Which of the following shows the true solution to the logarithmic equation below?
log(x)+ log(x+5) = log(6x +12)
©
X=-3
x=4
X=-3 and x = 4
X=-3 and x=-4

Answer:

[tex] ({ {x}^{m} )}^{3} = ( { {x}^{13} )}^{5} \times ( { {x}^{ - 8} )}^{ - 5} [/tex]

[tex] {x}^{3m} = {x}^{65} {x}^{40} [/tex]

[tex] {x}^{3m} = {x}^{105} [/tex]

[tex]3m = 105[/tex]

[tex]m = 35[/tex]

Answer:

5/12 ≈ 0.41667

Step-by-step explanation:

If the first die rolls a 1 and the second die rolls a 1, then the sum is 2.

If the first die rolls a 1 and the second die rolls a 2, then the sum is 3.

Repeating this, we can build a table showing all the possible outcomes:

[tex]\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right][/tex]

As we can see, of the 36 possible outcomes, 15 are greater than seven.  So the probability is 15/36, which reduces to 5/12.

Answer:

5 blocks

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for AC

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AC² = AB² + BC² ← substitute values

AC² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )

AC = [tex]\sqrt{25}[/tex] = 5

Answer:

Could you repost your question with a picture of the arc?

Answer:

The constant of proportionality in the equation y=5/9x​ is k=5/9.

Step-by-step explanation:

Equation for direct proportional function is  

y = kx, where k is a constant of proportionality

so for   y=5/9 x

k=5/9.

Use the midpoint formula

(x1 + x2/2, y1 + y2/2)

Input the corresponding numbers

(-12 +5/2, 3 + -10/2)

(-7/2,-7/2)

So, the midpoint of the line segment is (-7/2,-7/2)

The midpoint of the line segment is (-3.5, -3.5)

To find the midpoint of a line segment, we can use the midpoint formula. The formula is:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Using the coordinates (-12, 3) and (5, -10), we can substitute the values into the formula:

Midpoint = ((-12 + 5) / 2, (3 + -10) / 2)

After simplifying, the midpoint is (-3.5, -3.5).

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Answer:

x+3x+5=101 (Option C).

Step-by-step explanation:

This question requires to be solved using the supposition method.

Let Aylen's savings be $x. Therefore, Rich's savings would be $(3x+5). This is because it is mentioned that Rich has $5 more than 3 times the amount of money Aylen has. The sum of the savings is $101. Therefore the sum of the savings of Aylen and Rich is given by:

x + 3x + 5 = 101. Thus, Option C is the correct answer.

Solve the equation for x gives x = $24. This is Aylen's share. To calculate Rich's share, simply put x=24 in 3x+5. Thus, Rich's share will be $77.

In short, Rich's share = $77, Alan's share = $24, and this has been calculated using the equation x+3x+5=101 (Option C)!!!

Answer:

C x+3x+5=101

Step-by-step explanation:

Answer:

[tex]\large\boxed{x\approx-4.19\ \vee\ x\approx1.19}[/tex]

Step-by-step explanation:

[tex]x^2+3x-5=0\qquad\text{add 5 to both sides}\\\\x^2+3x=5\\\\x^2+2(x)(1.5)=5\qquad\text{add}\ 1.5^2=2.25\ \text{to both sides}\\\\x^2+2(x)(1.5)+1.5^2=5+2.25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1.5)^2=7.25\Rightarrow x+1.5=\pm\sqrt{7.25}\\\\x+1.5\approx\pm2.69\\\\x+1.5\approx-2.69\ \vee\ x+1.5\approx2.69\qquad\text{subtract 1.5 from both sides}\\\\x\approx-4.19\ \vee\ x\approx1.19[/tex]

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the coordinates of the given points G(-4, 1) and H(2, -2):

[tex]m=\dfrac{-2-1}{2-(-4)}=\dfrac{-3}{6}=-\dfrac{1}{2}[/tex]

J(1, 3). Let other point (x, y).

