solve the equation
log(5x)-log(x-3)=1​

Answer:

A(1,1)

Step-by-step explanation:

the system is :

2x-y=1

x+2y=3

so :

y = 2x-1  .....the line color : red

y= (-1/2)x+3/2......the line color : blue

the pair solution is the intersection point for this line : A(1 ; 1)

Answer:

V ≈ 915.7 cm³

LA ≈ 411.3 cm²

SA ≈ 596.9 cm²

Step-by-step explanation:

Volume of a pyramid is:

V = ⅓ Bh

where B is the area of the base and h is the height.

The base is a regular octagon.  The area of a regular octagon is 2(1 + √2) s², where s is the side length.

Substituting:

V = ⅔ (1 + √2) s² h

Given that s = 6.2 and h = 14.8:

V = ⅔ (1 + √2) (6.2)² (14.8)

V ≈ 915.7 cm³

The lateral surface area is the area of the sides of the pyramid.  Each side is a triangular face.  We know the base length of the triangle is 6.2 cm.  To find the area, we first need to use geometry to find the lateral height, or the height of the triangles.

The lateral height and the perpendicular height form a right triangle with the apothem of the octagon.  If we find the apothem, we can use Pythagorean theorem to find the lateral height.

The apothem is two times the area of the octagon divided by its perimeter.

a = 2 [ 2(1 + √2) s² ] / (8s)

a = ½ (1 + √2) s

a ≈ 7.484

Therefore, the lateral height is:

l² = a² + h²

l ≈ 16.58

The lateral surface area is:

LA = 8 (½ s l)

LA = 4 (6.2) (16.58)

LA ≈ 411.3 cm²

The total surface area is the lateral area plus the base area.

SA = 2(1 + √2) s² + LA

SA = 2(1 + √2) (6.2)² + 411.3

SA ≈ 596.9 cm²

The volume is 915.7 cm³

The lateral surface area is 411.3 cm²

The total surface area is 596.9 cm²

Answer:

y=(3/2)x+-14

First blank: 3

Second blank:2

Last blank:-14

Step-by-step explanation:

The line form being requested is slope-intercept form, y=mx+b where m is slope and b is y-intercept.

Also perpendicular lines have opposite reciprocal slopes so the slope of the line we are looking for is the opposite reciprocal of -2/3 which is 3/2.

So the equation so far is

y=(3/2)x+b.

We know this line goes through (x,y)=(4,-8).

So we can use this point along with our equation to find b.

-8=(3/2)4+b

-8=6+b

-14=b

The line is y=(3/2)x-14.

Answer:

(x+5)^2=34

Solutions: ≈ -10.831, 0.831

Step-by-step explanation:

First you divide the second term by two to complete the square.  The second term divided by two is 5, 5^2 is 25 which means you need a value of 25 to factor.  Add 3 to both sides so you have a value of 25 on the left side.

x^2+10x+25=34  Next, factor the left side.

(x+5)^2=34  

The solutions to this equation are not rational, you could use the quadratic formula to find the exact answer or put the equation into a graphing calculator to find approximate solutions.

Answer:

Step-by-step explanation:

If we divide 9,795 by 7 we get:

=1399.28571429

Rounding to the nearest hundredth:

Underline the hundredths place: 1399.28571429

Look to the right. If it is 5 or above 5 then we give it a shove.

If it is 4 or less than 4, we let it go.

In our case it is 5. We will add 1 in 8, then it will become 9. 28 will be rounded off as 29.

Therefore the answer after rounding off to the nearest hundredth is 1399.29....

Answer:

(12, 3.2) would be the max amount of gas he could buy.  (11.25, 3) for an even gallon amount.

Step-by-step explanation:

Answer:

(3.2, 12)

Step-by-step explanation:

Total cost for gas = $12

Cost per gallon = $3.75

Letting total cost of gas be y and number of gallons be x, maximum number of gallons of gas he can buy would be ;

Total cost of gas/ cost per gallon = 12 / 3.75 = 3.2 gallons

Therefore , the coordinate pair (x, y) = (3.2, 12)

Answer:

Choose something close to (1.8,2.6)

Choice A

Step-by-step explanation:

Without the graph provided, I would prefer to do this algebraically.

y=2x-1

y=-1/4x+3

Since both are solved for y, I'm going to replace the first y with what the second y equals.

-1/4x+3=2x-1

I don't really like to deal with fractions quite yet so I'm going to multiply both sides by 4.

-1x+12=8x-4

I'm going to add 1x on both sides.

     12=9x-4

I'm going to add 4 on both sides.

     16=9x

I'm going to divide both sides by 9

    16/9=x

This is the same as saying x=16/9.

