Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solutions are correct?

He is correct because both solutions satisfy the equation.
He is not correct because he made a sign error.
He is not correct because there are no solutions.
He is not correct because there is only one solution: x = 5.

Answer:

The area of DBE = 27 square units

Step-by-step explanation:

Area of ABC = 3 square units

In the figure, we can see that ABC was enlarged so that BDE is formed where side BD = 6 and AB was = 2

Hence ABC was enlarged 3 times its size.

We know by formula that:

Area of ABC = 1/2(base x perpendicular)

3 = 1/2(2 x p)

=> p = 3

As ABC was enlarged 3 times its size, the perpendicular of BDE must be 3*p

= 3*3 = 9

AREA OF DBE = 1/2(base*perp)

= 1/2(6*9)

= 27 square units

Answer:

The area of DBE = 27 square units

Step-by-step explanation:

Area of ABC = 3 square units

In the figure, we can see that ABC was enlarged so that BDE is formed where side BD = 6 and AB was = 2

Hence ABC was enlarged 3 times its size.

We know by formula that:

Area of ABC = 1/2(base x perpendicular)

3 = 1/2(2 x p)

=> p = 3

As ABC was enlarged 3 times its size, the perpendicular of BDE must be 3*p

= 3*3 = 9

AREA OF DBE = 1/2(base*perp)

= 1/2(6*9)

= 27 square units

Step-by-step explanation:

238(56)+238(34)+162(90)

=238(56+34) + 162(90)

=238(90) + 162(90)

=90(238+162)

=90(400)

=36000

For this case we must resolve the following expression:

[tex]238 (56) +238 (34) +162 (90) =[/tex]

We multiply term by term:

[tex]13328 + 8092 + 14580 =[/tex]

We add the terms:

[tex]13328 + 8092 + 14580 = 36000[/tex]

Finally, the answer is 36,000.

Answer:

[tex]238 (56) +238 (34) +162 (90) = 36,000.[/tex]

Answer:

[ - 6 , 6 ]

Step-by-step explanation:

This is because the value of f(t) for x values only ranges from -6 to 6.

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Answer:

See attached!

Step-by-step explanation:

Answer:

y=-12

Step-by-step explanation:

For the slope of line given two points I like to line up and subtract. Then put 2nd diff/1st diff.

Let's do that:

(-6  , -12 )

(0 ,  -12)

-----------

-6      0

2nd/1st=0/-6=0  slope should have been obvious as 0 since there is no rise in the points (you can see this from their y-coordinate)

Anyways the y-intercept is when it crosses the y-axis. The y-axis is crossed when the x-coordinate is 0. You have that given here which is -12.

So the equation is y=0x-12 or jusy y=-12

If you already knew that horizontal lines were of the form y=a number

then you could have just skip to y=-12

y=-12 just means all the ordered pairs on this line have the y-coordinate being -12 which is what we have in the set of points you gave

Answer:

Second option.

Step-by-step explanation:

You can use the formula for calculate the area of a trapezoid. This is:

[tex]A_{(trapezoid)}=\frac{h}{2}(B+b)[/tex]

Where "B" is the larger base, "b" is the minor base and "h" is the height.

You can identify in the figure that:

[tex]B=8units\\b=4units\\h=4units[/tex]

Then you can substitute values into the formula, getting that the area of the trapezoid is:

[tex]A_{(trapezoid)}=\frac{4units}{2}(8units+4units)[/tex]

 [tex]A_{(trapezoid)}=24units^2[/tex]

Answer: 24 units or answer b

Step-by-step explanation:

Answer:

H 16x2–11x

Step-by-step explanation:

4(x2 – 3x) + 12x2 + x

4x^2-12x + 12x^2+x=

16x^2-11x

H 16x2–11x

The simplified value of  4(x² – 3x) + 12x² + x will be 16x² – 11x, i.e. option H.

System of equations is a finite set of equations for which common solutions are sought.

