red

Probability of blindly picking a red marble is 4/10 or 2/5 which can be written as 40%

The probability of picking a red marble from a bag containing 10 marbles, where 4 are red, is 4 out of 10 or 0.4.

The question asks about the probability of picking a red marble from a bag containing 6 yellow marbles and 4 red marbles, totaling 10 marbles. To calculate the probability, you divide the number of favorable outcomes (picking a red marble) by the number of possible outcomes (total marbles). In this case, the probability of picking a red marble is 4 out of 10, which can be simplified to 2 out of 5 or 0.4.

Answer:

[tex]\frac{\pi}{4}[/tex]

[tex]\frac{5\pi}{6}[/tex]

Step-by-step explanation:

The answer uses the unit circle and that sine and cosecant are reciprocals.

The first choice doesn't even fit the criteria that [tex]x[/tex] is between [tex]0[/tex] and [tex]2\pi[/tex] (inclusive of both endpoints) because of the [tex]x=\frac{-7\pi}{6}[/tex].

Let's check the second choice.

[tex]\csc(\frac{\pi}{4})=\frac{2}{\sqrt{2}} \text{ since } \sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}[/tex].

[tex]\csc(\frac{\pi}{4})>1 \text{ since } \frac{2}{\sqrt{2}}>1[/tex]

[tex]\csc(\frac{\pi}{2})=1 \text{ since } \sin(\frac{\pi}{2})=1[/tex] which means [tex]\csc(\frac{\pi}{2})=1[/tex] which is not greater than 1.

So we can eliminate second choice.

Let's look at the third.

[tex]\csc(\frac{5\pi}{6})=2 \text{ since } \sin(\frac{5\pi}{6})=\frac{1}{2}[/tex] which means [tex]\csc(\frac{5\pi}{6})>1[/tex].

[tex]\csc(\pi)[/tex]  isn't defined because [tex]\sin(\pi)=0[/tex].

So we are eliminating 3rd choice now.

Let's look at the fourth choice.

[tex]\csc(\frac{7\pi}{6})=-2 \text{ since } \sin(\frac{7\pi}{6})=\frac{-1}{2}[/tex] which means [tex]\csc(\frac{7\pi}{6})<1[/tex] and not greater than 1.

I was looking at the rows as if they were choices.

Let me break up my choices.

So we said [tex]x=-\frac{7\pi}{6}[/tex] doesn't work because it is not included in the inequality [tex]0\le x \le 2\pi[/tex].

How about [tex]x=0[/tex]?  This leads to [tex]\csc(0)[/tex] which doesn't exist because [tex]\sin(0)=0[/tex].

So neither of the first two choices on the first row.

Let's look at the second row again.

We said [tex]\frac{\pi}{4}[/tex] worked but not [tex]\frac{\pi}{2}[/tex]

Let's look at the choices on the third row.

We said [tex]\frac{5\pi}{6}[/tex] worked but not [tex]x=\pi[/tex]

Let's look at at the last choice.

We said it gave something less than 1 so this choice doesn't work.

Answer:x=pi/4 and x=5pi/6

Step-by-step explanation:

on edge just did it

Answer:

Option A

Step-by-step explanation:

The domain must be

[a,∞)

That means that x must have as an argument a square root, because, it cannot take negative arguments for real numbers (a>0)

√(x-a)

x-a≥0

x ≥ a

The only possible option is

Option A.

Please take a look at the attached graph

Answer:

The length of each piece of cloth =1/12 yard

Step-by-step explanation:

Number of pieces = 5

Carlos cut 5/12 of a yard of cloth

Length of each piece = ?

To find the length of each piece simply divide 5/12 by 5.

Length of each piece of cloth = 5/12/5

Length of each piece of cloth =5/12 * 1/5

Length of each piece of cloth=1/12

Therefore the length of each piece of cloth =1/12 yard....

Answer:

the answer is a

Step-by-step explanation:

Answer:

option a

Step-by-step explanation:

To find the slope 'm' we use 2 points from the line, those are given in the statement:

[tex]x_{1} =3\\y_{1} =6\\\\x_{2} =5\\y_{2} =3\\m=\frac{y_{2} -y_{1} }{x_{2}-x_{1}}\\m=\frac{3 -6 }{5-3}}\\m=\frac{-3 }{2}}[/tex]

Answer:

720

Step-by-step explanation:

permutation formula=

n!/(n-r)!