Substitute to the slope:

[tex]\dfrac{y-3}{x-1}=\dfrac{-1}{2}[/tex]            cross multiply

[tex]2(y-3)=-1(x-1)[/tex]    use the distributive property

[tex]2y+(2)(-3)=-x+(-1)(-1)[/tex]

[tex]2y-6=-x+1[/tex]        add 6 to both sides

[tex]2y=-x+7[/tex]      divide both sides by 2

[tex]y=-\dfrac{1}{2}x+\dfrac{7}{2}[/tex]

Check the equality for coordinates of each point:

[tex](-3, 5)\\\\5=-\dfrac{1}{2}(-3)+\dfrac{7}{2}\\\\5=\dfrac{3}{2}+\dfrac{7}{2}\\\\5=\dfrac{10}{2}\\\\5=5\qquad\bold{CORRECT}[/tex]

[tex](1,\ 5)\\\\5=-\dfrac{1}{2}(1)+\dfrac{7}{2}\\\\5=-\dfrac{1}{2}+\dfrac{7}{2}\\\\5=\dfrac{6}{2}\\\\5=3\qquad\bold{FALSE}[/tex]

[tex](3,\ -2)\\\\-2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\-2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\-2=\dfrac{4}{2}\\\\-2=2\qquad\bold{FALSE}[/tex]

[tex](3,\ 2)\\\\2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\2=\dfrac{4}{2}\\\\2=2\qquad\bold{CORRECT}[/tex]

[tex](5,\ 1)\\\\1=-\dfrac{1}{2}(5)+\dfrac{7}{2}\\\\1=-\dfrac{5}{2}+\dfrac{7}{2}\\\\1=\dfrac{2}{2}\\\\1=1\qquad\bold{CORRECT}[/tex]

To identify which points could be on a line that is parallel to another and passes through a specific point, we need to know the slope of the original line or the coordinates of the given point. Without this information, it is impossible to accurately determine which points from the list might be on the parallel line.

The question asks, Which points could be on the line that is parallel to and passes through point J? This problem is a part of geometry in mathematics where we study about points, lines, and planes.

The location of point J was not specified, but the line that is parallel to another would have the same slope, regardless of its y-intercept. As such, to find the points that can lie on a line that is parallel, we must know the slope of the primary line. If we are given the slope 'm', any points that fall on the line would satisfy the equation of a line, y = mx + b, where 'b' is the y-intercept. The points whose 'y' value remains constant in the given x-y pairs would lie on the line parallel to the original line.

Without the proper information about the slope of the line or the position of point J, it is impossible to accurately determine which points from the given list can lie on the line that is parallel and passes through point J.

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Answer:

12.25 miles

Step-by-step explanation:

We can write a proportion to solve.  Miles over time in minutes

1 hour = 60 minutes

1 hours 10 minutes = 60+10 = 70 minutes

3.5 miles         x miles

---------------   = --------------

20 minutes         70 minutes

Using cross products

3.5 *70 = 20x

245 = 20x

Divide each side by 20

245/20 = 20x/20

12.25 =x

Jimmy can go 12.25 miles

Answer:

C' = (-6, -5)

Step-by-step explanation:

We are given that a triangle ABC is reflected over the line y = x.

Given the points of the vertices of the triangle ABC to be (-6, -1) (-2, -1) and (-5, -6) respectively, we are to determine the coordinates of C'.

When reflected over the line y = x, the x and y coordinates exchange their place.

(x, y) ---> (y, x)

Therefore, if C = (-5,-6) then C' = (-6, -5).

Answer:

[tex]\boxed{(-6,-5)}}[/tex]

Step-by-step explanation:

When you reflect a point (x, y) across the line y = x, the coordinates get interchanged. Thus,

(a,b) ⟶ (b,a)

Here are the coordinates of your triangle before and after the reflection.

[tex]\begin{array}{rcl}\textbf{Before} & & \textbf{After}\\A(-6,-1) & \longrightarrow \, & A'(-1,-6)\\B(-2,-1) & \longrightarrow \, & B'(-1,-2)\\C(-5,-6) & \longrightarrow \, & C'(-6,-5)\\\end{array}[/tex]

The diagram below shows ∆ABC with its reflection ∆A'B'C'.

[tex]\text{The coordinates of C' have become } \boxed{\mathbf{(-6,-5)}}[/tex]

Use the distance formula to find the distance between each vertices:

Distance formula: √((x2-x1)^2 + (y2-y1)^2)

(-1,4) (2,7) = 4.24

(-1,4) (1,5) = 2.24

(2,7) (1,5) = 2.24

Perimeter = 4.24 + 2.24 + 2.24 = 8.72

Answer:

7.40 units

Step-by-step explanation:

Answer: 21

Step-by-step explanation:

x is a tangent line, 56-7 is a secant line.  The length is equal to the outside segment times the entire segment. Notice that the length of the outside of the segment is equal to the entire segment for the tangent line.

