A 12 feet piece of wood is to be cut into two pieces. One piece must be 8 feet longer than the other. Find the length of each piece​

Answer:

1. G IS A DEPENDENT VARIABLE

2.U IS THE INDEPENDENT VARIABLE

Step-by-step explanation:

G is a dependent variable because its values will rely on the values of U multiplied by 748. A dependent variable in most cases is isolated on one side of an equation ( mostly the left-hand side) and it value is affected by the values selected on the other side of the equation.

U is an independent variable because it stands on its own such that it does not rely on the behavior of another variable to determine its value/characteristic.Characteristic here i mean , U is freely selected without considering the behavior of other variable, thus it does not face any restrictions as compared to G.

Answer:

x=30

Step-by-step explanation:

The two angles form a straight line

4x+2x = 180

6x= 180

Divide each side by 6

6x/6 = 180/6

x = 30

Answer:

X=30

Step-by-step explanation:

the degree of a straight line is 180

Add 2x and 4x together = 6x

Then divide 6x = 180 by 6 to get the x value.

The answer is 30

Answer:

A.) 1/81

Step-by-step explanation:

This is your equation:

f(x) = 9^x

They want you to solve for x = -2, so substitute -2 in for x.

f(-2) = 9^-2

When you solve this, you get, 1/81.

So, the answer is A.)

I hope this helps! :)

Answer:

14 yds

Step-by-step explanation:

To find the perimeter, we add up all the sides

P = s1 + s2+ s3 + s4

38 = 5.8+7+11.2 + s4

Combine like terms

38 = 24+s4

Subtract 24 from each side

38-24 = 24-24 +s4

14 = s4

The 4th side is 14 yds

Answer:

14yd

Step-by-step explanation:

If the quotient of two numbers is negative, it means that the result of dividing one number by the other is negative.

This situation can only occur if the two numbers have opposite signs. In other words, one number must be positive, and the other must be negative.

When we divide a positive number by a negative number or a negative number by a positive number, the resulting quotient will always be negative. So, to satisfy the given condition, the two numbers must have opposite signs—one positive and one negative.

Therefore, If the quotient of two numbers is negative, it means that the result of dividing one number by the other is negative.

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Final answer:

For the quotient of two numbers to be negative, one of the numbers must be positive and the other must be negative. This principle follows the general rules for multiplication and division involving signed numbers.

Explanation:

For a quotient of two numbers to be negative, one number must be positive and the other negative. This rule aligns with the multiplication and division rules for signs, whereby the product or quotient of two numbers with opposite signs results in a negative outcome.

Essentially, this can be understood by considering examples of multiplication, such as (-3) x 2 = -6 and 4 x (-4) = -16, which similarly apply to division. The same principle holds when dividing two numbers; if their signs are opposite, the result is negative.

This mathematical rule is fundamental and applies universally across mathematics, ensuring consistency in the calculation and understanding of operations involving signed numbers.

Answer with explanation:

 [tex]\rightarrow \frac{\frac{2y^2-6 y-20}{4 y+12}}{\frac{y^2+5 y+6}{3 y^2+28 y+27}}\\\\\rightarrow \frac{\frac{y^2-3y-10}{2 y+6}}{\frac{(y+2)(y+3)}{3 y^2+28 y+27}}\\\\\rightarrow \frac{\frac{(y-5)(y+2)}{2 (y+3)}}{\frac{(y+2)(y+3)}{3 y^2+28 y+27}}\\\\\rightarrow \frac{(y-5)(y+2)}{2 (y+3)}} \times {\frac{3 y^2+28 y+27}{(y+2)(y+3)}}\\\\ \rightarrow\frac{(y-5)\times(3 y^2+28 y+27)}{2 (y+3)^2}}[/tex]

→y²+5y+6

=y²+3 y+2 y+6

=y×(y+3)+2×(y+3)

=(y+2)(y+3)

→y² -3 y-10

=y² -5 y+2 y -10

=y×(y-5)+2×(y-5)

=(y+2)(y-5)

Answer:

B. 3(y-5)/2 on edge

Step-by-step explanation:

Answer:

negative angles are clockwise

Step-by-step explanation:

negative angel: An angle whose generating line is rotated clockwise.

hope this helps!!

Clockwise and counterclockwise are used to indicate the direction of an angle.