There are 720 different starting position configurations possible for the 6 starting players of a volleyball team that follows the rule.

We have

To determine the number of different starting position configurations for a volleyball team with 6 players, we can use the concept of permutations.

Since each player has a unique designated position on the court, we can think of this as arranging 6 distinct objects (the players) in 6 distinct positions (the court positions).

The number of possible arrangements can be calculated using the formula for permutations, denoted as "n P r," which represents the number of ways to select and arrange r objects from a set of n objects.

In this case, we want to arrange 6 players in 6 positions, so we can calculate 6 P 6:

6 P 6 = 6!

Using the formula for factorial:

6! = 6 * 5 * 4 * 3 * 2 * 1

= 720

Therefore,

There are 720 different starting position configurations possible for the 6 starting players of a volleyball team that follows the rule of having exactly 6 players on the court, each with a unique designated position.

Learn more about permutations here:

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Answer:

The solution of kx-2=7 is x = 9/k

Step-by-step explanation:

Given:

kx-2 = 7

In order to get the solution of the given equation, we have to isolate x so that we can determine its value.

Adding 2 on both sides

kx-2+2 = 7+2

kx = 9

Dividing both sides by k

kx/k = 9/k

x = 9/k

Therefore, the solution of kx-2=7 is x = 9/k ..

Answer:

X=9/k

Step-by-step explanation:

^^^ person is right

Answer:

=3/4

Step-by-step explanation:

A bus arrives at a bus stop every 40 minutes.

You arrive at a bus stop at a random time.

So, probability that you will wait at most 10 minutes = 10/40

So, The probability that you will wait at least 10 minutes= 1-10/40

=1- 10/40

By taking L.C.M we get;

=40-10/40

=30/40

=3/4

Thus the probability that you will have to wait at least 20 minutes for the bus is 3/4....

Answer:

3/4

Step-by-step explanation:

hahahaha to you asell

Answer:

the answer is B

Step-by-step explanation:

the sum of both angles is 90 degree.

By definition if the sum of two angles is 180 is supplementary

If the sum of two angles is 90 is complementary

Then, 70 + 20 =90 degree

So, They are complementary angles

Answer:

Option B.

Step-by-step explanation:

Measure of ∠ABC = 20°

and measure of ∠NML = 70°

Then ∠ABC + ∠NML = 20 + 70

                                  = 90°

Therefore, ∠ABC and ∠NML are complementary angles because sum of complementary angles is 90°.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-3y=6&\text{multiply both sides by (-2)}\\2x+2y=4\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-2x+6y=-12\\2x+2y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad8y=-8\qquad\text{divide both sides by 8}\\.\qquad\qquad y=-1\\\\\text{Put the value of y to the first equation:}\\\\x-3(-1)=6\\x+3=6\qquad\text{subtract 3 from both sides}\\x=3[/tex]

Answer: y = -1 and x = 3

Step-by-step explanation:

x - 3y = 6 --------(1)

2x + 2y = 4 -------(2)

we multiply (1) by 2

2x - 6y = 12 --------(3)

(3) - (1)

-8y = 8

y = -1

Putting y = -1 into equation (1)

x - 3 (-1) = 6

x + 3 =6

collect the like term

x = 6 - 3

x = 3

Therefore x= 3 and y = -1

Answer:

B

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 3, 5 ]

From the table of values

f(b) = f(5) = 32

f(a) = f(3) = 8

Hence

average rate of change = [tex]\frac{32-8}{5-3}[/tex] = [tex]\frac{24}{2}[/tex] = 12

Answer:

The average rate of change is [tex]12[/tex]

Step-by-step explanation:

Given:

Interval; x = 3 to x = 5

We'll represent these by

x1 = 3

x2 = 5

The corresponding y values are:

When x = 3, y = 8

When x = 5, y = 32

This will also be represented

y1 = 8

y2 = 32

Average rate of change is then calculated as follows

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

Where m represent average rate of change

By Substitution, we have

[tex]m = \frac{32 - 8}{5 - 3}[/tex]

[tex]m = \frac{24}{2}[/tex]

[tex]m = 12[/tex]

Hence, the average rate of change is [tex]12[/tex]

Answer:

The value is 14/9.

Step-by-step explanation:

xy/9

Put the value of x= -7 and y= -2 in the expression.

=(-7) (-2)/9

=14/9

Answer: A. M=2, y int=3

Step-by-step explanation:

In slope intercept form the equation is y=2x+3, in the formula y=mx+b m=slope and b=y intercept.