[tex]x^2=7(56+7)\\\\x^2=7(63)\\\\x=\sqrt{7(63)}\\\\x=\sqrt{7(7\cdot 9)}\\\\x=7\cdot 3\\\\\large\boxed{x=21}[/tex]

Answer:

m=4

Step-by-step explanation:

add 10 to both sides m-10+10=-6+10

m=4

Answer:

Step-by-step explanation:

Answer:

Attached below

Step-by-step explanation:

Given f(x) =1/x    and g(x) = x-2   then;

f.g (x) = f (g(x) )

         =f(x-2)

        =1/x⇒⇒⇒1/x-2

    f.g(x)    =  

[tex]\frac{1}{x-2}[/tex]

Answer:

Step-by-step explanation:

All marbles here are identical. Also, the question isn't concerned about the order in which the marbles are drawn. Thus, all calculations here shall be combinations rather than permutations.

How many ways to choose three out of six identical red marbles without replacement?

[tex]\displaystyle _6C_3 = c(6, 3) = {6\choose 3} = 20[/tex].

Note that these three expressions are equivalent. They all represent the number of ways to choose 3 out of 6 identical items without replacement.

How many ways to choose three out of all the 6 + 10 + 6 = 22 marbles?

[tex]\displaystyle _{22} C_{3} = 1540[/tex].

The probability of choosing three red marbles out of these 22 marbles will be:

[tex]\displaystyle \frac{\text{Number of ways for choosing three out of six red marbles}}{\text{Number of ways to choose three out of 22 marbles}} = \frac{20}{1540} = \frac{1}{77}[/tex].

How many ways to choose two out of six identical red marbles without replacement?

[tex]\displaystyle _6 C_2 = 15[/tex].

How many ways to choose one out of 10 + 6 = 16 non-red marbles?

[tex]_{16} C_1=16 [/tex].

Choosing two red marbles does not influence the number of ways of choosing a non-red marble. Both event happen and are independent of each other. Apply the product rule to find the number of ways of choosing two red marbles and one non-red marble out of the pile of 22.

[tex]_6 C_2 \cdot _{16} C_1= 240[/tex].

Probability:

[tex]\displaystyle \frac{240}{1540} = \frac{12}{77}[/tex].

Double check that the order doesn't matter here.

None of the marbles are red. In other words, all three marbles are chosen out of a pile of 10 + 6 = 16 white and blue marbles. Number of ways to do so:

[tex]_{16} C_{3} = 560[/tex].

Probability:

[tex]\displaystyle \frac{560}{1540}= \frac{4}{11}[/tex].

Answer:

A) 1/77; B) 12/77; C) 4/11

Step-by-step explanation:

A) There are a total of 22 marbles.  6 of them are red.

On the first draw, the probability of getting a red marble is 6/22.

On the second draw, there's one less red marble and one less marble total, so the probability of getting another red marble is 5/21.

Similarly, on the third draw, the probability of getting a red marble is 4/20.

So the probability that all three draws are red marbles is:

P = (6/22) (5/21) (4/20)

P = 1/77

Another way this can be calculated is with combinations:

P = (ways to choose 3 red marbles from 6) / (ways to choose 3 marbles from 22)

P = ₆C₃ / ₂₂C₃

P = 20 / 1540

P = 1/77

B) The same logic can be repeated here.  Using the first method, if the first two selection are red:

P = (6/22) (5/21) (16/20) = 4/77

If the first and third are red:

P = (6/22) (16/21) (5/20) = 4/77

If the last two are red:

P = (16/22) (6/21) (5/20) = 4/77

So the total probability is:

P = 4/77 + 4/77 + 4/77

P = 12/77

Using the second method:

P = (ways to choose 2 red from 6) × (ways to choose 1 non-red from 16) / (ways to choose 3 from 22)

P = ₆C₂ ₁₆C₁ / ₂₂C₃

P = 15 × 16 / 1540

P = 12/77

C)

Same logic:

P = (16/22) (15/21) (14/20)

P = 4/11

Or:

P = ₁₆C₃ / ₂₂C₃

P = 560 / 1540

P = 4/11

Answer:

0x + 2y = 22 ✔️

Step-by-step explanation:

To substract the equations, we should do the following:

5x + 4y = 25

5x + 2y = 3

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

0x + 2y = 22 ✔️

The value of y is: y = 11 ✅✅

The value of x is: x = 3.8 ✅✅

Answer:

To substract the equations, we should do the following:

5x + 4y = 25

5x + 2y = 3

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

0x + 2y = 22

Step-by-step explanation:

Answer:

6m

Step-by-step explanation:

The area of the rectangular plot is

A = l*w

   = 4*9

    = 36 m^2

To find the area of the square plot

A = s^2

36 = s^2

Take the square root of each side

sqrt(36) = sqrt(s^2)

6 = s

The length of the side of the square plot is 6 m

Answer:

14 1/4

Step-by-step explanation:

Answer: AD = 5

because AB equals 10, logically we assume AD equals 5, hopefully this helps you.

Answer:

AD=5

Step-by-step explanation:

We are given that

[tex]\angle 1=\angle 2[/tex]

AB=10, AC=6 BC=6

We have to find the value of AD.

Let AD=x

BD=AB-AD

BD=10-x

By angle bisector theorem

[tex]\frac{AC}{AD}=\frac{BC}{BD}[/tex]

Substitute the values then we get

[tex]\frac{6}{x}=\frac{6}{10-x}[/tex]

[tex]\frac{10-x}{x}=\frac{6}{6}[/tex]

[tex]\frac{10-x}{x}=1[/tex]

[tex]10-x=x[/tex]

[tex]x+x=10[/tex]

[tex]2x=10[/tex]

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

Hence, the value of AD=5 units

Answer:

120°

Step-by-step explanation:

The arc ABC is twice that of the angle created at D. This is the central angle theorem extension.

So we can say that arc ABC = 2* 120 = 240

We know total circle angle is 360 degrees so, arc ADC + arc ABC = 360

Hence,

arc ADC + 240 = 360

arc ADC = 360 - 240 = 120

For this case we give as data the following equation:

[tex]4x + 12 = 48[/tex]

Where "x" represents the cost of a ticket.

By clearing the value of "x" of the equation we can know the cost of a ticket.

If we subtract 12 from both sides of the equation, we have:

[tex]4x = 48-12\\4x = 36[/tex]

If we divide between 4 on both sides of the equation:

[tex]x = \frac {36} {4}\\x = 9[/tex]

Therefore, the cost of a ticket is $ 9.00

Answer:

Option C

C. to show the populations of major cities in 1500

Answer:

C. to show the populations of major cities in 1500

Step-by-step explanation:

correct on edge

Answer:

13170

Step-by-step explanation:

We could just use heron's formula

S=(a+b+c)/2=(155+175+260)/2=295

area=sqrt(S(S-a)(S-b)(S-c))

area=sqrt(295(140)(120)(35))

area=sqrt(173460000)

area=13170 is closest whole number

you could check my work for little errors before you enter anything in if you want :p

Answer:

13170 units^2 to the nearest whole number.

Step-by-step explanation:

Use Heron's formula:

Area = √s(s-a)(s-b)(s-c)

s = the semi-perimeter

= (155 + 175 + 260) / 2

= 590/2 =  295.

Area = √ [295(295-155)(295-175(295-260)]

= √ 173460000

= 13170.42 units^2.

Answer:Correct. He transformed the triangle according to the rule (x, y) → (-y, x).

Answer:

Option A.

Step-by-step explanation:

Consider the below diagram is attached with this question.

Quinton tried to transform triangle FGH according to the rule (x, y) → (–y, x).

From the below figure it is clear that the vertices of triangle FGH are F(3,2), G(1,2) and H(4,5).

The vertices of image after transformation are F'(-2,3), G'(-2,1) and H'(-5,4).

The relation between preimage and image is defined by the rule

[tex](x,y)\rightarrow (-y,x)[/tex]

Since Quinton transformed the triangle according to the rule (x, y) → (–y, x), therefore he is correct.

Thus the correct option is A.

Answer:

3

Step-by-step explanation:

5x-3y=23

4x-4y=20

---------------I'm going to try to set this up for elimination. I notice the bottom equation contains terms that are divisible by 4 so I'm going to divide both sides by 4 on that last equation only...

5x-3y=23

 x-  y=  5

Now I'm going to multiply the bottom equation by -3 so the y terms will be opposite. When you add opposites you do get 0.  That is the whole point of elimination.  