The terminal quadrant of -400 degrees is in the clockwise direction

The angle is given as:

[tex]\mathbf{\theta = -400^o}[/tex]

The condition for clockwise direction is: [tex]\mathbf{\theta < 0}[/tex]

While the condition for counterclockwise direction is:[tex]\mathbf{\theta > 0}[/tex]

By comparison:

[tex]\mathbf{-400 < 0}[/tex]

Hence, the terminal quadrant of -400 degrees is in a clockwise direction

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Answer:

fast bike speed = 41/3= 17mph

slower bike speed = 37/3 =12.33 mph

Final answer:

The slower biker's speed is 12 mph and the faster biker's speed is 14 mph, determined by setting up an equation with their combined distances equating to 78 miles after 3 hours.

Explanation:

To resolve the puzzle of the two bikers departing from the same location and traveling in opposite directions, we can apply concepts of rate, time, and distance. We are given that the two bikers are 78 miles apart after 3 hours and that one biker is traveling at a speed that is 2 mph faster than the other.

Let's denote the speed of the slower biker as $x$ mph. Consequently, the speed of the faster biker would be $x + 2$ mph. Considering that they have been traveling for 3 hours, the slower biker would have covered 3$x$ miles and the faster biker 3($x + 2$) miles. The sum of these distances is the total distance between the bikers after 3 hours, which is 78 miles.

Mathematically, we can represent the situation as:

3$x$ + 3($x + 2$) = 78

Simplifying the equation:

3$x$ + 3$x$ + 6 = 78

6$x$ + 6 = 78

6$x$ = 72

$x$ = 12

Thus, the slower biker's speed is 12 mph and the faster biker's speed is 12 mph + 2 mph = 14 mph.

Answer: The faster biker travels at 14 mph and the slower biker travels at 12 mph

Answer:

543.7

Step-by-step explanation:

.67 is closer to .7 than to .6

Answer:

543.7

Step-by-step explanation:

The 7 rounds up to a 6 in the tenth place.

Answer:

100

Step-by-step explanation:

100% of a number + 30% of a number is 130% of a number.

This means 130 = 1.3x.

Now we simplify:

130=1.3x

/1.3   /1.3

100=x

x=100

Therefore, the number is 100.

The unknown number is 100.

Given that, 30% of a number is added to the number, the result is 130.

The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of the whole is always taken as 100.

Let the unknown number be x.

30% of x+x=130

⇒0.3x+x=130

⇒1.3x=130

⇒x=100

Therefore, the unknown number is 100.

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The origin O appears rotated by 180° about ’( -2,0), (-4,0), (-5,2) , ’(-1,2).

Coordinate geometry (or analytic geometry) is described as the examination of geometry and the use of coordinate factors. using coordinate geometry.

Coordinate using the horizontal and vertical distances from the two reference axes. generally represented by way of (x,y) the x-price and y-cost.

Coordinate geometry is used to control and regulate air visitors. The coordinates of the flight are used to describe the plane's modern location. despite the fact that a plane actions a tiny distance (up, down, forward, or backward), the machine updates the coordinates of flight for each small change in its role.

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Answer:

there is no graph

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Range is the largest number minus the smallest number

4-1 = 3

The range is 3

Answer:

3

Step-by-step explanation:

The range of a set of data is the difference between the highest and lowest values in the set.

Sort your data from lowest to highest. You get

1, 2, 3, 4, 4, 4, 4, 4

Highest value = 4

Lowest value = 1

           Range = 3  chocolate chips

Answer:

B

Step-by-step explanation:

To evaluate (f ￮ f)(2) substitute x = 2 into f(x) and evaluate. Then substitute this value into f(x)

f(2) = 15 - 2 = 13, then

f(13) = 15 - 13 = 2

Hence (f ￮ f)(2) = 2

Answer:

Option C is correct.

Step-by-step explanation:

We are given the expression:

[tex](\frac{3^2a^{-2}}{3a^{-1}})^k[/tex]

The value of a =5 and k = -2

Putting the values and solving

[tex]=(\frac{3^2*5^{-2}}{3*5^{-1}})^-2\\=(\frac{3^{2-1}}{5^{-1+2}})^-2\\=(\frac{3^{1}}{5^{1}})^-2\\\\=(\frac{3}{5})^-2\\if \,\,a^{-1} \,\,then\,\, 1/a\\=\frac{(3)^{-2}}{(5)^{-2}}\\ Can\,\,be\,\,written\,\,as\\\\=\frac{(5)^{2}}{(3)^{2}} \\=\frac{25}{9}[/tex]

Option C is correct.