We have,

4(x² – 3x) + 12x² + x

Now,

Simplify the given equation by removing brackets,

i.e.

4x² – 12x + 12x² + x

Now,

Add or subtract the like terms,

i.e.

16x² – 11x

So, the simplified value of the given equation is 16x² – 11x .

Hence, we can say that the simplified value of  4(x² – 3x) + 12x² + x will be 16x² – 11x, i.e. option H.

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ANSWER

[tex]y + 1=2(x-6)[/tex]

EXPLANATION

The point-slope form of a line is given by;

[tex]y-y_1=m(x-x_1)[/tex]

where

[tex]m = 2[/tex]

is the slope of the line and (6,-1) is point.

We substitute the point and the slope into the formula to obtain:

[tex]y + 1=2(x-6)[/tex]

Hence the b point slope form of the line with the given properties is

Answer:

y = -5

Step-by-step explanation:

To find the slope , we use

m = (y2-y1)/(x2-x1)

3/2 = (-2-y)/(2-0)

3/2 = (-2-y)/2

Since the denominators are the same, the numerators have to be the same

3 = -2-y

Add 2 to each side

3+2 = -2-y+2

5 = -y

Divide each side by -1

5/-1 = -y/-1

-5 = y

Answer:

16 centimeters cubed

Step-by-step explanation:

Volume of cone is equal to 1/3 * pi * r^2 * h

We are using 3.14 for pi so I'm going to rewrite my formula for volume.

V=1/3 * 3.14 * r^2 * h

We are given diameter is 3 but we need the radius.  We know the radius is half of the diameter so the radius is 1.5 since that is half of 3.

We are given the height is 7.

V=1/3 * 3.14 * 1.5^2 *7

Put into calculator

V=16.485

The whole number that this is closest to is .... 16

So

The Volume of the cone is approximately 16 centimeters cubed.

Answer: [tex]16\ cm^3[/tex]

Step-by-step explanation:

You can use this formula for calculate the volume of a cone:

[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height of the cone.

To find the radius, you need to divide the diameter by 2. Then:

[tex]r=\frac{3\ cm}{2}=1.5\ cm[/tex]

Knowing the radius and the height ([tex]h=7\ cm[/tex]), you can substitute them into the formula.

Therefore, the volume of the cone rounded  to the nearest whole number is:

 [tex]V_{(cone)}=\frac{1}{3}(3.14)(1.5\ cm)^2(7\ cm)\\\\V_{(cone})=16\ cm^3[/tex]

The air conditioning system can circulate approximately 14.44 cubic yards of air per minute.

To convert cubic feet to cubic yards, we need to know that there are 27 cubic feet in one cubic yard. Using this conversion factor, we can find the number of cubic yards of air that the air conditioning system can circulate per minute.

1. Start with the given value of 390 cubic feet per minute.

2. Divide this value by the conversion factor of 27 cubic feet per cubic yard:

390 cubic feet ÷ 27 cubic feet per cubic yard = 14.44 cubic yards

3. Rounding to the nearest hundredth, the air conditioning system can circulate approximately 14.44 cubic yards of air per minute.

In summary, the air conditioning system can circulate approximately 14.44 cubic yards of air per minute.

Answer:

D = 9.4868

Step-by-step explanation:

The expression is the following

D = √((x2-x1)^2+(y2-y1)^2)

Where

(x1,y1) = (4,6)

(x2,y2) = (7,-3)

D = √((7-4)^2+(-3-6)^2)

D = √((3)^2+(-9)^2)

D = √(9+81)

D = √(90)

D = 9.4868

Answer:

[tex]d = \sqrt{(7-4)^{2}+(-3-6)^{2}}[/tex]

Step-by-step explanation:

The expression used for calculating distance between two points involves the square root of sum of squares of differences of x-intercepts and y-intercepts.