5x-3y=23

-3x+3y=-15

------------------ adding

2x+0=8

2x    =8

 x    =4

So  using that second equation x-y=5 I will find y given that x=4.

4-y=5

-y =1

 y=-1

So the solution to the system is (4,-1)

You are asked to find x+y

So x+y=4+(-1)=3

Answer:

f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192

Step-by-step explanation:

We have the function f(x) = x^2 − x − 12  and g(x) = x^2 − 16 and we need to find the multiplication of both functions.

f(x) × g(x) = ( x^2 − x − 12)(x^2 − 16) = x^4 - 16x^2 -x^3 + 16x -12x^2 + 192

Simplifying:

f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192

Answer: [tex]f(x)*g(x)=x^4-x^3-28x^2+16x+192[/tex]

Step-by-step explanation:

Given the function f(x) and g(x):

[tex]f(x)=x^2 - x -12\\\\g(x)= x^2 - 16[/tex]

We need to multiply them. To do this we need to remember the Product of power property, which states:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

And the multiplication of signs:

[tex](+)(+)=+\\(+)(-)=-\\(-)(-)=+[/tex]

Then:

[tex]f(x)*g(x)=(x^2 - x -12)(x^2 - 16)\\\\f(x)*g(x)=x^4-16x^2-x^3+16x-12x^2+192[/tex]

Adding like terms, we get:

[tex]f(x)*g(x)=x^4-x^3-28x^2+16x+192[/tex]

Answer:

If two pyramid have the same height , for volume to be the same the base area of the pyramids should be equal

Step-by-step explanation:

Volume of a pyramid is given by;

[tex]V=l*w*h /3[/tex]

where l is length of base, w is width of base, and h is height of base

If two pyramid have the same height , for volume to be the same the base area of the pyramids should be equal

The base area= l×w

For example if we have two pyramids A and B with the following properties;

A= height= x , length=l₁ and width = w₁

B= height=x, length=l₂ and width = w₂

Then the volume of the two pyramid will be the same if;

l₁*w₁=l₂*w₂

Thus

V₁= (l₁*w₁*x )/3  = (l₂*w₂*x)/3

For two pyramids with the same height to have the same volume, they must have bases with equal areas.

The volume [tex]\( V \)[/tex] of a pyramid can be calculated using the formula:

[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]

Given that the height [tex]\( h \)[/tex] is the same for both pyramids, the volume formula simplifies to:

[tex]\[ V = \frac{h}{3} \times \text{base area} \][/tex]

For the volumes [tex]\( V_1 \)[/tex] and [tex]\( V_2 \)[/tex] of the two pyramids to be equal, the following equation must hold:

[tex]\[ \frac{h}{3} \times \text{base area}_1 = \frac{h}{3} \times \text{base area}_2 \][/tex]

Since the height [tex]\( h \)[/tex] is constant for both pyramids, it can be cancelled out from both sides of the equation:

[tex]\[ \text{base area}_1 = \text{base area}_2 \][/tex]

Therefore, the bases of the two pyramids must have equal areas to ensure that they have the same volume, given that they have the same height.

Answer:

Option C. Seven was not multiplied by 5/8

Step-by-step explanation:

we know that

To determine the height of a stack of 7 books that are each 2 5/8  inches thick. multiply 7 by 2 5/8

so

[tex]7(2\frac{5}{8})\\ \\7(2+\frac{5}{8})\\ \\7*2+7*\frac{5}{8}\\ \\14+\frac{35}{8}\\ \\14+4+\frac{3}{8}\\ \\18\frac{3}{8}\ in[/tex]

therefore

Seven was not multiplied by 5/8

Answer:

Option B.

Step-by-step explanation:

Giovanna did the calculations to determine the height of a stacks of 7 books having [tex]2\frac{5}{8}[/tex] inches thickness of each book.

[tex]7(2\frac{5}{8})[/tex]

[tex]=7(2+\frac{5}{8})[/tex]

[tex]=(7\times 2)+7(\frac{5}{8})[/tex]

[tex]=14+\frac{35}{8}[/tex]

[tex]=14+4+\frac{3}{8}[/tex]

=18+[tex]\frac{3}{8}[/tex]

[tex]=18\frac{3}{8}[/tex]

Now when compare this solution with Giovanna's solution we find error in 3rd step, in which she hasn't mutiplied the fraction [tex]\frac{5}{8}[/tex] by 7.

Therefore, option B is the correct one.