[tex]\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{y}{xy}+\dfrac{x}{xy}=\dfrac{x+y}{xy}=\dfrac{12}{-5}=-\dfrac{12}{5}=-2,4[/tex]

Answer:

x = 10000

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

log x = 4 ( noting that log x has base 10 ), then

x = [tex]10^{4}[/tex] = 10000

Answer:

The ordered pair that is a solution to the equation  (5, 2)

Step-by-step explanation:

It is given that,

2x + 5y = 20

To find the ordered pairs

Multiples of 2 are,

2, 4, 6, 8, 10, 12....

Multiples of 5 are,

5, 10, 15, 20,...

20 can be written as,

20 = 2x + 5y

2x is the multiple of 2 and 5y is the multiple of 5

From the above data we get, 20 = 10 + 10

2x = 10 then x = 5

5y = 10 then y = 2

Therefore  the ordered pair that is a solution to the equation  (5, 2)

Final answer:

To determine if an ordered pair is a solution to the equation 2x + 5y = 20, substitute the values into the equation and check if the simplified result equals 20.

Explanation:

To find an ordered pair that is a solution to the equation 2x + 5y = 20, we need to check which pair (x, y) satisfies the equation when we substitute the values of x and y into it. This involves basic algebraic skills, including substitution and simplification.

Step-by-Step Explanation

If the left side of the equation equals the right side after substitution, then the ordered pair is a solution to the equation. For example, if we substitute x = 2 and y = 4, we get 2(2) + 5(4) = 20 which simplifies to 4 + 20 = 24, not equal to 20. Thus, (2,4) is not a solution. Find an ordered pair where, after the substitution and simplification, the equation is satisfied.

Answer:

The correct answer option is B. 60%.

Step-by-step explanation:

We are given the results of a survey which asked the students whether they have any siblings and pets.

We are to determine the likelihood that student has a pet, given that he or she does not have a sibling.

Assuming A to be the event showing that a student does not have a sibling and B to be the event that a students has a pet.

Then P(B|A) is:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

Substituting the given values, P(A)=0.25 and P(A∩B)=0.15:

[tex]P(B|A)=\dfrac{0.15}{0.25}\\\\P(B|A)=\dfrac{3}{5}\\\\P(B|A)=0.6[/tex]

So the percentage will be:

[tex]0.6\times 100 = [/tex] 60%

Final answer:

A linear equation represents a straight line and is written in the form y = mx + b. A quadratic equation represents a parabolic curve and is written in the form y = ax² + bx + c.

Explanation:

A linear equation is an equation that represents a straight line when graphed. It is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope describes the rate of change between the independent and dependent variables, while the y-intercept is the point where the graph crosses the y-axis.

On the other hand, a quadratic equation is an equation that represents a parabolic curve when graphed. It is typically written in the form y = ax² + bx + c, where a, b, and c are constants. The graph of a quadratic equation is symmetric around a vertical line called the axis of symmetry, and it has either a maximum point or a minimum point.

Answer:

(2,-4) And (3,-2)

Step-by-step explanation:

Here we have to solve one linear equation and a quadratic equation.

First we find the value of y in terms of x from linear equation and then substitute this value in our quadratic equation to solve it for x , Let us see how :

we have y-2x=8

y=2x-8

Now we substitute this in [tex]x^2-3x-y=2[/tex]

Hence we have

[tex]x^2-3x-(2x-8)=2\\x^2-3x-2x+8=2\\x^2-5x+8=2\\x^2-5x+8-2=0\\x^2-5x+6=0\\x^2-2x-3x+6=0\\x(x-2)-3(x-6)=0\\(x-2)(x-3)=0\\[/tex]

Thus we have

either (x-2)= 0 or (x-3)=0

or  x=2 or x=3

Now let us find the value of y by substituting them in y=2x-8 one by one.

y=2(2)-8= 4-8=-4

y+2((3)-8=6-8=-2

Hence our coordinates are

(2,-4) and (3,-2)

Answer:

(2, - 4), (3, - 2)