The formula is given by:

[tex]d = \sqrt{(x_{2} -x_{1} )^{2}+(y_{2}- y_{1} )^{2} }[/tex]

Here,

[tex](x_{1},y_{1}) = (4,6)\\ (x_{2},y_{2}) = (7,-3)\\Putting\ the\ values\\d = \sqrt{(7-4)^{2}+(-3-6)^{2}}[/tex]

Hence, the following expression will give the distance between given points

[tex]d = \sqrt{(7-4)^{2}+(-3-6)^{2}}[/tex]

Solving it will give:

[tex]d = \sqrt{(3)^{2}+(-9)^{2}}\\= \sqrt{9+81}\\=\sqrt{90}[/tex]

[tex]\bf \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 4\log_9(3)=\log_9(x)\implies \log_9(3^4)=\log_9(x)\implies 3^4=x\implies 81=x[/tex]

The value of x will be equal to 81.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

4log₉(3)   =  log₉x

By using the logarithmic property:-

Log[tex]_a[/tex]( x[tex].^b[/tex])  =  b Log[tex]_a[/tex](x)

4log₉(3)   =  log₉x

log₉ ( 3 )⁴  =  log₉ ( x )

3⁴   =  x

x   =  81

Therefore the value of x will be equal to 81.

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Answer:

A

Step-by-step explanation:

f(x) - g(x) = 3x-2 - (2x + 1)      Remove the brackets

f(x) - g(x) = 3x - 2 - 2x -1       Combine terms.

f(x) - g(x) = x - 3

The answer is A

Hello There!

70% of 420 is 294

You want to divide 70% by 100 and you get a quotient of 0.7

Next, you want to multiply that by 420 because your trying to find 70% of it.

Finally, once you multiply you will get a product of 294.

Have A Great Day!

The mean of this data set is 18.8

Answer:

The mean of this data set is  [tex]\mu = 18.8[/tex]

Step-by-step explanation:

By definition, the mean of a data set [tex]x_1, x_2, x_3, ..., x_n[/tex] is

[tex]\mu = \frac{\sum^n_i x_i}{n}[/tex]

Where n is the total number of data.

In this case we have 10 data

14, 12, 21, 26, 19, 15, 22, 17, 24, 18

So the mean is:

[tex]\mu = \frac{14 +12 +21 +26 +19 +15 +22+ 17 +24 +18}{10}[/tex]

[tex]\mu = 18.8[/tex]

Answer:3.4

Step-by-step explanation:

Answer:

[tex]m = -4[/tex]

Step-by-step explanation:

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

[tex]\frac{-4 - 8}{2-(-1)}[/tex]

[tex]-4 - 8 = -12\\ 2-(-1)=3[/tex]

[tex]\frac{-12}{3} = -4[/tex]

[tex]m = -4[/tex]

Answer:

M=-4

Step-by-step explanation:

The formula for the slope is:

m=[tex]\frac{y^{2} -y^{1} }{x^{2} -x^{1} }[/tex]

You have two points the first one would be: (-1,8)

So [tex]x^{1}= -1  y^{1}= 8 [/tex]

The second point is: (2,4)

So [tex]x^{2}= 2  y^{2}= 4 [/tex]

Now you just have to put the values inside the formula:

m=[tex]\frac{-4-8)}{2-(-1)}[/tex]

m=[tex]\frac{-12}{3}[/tex]

m=-4

[tex]\displaystyle\\\lim_{x\to 2}\dfrac{x^2+2x-3}{x-3}=\dfrac{2^2+2\cdot2-3}{2-3}=\dfrac{5}{-1}=-5[/tex]

The right-hand limit of the function f(x) = (x^2 + 2x - 3)/(x - 3) as x approaches 2 is -5 after substitution of x = 2 into the function.

The question asks about the right-hand limit of the function f(x) = (x^2 + 2x - 3)/(x - 3) as x approaches 2. The first step in finding this limit is to simplify the function, if possible. In this case, we can factor the numerator to obtain (x - 1)(x + 3). However, since we are looking for a limit as x approaches 2, the denominator x - 3 will not be zero, and the expression does not need further simplification for this purpose. We then substitute x = 2 directly into the simplified function and find the limit.