Now to find y, just choose one of the equations and replace x with 16/9.

y=2x-1

y=2(16/9)-1

y=32/9-1

y=32/9-9/9

y=(32-9)/9

y=23/9

So the exact solution is (16/9,23/9).

Round these numbers to the nearest tenths you get:

(1.8, 2.6) .

To get this I just typed into my calculator 16 divided by 9 and 23 divided by 9

16 divided by 9 gave me 1.777777777777777777777777777

23 divided by 9 gave me 2.5555555555555555555555555

So choose something close to (1.8, 2.6).

So your ordered pair (1.75,2.5) is pretty close to that so choice A.

Answer:

see explanation

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 5x + 4 ( subtract 4 from both sides )

y - 4 = 5x ( divide both sides by 5 )

[tex]\frac{y-4}{5}[/tex] = x

Change y back into terms of x

[tex]f^{-1}[/tex] (x) = [tex]\frac{x-4}{5}[/tex]

Answer:

f (gx) = 1/ -2(1/x^2+6x+10) + 9

Step-by-step explanation:

f (gx) = 1/ -2(1/x^2+6x+10) + 9

Answer:

The domain is all real numbers where

[tex](f \circ g)(x)=\frac{x^2+6x+10}{9x^2+54x+88}[/tex]

Step-by-step explanation:

[tex](f \circ g)(x)=f(g(x))[/tex]

So g(x) must exist before plugging it into f(x).

Let's find where g(x) doesn't exist.

[tex]x^2+6x+10[/tex] is a quadratic expression.

[tex]b^2-4ac[/tex] is the discriminant and will tell us if [tex]x^2+6x+10=0[/tex] will have any solutions.  I'm trying to solve this equation because I want to figure out what to exclude from the domain.  Depending on what [tex]b^2-4ac[/tex] we may not have to go full quadratic formula on this problem.

[tex]b^2-4ac=(6)^2-4(1)(10)=36-40=-4[/tex].

Since the discriminant is negative, then there are no real numbers that will make the denominator 0 here.  So we have no real domain restrictions on g.

Let's go ahead and plug g into f.

[tex]f(g(x))[/tex]

[tex]f(\frac{1}{x^2+6x+10})[/tex]  

I replaced g(x) with (1/(x^2+6x+10)).

[tex]\frac{1}{-2(\frac{1}{x^2+6x+10})+9}[/tex]  

I replaced old input,x, in f with new input (1/(x^2+6x+10)).

Let's do some simplification now.

We do not like the mini-fraction inside the bigger fraction so we are going to multiply by any denominators contained within the mini-fractions.

I'm multiplying top and bottom by (x^2+6x+10).

[tex]\frac{1}{-2(\frac{1}{x^2+6x+10})+9} \cdot \frac{(x^2+6x+10)}{(x^2+6x+10)}[/tex]  

Using distributive property:

[tex]\frac{1(x^2+6x+10)}{-2(\frac{1}{x^2+6x+10})\cdot(x^2+6x+10)+9(x^2+6x+10)}[/tex]

We are going to distribute a little more:

[tex]\frac{x^2+6x+10}{-2+9x^2+54x+90}[/tex]

Combine like terms on the bottom there (-2 and 90):

[tex]\frac{x^2+6x+10}{9x^2+54x+88}[/tex]

Now we can see if we have any domain restrictions here:

[tex]b^2-4ac=(54)^2-4(9)(88)=-252[/tex]

So again the bottom will never be zero because [tex]9x^2+54x+88=0[/tex] doesn't have any real solutions.  We know this because the discriminant is negative.

The domain is all real numbers where

[tex](f \circ g)(x)=\frac{x^2+6x+10}{9x^2+54x+88}[/tex]

The distance from point A to A' after translation is 2 sqrt(13).

The given points are A(-6,-5) and A' is obtained by translating A using the transformation T: (x,y) -> (x + 4, y + 6).

So the coordinates of A' are (-6 + 4, -5 + 6) which is (-2,1).

To find the distance from A to A', we can use the distance formula.

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of A and A' into the formula, we get Distance = sqrt((-2 - (-6))^2 + (1 - (-5))^2).

Calculating the distance, we get Distance = sqrt((4)^2 + (6)^2) = sqrt(16 + 36) = sqrt(52) = 2 sqrt(13).