Step-by-step explanation:

Given the 2 equations

y - 2x = - 8 → (1)

x² - 3x - y = 2 → (2)

Rearrange (1) expressing y in terms of x

y = 2x - 8 → (3)

Substitute y = 2x - 8 in (2)

x² - 3x - 2x + 8 = 2

x² - 5x + 6 = 0 ← in standard form

(x - 2)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 3 = 0 ⇒ x = 3

Substitute these values into (3) for corresponding values of y

x = 2 : y = (2 × 2) - 8 = 4 - 8 = - 4 ⇒ (2, - 4)

x = 3 : y = (2 × 3) - 8 = 6 - 8 = - 2 ⇒ (3, - 2)

ANSWER

The correct answer is B.

EXPLANATION

If the point B(x,y) partitions

[tex]A(x_1,y_1)[/tex]

and

[tex]C(x_2,y_2)[/tex]

in the ratio m:n then, then we have

[tex]x = \frac{mx_2+nx_1}{m + n} [/tex]

and

[tex]y= \frac{my_2+ny_1}{m + n} [/tex]

We want to find the coordinates of the point B(x,y) that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.

This implies that:

[tex]x = \frac{5 \times 11+3 \times - 5}{5 + 3} [/tex]

[tex] \implies \: x = \frac{55 - 15}{8} [/tex]

[tex] \implies \: x = \frac{40}{8} = 5[/tex]

[tex]y = \frac{5 \times 0 + 3 \times 2}{5 + 3} [/tex]

[tex]y = \frac{0 + 6}{8} [/tex]

[tex]y = \frac{6}{8} = \frac{3}{4} [/tex]

Therefore the coordinates of B are

[tex](5, \frac{3}{4} )[/tex]

Answer:

B. (5,3/4)

Step-by-step explanation:

Since, when a segment having end points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is divided by or partitioned by a point, that lies on the segment, in the ratio of m : n,

Then the coordinates of that points are,

[tex](\frac{mx_2+nx_1}{m+n}, \frac{my_2+my_1}{m+n})[/tex]

Here, point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3,

Thus, the coordinates of B are,

[tex](\frac{5\times 11+3\times -5}{5+3}, \frac{5\times 0+3\times 2}{5+3})[/tex]

[tex](\frac{55-15}{8}, \frac{0+6}{8})[/tex]

[tex](\frac{40}{8}, \frac{6}{8})[/tex]

[tex](5, \frac{3}{4})[/tex]

Option 'B' is correct.

The conjugate of the complex number a+bi is a-bi

you just reverse the sign of the imaginary part of the number; so it is 4 -51i

The complex conjugate of the complex number is Option C. 4-51i

To simplify this fraction we multiply the numerator and the denominator by the complex conjugate of the denominator. When we change the sign of the imaginary part, we have the complex conjugate. Another way to think of this is to return all the i with -i. As we can see here, the complex conjugate of 3 - 4i is 3 + 4i.

You find the complex conjugate simply by reversing the sign of the imaginary part of the complex number. To find the complex conjugate of 4+7i we change the sign of the imaginary part. Thus the complex conjugate of 4+7i is 4 - 7i.

Complex conjugate is when "Each of two complex numbers having their real parts equal and their imaginary parts of equal magnitude but opposite sign."

The notation for the complex conjugate of z is either ˉz or z∗. The complex conjugate has the exact real part as z and the same imaginary part but with the opposite sign.

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For this case we have the following equation:

[tex]81x = x ^ 2[/tex]

Rewriting we have:

[tex]x ^ 2-81x = 0[/tex]

We take common factor "x" from both terms:

[tex]x (x-81) = 0[/tex]

It is observed that equality is fulfilled when x = 0 and when x = 81

So, the roots are:

[tex]x_ {1} = 0\\x_ {2} = 81[/tex]

Answer:

[tex]x_ {1} = 0\\x_ {2} = 81[/tex]

Answer:

13 Cars Have Been Loaded, Equation: 12x + 6 = 162

Step-by-step explanation:

If a car holds 12 people, and there are 162 people waiting divide 162 by 12. This gives you 13.5,  which means that 13 total cars have been loaded, while .5 or 6 are left waiting on the line. So 13!