So, the right-hand limit as x approaches 2 is simply f(2) = ((2)^2 + 2*2 - 3)/(2 - 3) = (4 + 4 - 3)/(-1) = 5/(-1) = -5.

The exact value of sin(11π/12) is (√6 - √2)/4.

To find the exact value of sin(11π/12), we can use trigonometric identities to determine the value of an equivalent angle in the first quadrant. Since π/12 is the reference angle of 11π/12, which is in the second quadrant, we can find the sine of the equivalent angle in the first quadrant. The reference angle in the first quadrant is π/12. Therefore, the exact value of sin(11π/12) is the same as the exact value of the sine of π/12. Using a trigonometric identity, we find that sin(π/12) = (√6 - √2)/4.

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Answer:

10

Step-by-step explanation:

Leave the 5 , change division to multiplication and turn the fraction upside down.

5 × [tex]\frac{2}{1}[/tex] = 5 × 2 = 10

Answer:

(-7, 2).

Step-by-step explanation:

x + 12y = 17

x - y = -9

Subtracting:

0 + 13y = 26

y = 2.

Substitute for y in the second equation:

x - 2 = -9

x = -7.

Answer:

{-7,2}

Step-by-step explanation:

Given

x+12y=17     Eqn 1

x-y=-9          Eqn 2

We will use the substitution method to solve the system of equations. So, from eqn 2:

[tex]x-y=-9\\x=y-9[/tex]

Putting the value of x in equation 1:

[tex](y-9)+12y=17\\y-9+12y=17\\y+12y-9=17\\13y=17+9\\13y=26\\\frac{13y}{13}=\frac{26}{13}\\ y=2[/tex]

Putting the value of y in eqn 2:

[tex]x-2=-9\\x=-9+2\\x=-7\\So,\\Solution set = \{-7,2\}[/tex]

Answer:

Step-by-step explanation:

The given inequality is

[tex]-4(2x-1)>5-3x[/tex]

The first step we need to do is to apply distributive property to relase the binomial inside the parenthesis

[tex]-8x+4>5-3x[/tex]

Then, we move all variables to the left side, and all constants to the right side

[tex]-8x+3x>5-4\\-5x>1[/tex]

Now, we divide the inequality by -5, which changes the sign orientation

[tex]\frac{-5x}{-5} <\frac{1}{-5}\\ x<-\frac{1}{5}[/tex]

Therefore, the solution is a set with all values less than -1/5. The graph attached shows this solution.

Answer: Cross section

Step-by-step explanation: A cross section sounds just like what it is. It’s a plane that intersects a solid figure. A cross section can happen on any solid figure.

Answer:

[tex]\frac{1}{(m-4)(m-3)}[/tex]

Step-by-step explanation:

The question requires you to simplify using quadratic identities

Re-write the numerator.

[tex]\frac{m+3}{m^2-16} \\\\\\\\=\frac{m+3}{(m+4)+(m-3) }[/tex]

Re-write the denominator as;

[tex]\frac{(m+3) +(m-3)}{m+4}[/tex]

Re-arrange expression

[tex]\frac{m+3}{(m+4)+(m-4)} * \frac{m+4}{(m+3)+(m-3)}[/tex]

cancel the terms that are alike to remain with

[tex]\frac{1}{(m-4)(m-3)}[/tex]

Answer:

The expression which equivalent is 1/[(m - 4)(m - 3)] ⇒ 2nd answer

Step-by-step explanation:

* Lets revise how to divide two fractions

- To divide a/b and c/d change the division operation to multiplication

  operation and reciprocal the fraction after the division sign

# a/b ÷ c/d = a/b × d/c

* Lets solve the problem

∵ (m + 3)/(m² - 16) ÷ (m² - 9)/(m + 4)

- Use the factorization to simplify the fractions

∵ m² - 16 is a different of two squares

- The factorization of the different of two squares a² - b² is

∵ a² = a × a , -b² = b × -b

∴ a² - b² = (a + b)(a - b)