The slope and y-intercept of the equation 6x - 1 = 3y - 10 is Option(A) m=2, b = 3 .

The slope of a straight line is the measure of its inclination or tangent to the point of the straight line.

The y-intercept gives the value of the y-coordinate where the straight line intercepts with the y-axis.

For general representation of a straight line y = mx + c , the slope is the value of m and its y-intercept is c.

The given equation is 6x - 1 = 3y - 10 .

⇒ 3y = 6x + 10 - 1

⇒ 3y = 6x + 9

∴  y = 2x + 3

Comparing with the general equation of straight line, y = mx + c we get slope = 2 and y-intercept = 3.

Thus, the slope and y-intercept of the equation 6x - 1 = 3y - 10 is Option(A) m=2, b = 3 .

To learn more about slope refer -

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Answer:

(a,b)

Step-by-step explanation:

simply we find the midpoint of AC and the midpoint of Bd by dividing over 2

Answer:

We choose D.

Step-by-step explanation:

Let the midpoint is O

We will use Angle-SIde-Angle principle to prove that the diagonals of a rectangle bisect each other.

Have a look at the two triangles: AOB and DOC, they are congruent because:

So we can conclude that: OB = OB  when two triangles: AOB and DOC are congruent.

Similar, apply for the two triangles: AOD and BOC are congruent so we have OA = OC .

=> It proves that the point O simultaneously is the midpoint and intersection point for the diagonals.

=> The midpoint of AC is ([tex]\frac{2a+ 0}{2}[/tex] , [tex]\frac{0 + 2b}{2}[/tex] ) = (a, b), we choose D.

Answer:

Fig A

Step-by-step explanation:

in fig A, we can see that the subset that represents "trees", lies inside the subset that "has leaves". Hence in figure A, we can say that "All trees have leaves" or "if it is a tree, it has leaves"

in fig B however, we see that "has leaves" is inside of "trees", this means that the area in-between  "has leaves" and "tree" represents the subset that there are trees without leaves. This is in contradiction to the statement "if it is a tree, it has leaves", hence this is not the answer.

Answer

A

Step-by-step explanation:

hope this helps :)

Answer:

B.  3 and 4

Step-by-step explanation:

In order to find the numbers between which √11 lies, let us first guess the nearest perfect squares to √11. These are 9 and 16. Where 9 comes just before 11 and 16 comes just after 11. Now we have to write all three of them in ascending order.

√9 , √11  ,  √16

also

√9= 3 and √16 = 4

and

√9 < √11 < √16

3 < √11 < 4

hence we can see that √11 must lies between 3 and 4  

Answer:

B.3 and 4

Step-by-step explanation:

3x3=9

4x4=16

so, 11 goes between 3 and 4

I just gave myself a bad rating because I did not want you guys to get the answer wrong because I posted an answer that was wrong and forgot that I could edit so now that I fixed it is a safe answer

Answer:

9÷2+4

Step-by-step explanation:

Answer:

[tex]h(x)=+-\sqrt{\frac{x+4}{9} }[/tex]

Step-by-step explanation:

Hello

I think  I can help you with this

Let

[tex]y = 9x^{2}-4\\h(x)=y^{-1}[/tex]

to find the inverse of y([tex]y^{-1}[/tex])

Step 1

switch x and y

[tex]y = 9x^{2}-4\\\\x= 9y^{2}-4[/tex]

Step 2

Now solve the equation for y (isolating y)

[tex]x= 9y^{2}-4\\Add\ 4\ to\ both\ sides\\x+4= 9y^{2}-4+4\\x+4=9y^{2}\\divide\ each\ side\ by\ 9\\\frac{x+4}{9} =\frac{9y^{2}}{9}\\\\x+4=y^{2} \\[/tex]

[tex]h(x)=+-\sqrt{\frac{x+4}{9} }[/tex]

Have a great day

Answer:

[tex]\large\boxed{(f+g)(x)=4^x+17x-1}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=4^x+12x,\ g(x)=5x-1\\\\(f+g)(x)=(4^x+12x)+(5x-1)=4^x+17x-1[/tex]

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-5}{4-(-3)}\implies \cfrac{-7}{4+3}\implies \cfrac{-7}{7}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=1[x-(-3)]\implies y-5=1(x+3) \\\\\\ y-5=x + 3\implies y=x+8[/tex]