Answer:

162

Step-by-step explanation:

ADD EMMM UPPP GIRLLLLLGET IT TOGETHER

Answer:

[tex]\boxed{\text{1172 in}^{2}}[/tex]

Step-by-step explanation:

SA = SA(prism) + SA(cylinder) – 2SA(cylinder base)

1. Surface area of rectangular prism

The formula for the surface area of a rectangular prism is

S = 2(lw + lh + wh)

Data:  

 l = 16 in

w = 11  in

h = 11  in

Calculations:

2(Top + Bottom) = 2lw  = 2 × 16 × 11 = 352 in²

 2(Front + Back) = 2lh   = 2 × 16 × 11 = 352 in²

   2(Left + Right) = 2wh = 2 × 11 × 11  = 242 in²

                                        Total area =  946 in²

2. Surface area of cylinder

A = A(top) + A (base) + A(side)  = 2A(base) + A(side)

Data:

d = 8 in

h = 9 in

Calculations:

r = ½d  = ½ × 8 = 4 in

[tex]\begin{array}{rcl}SA & = & 2\pi r^{2}+ 2\pi rh \\& = & 2 \times 3. 14\times 4^{2} +2\times 3. 14 \times 4\times 9\\& = & 6.28\times 16 + 226.08\\& = & 100.48 + 226.08\\& = & 326.56 \text{ in}^{2}\\\end{array}[/tex]

3. Excluded area

Excluded area = 2A(base) = 100.48 in²

4. Total area  

[tex]A = 946 + 326.56 - 100.48 \approx \boxed{\textbf{1172 in}^{2}}[/tex]

[tex]\bf \cfrac{x-2}{x^2+4x-12}\implies \cfrac{\begin{matrix} x-2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{(x+6)~~\begin{matrix} (x-2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies \cfrac{1}{x+6}\qquad \{x|x\in \mathbb{R};x\ne 2,x\ne -6\}[/tex]

Answer:

{-6,4}

Step-by-step explanation:

Given

x-4y=-22      Eqn 1

x-y=-10         Eqn 2

Subtracting both equations:

The left hand side of equation 2 will be subtracted from left hand side of eqn 1 and the right side of equation 2 will be subtracted from right hand side of eqn 1.

[tex](x-4y)-(x-y)=-22-(-10)\\x-4y-x+y=-22+10\\-4y+y=-12\\-3y=-12\\\frac{-3y}{-3}=\frac{-12}{-3}\\ y=4[/tex]

Putting y=4 in eqn 2

[tex]x-4=-10\\x=-10+4\\x=-6\\So,\\Solution Set = \{-6,4\}[/tex]

Answer:

{x, y} = {-6, 4}

Step-by-step explanation:

It is given that,

x - 4y = -22    ------(1)

x -  y= -10   -------(2)

To ind the value of x and y

subtract eq(2) from eq(1)

x - 4y = -22    ------(1)

x -  y= -10   -------(2)

0  -3y = -12

3y = 12

y = 12/3 = 4

Substitute the value of y in eq (1)

x - 4y = -22    ------(1)

x - (4*4) = -22

x - 16 = -22

x = -22 +16 = -6

Therefore {x, y} = {-6, 4}

Answer:

[tex]\frac{\sqrt{30}-3\sqrt{2}+\sqrt{55}-\sqrt{33} }{2}[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{\sqrt{6}+\sqrt{11}}{\sqrt{5}+\sqrt{3} }[/tex]

To solve this quotient, we just have to apply a rationalization, which consists in eliminating every root in the denominator. To do so, we multiply and divide the expression by the opposite binomial of the denominator, as follows

[tex]\frac{\sqrt{6}+\sqrt{11}}{\sqrt{5}+\sqrt{3} }=\frac{\sqrt{5}-\sqrt{3} }{\sqrt{5}-\sqrt{3} }\\\\\frac{(\sqrt{6}+\sqrt{11})(\sqrt{5}-\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}\\\\\frac{\sqrt{30}-\sqrt{18}+\sqrt{55}-\sqrt{33} }{5-3}\\ \\\frac{\sqrt{30}-3\sqrt{2}+\sqrt{55}-\sqrt{33} }{2}[/tex]

Therefore, the right answer is the second option.

Answer:

5.94×10^6

Step-by-step explanation:

you have to move the decimal 6 times before reaching the next number then you have to mutiply it by 10 and put the 6