- Use this way with m² - 16

∵ m² = m × m

∵ -16 = 4 × -4

∴ m² - 16 = (m + 4)(m - 4)

- Similar factorize m² - 9

∵ m² = m × m

∵ -9 = 3 × -3

∴ m² - 9 = (m + 3)(m - 3)

- Now lets write the fraction and simplify it

∵ (m + 3)/(m² - 16) ÷ (m² - 9)/(m + 4)

∴ (m + 3)/[(m + 4)(m - 4)] ÷ [(m + 3)(m - 3)]/(m + 4)

- Change the division operation to multiplication operation and

  reciprocal the fraction after the division sign

∴ (m + 3)/[(m + 4)(m - 4)] × (m + 4)/[(m + 3)(m - 3)]

- We can cancel (m + 4) in the denominator of the first fraction with

 (m + 4) in the numerator of the second fraction and cancel (m + 3)

 in the numerator of the first fraction with (m + 3) in the denominator

 of the second fraction

∴ 1/(m - 4) × 1/(m - 3) ⇒ multiply the two fractions

∴ 1/[(m - 4)(m - 3)]

* The expression which equivalent is 1/[(m - 4)(m - 3)]

Answer:

x = 1 or x = -7

Step-by-step explanation:

Step-by-step explanation:

Do you mean by completing the square?

x² + 6x - 7 = 0

x² + 6x = 7

Take half of 6, square it, and add to both sides.  (6/2)² = 9.

x² + 6x + 9 = 7 + 9

(x + 3)² = 16

x + 3 = ±4

x = -3 ± 4

x = -7, 1

So the roots are x=-7 and x=1.

Answer: I think problem 2

Step-by-step explanation: hope this helps

Answer:

Harold typed 76, Rebecca typed 62  

Step-by-step explanation:

It's Easy. For the first one, convert 1/5 and 2/3 to the like denominator of 15.  

Therefore, you have 3/15 and 10/15. Add these to get 13/15. Now, find 13/15 of 60. To do this you will have to multiply 13 and 15 by 4 to get 52/60. Since the question asks you for how many are left, you subtract 52 from 60 to get 8.  

And For the second one, first subtract 14 from 138. You have 124. Divide 124 by 2 to get 62. Then add 14 to Harold's total pages to get 76. 62 +76 = 138.

Answer:

4 is the first blank

-2 is the second blank

3 is the third blank

Step-by-step explanation:

Table:

x   |  y

__    0         So this means we replace y with 0 in x-0=4 which means x=4

4      0    

4 is the first blank

Table:

x |  y

2   ___     So this means we replace x with 2 in 2-y=4 which means y=-2

2   -2

-2 is the second blank

Table:

x  | y

__  -1    So this means we replace y with -1 in x-(-1)=4 which means x=3

3    -1

3 is the third blank

Answer:

Step-by-step explanation:

[tex]4(4^x-2^x)+1=0\\\\4\bigg((2^2)^x-2^x\bigg)+1=0\qquad\text{use}\ (a^n)^m=a^{nm}\\\\4(2^{2x}-2^x)+1=0\\\\4\bigg((2^x)^2-2^x\bigg)+1=0\qquad\text{substitute}\ 2^x=t>0\\\\4(t^2-t)+1=0\qquad\text{use the distributive property}\\\\4t^2-4t+1=0\\\\4t^2-2t-2t+1=0\\\\2t(2t-1)-1(2t-1)=0\\\\(2t-1)(2t-1)=0\\\\(2t-1)^2=0\iff2t-1=0\qquad\text{add 1 to both sides}\\\\2t=1\qquad\text{divide both sides by 2}\\\\t=\dfrac{1}{2}[/tex]

[tex]\text{We're going back to substitution}\\\\t=\dfrac{1}{2}\Rightarrow2^x=\dfrac{1}{2}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\2^x=2^{-1}\iff x=-1[/tex]