Answer:

y = 3/2 x + 3

Step-by-step explanation:

2/3 x + y = -14/3

y = -2/3 x − 14/3

The slope of this line is -2/3.  So the perpendicular slope is the opposite of the inverse:

m = -1 / (-2/3)

m = 3/2

We know the slope of the line and a point on the line, so using point-slope form:

y − 0 = 3/2 (x − (-2))

Simplifying into slope-intercept form:

y = 3/2 (x + 2)

y = 3/2 x + 3

Answer:

(1, - 6 )

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y )

The point J has coordinates (0, 3 ), hence

J'(0, - 3 ) ← after reflection in x- axis

A translation (x, y ) → (x + 1, y - 3 )

Means add 1 to the x- coordinate and subtract 3 from the y- coordinate

J'(0, - 3 ) → J''(0 + 1, - 3 - 3 ) → J''(1, - 6 ) ← final image

Answer:

cross multiplication

Step-by-step explanation:

Answer:

x= 5/3

Step-by-step explanation:

3x- 5 = 1

first you have to move the constant or in this case the 5 to the other side to isolate x so to do that you have to ad 5 from both sides, that way itll cancel out from the left and add on the right

3x= 5

now, to isolate x, we have to divide by 3, that way you get

x= 5/3

Answer:

The answer is -1

Step-by-step explanation:

f(x) = 2x³ + x² - 3x - 1  

f(1) = 2(1)³ + (1)² - 3(1) - 1

f(1)= 2 + 1 - 3 - 1

f(1)=3-3-1

f(1)=0-1

f(1)= -1

Thus the answer is -1 ....

Answer:

-1

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Given

x + 10 = 15 ( subtract 10 from both sides )

x = 5 → B

Answer:

A) -0.3 of an inch per second

Step-by-step explanation:

You'll have to put (2, 8.4) and (4, 7.8) into the slope formula.

It's represented as (∆y)/(∆x) = m

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

You subtract both y's in the numerator and subtract both x's in the denominator.

Like this:

(8.4-7.8)/(2-4) = m

(0.6)/(-2) = m

-0.3 = m

Answer:

y = (-0.3 in/sec)x + 9.0 in

Step-by-step explanation:

(2, 8.4) and (4, 7.8) are points on a linear graph.

As we go from  (2, 8.4)  to  (4, 7.8), x increases by 2 and y decreases by 0.6.

Thus, the slope of the line is m = rise / run = -0.6 / 2, or m = -0.3 inches/sec

Let's use the slope-intercept form of the equation of a straight line, with m = -0.3 in/sec and one point being (2, 8.4).

Then y = mx + b becomes 8.4 = (-0.3 in/sec)(2) + b, or

8.4 = -0.6 + b.  Thus, b = 9.0, and the desired equation is thus:

y = (-0.3 in/sec)x + 9.0 in

Answer:

Step-by-step explanation:

we have

[tex]18 > -5x+2 > -48[/tex]

This is a compound inequality

Remember that

A compound inequality i can divide in a system of two inequalities

so

[tex]18 > -5x+2[/tex] -----> inequality A

[tex]-5x+2 > -48[/tex] ---> inequality B

step 1

Solve the inequality A

[tex]18 > -5x+2[/tex]

Multiply by -1 both sides

[tex]-18< 5x-2[/tex]

[tex]-18+2< 5x[/tex]

[tex]-16< 5x[/tex]

Divide by 5 both sides

[tex]-3.2< x[/tex]

Rewrite

[tex]x > -3.2[/tex]

The solution of the inequality A is the interval ----> (-3.2,∞)

step 2

Solve the inequality B

[tex]-5x+2 > -48[/tex]

Multiply by -1 both sides

[tex]5x-2 < 48[/tex]

[tex]5x < 48+2[/tex]

[tex]5x < 50[/tex]

Divide by 5 both sides

[tex]x < 10[/tex]

The solution of the inequality B is the interval ----> (-∞, 10)

step 3

Find the solution of the compound inequality

(-3.2,∞) ∩ (-∞, 10)=(-3.2,10)

All real numbers greater than -3.2 and less than 10

The graph in the attached figure

Answer:

value of a.b = -4

Step-by-step explanation:

We need to find a.b

a= 4i-4j

b = 4i+5j

We know that i.i =1, j.j=1, i.j =0 and j.i=0

a.b = (4i-4j).(4i+5j)

a.b = 4i(4i+5j)-4j(4i+5j)

a.b = 16i.i +20i.j-16j.i-20j.j

a.b = 16(1) +20(0)-16(0)-20(1)

a.b = 16 +0-0-20

a.b = 16-20

a.b =-4

So, value of a.b = -4

ANSWER

[tex]a \cdot \: b = - 4[/tex]

EXPLANATION

The dot product of two vectors

[tex]a = xi + yj[/tex]

and

[tex]b = mi + nj[/tex]

is given by

[tex]a \cdot \: b = mx + ny[/tex]

The given vectors are:

[tex]a = 4i - 4j[/tex]

[tex]b = 4i + 5j[/tex]

Applying the above definition of dot products, we obtain:

[tex]a \cdot \: b = 4 \times 4 + - 4 \times 5[/tex]

[tex]a \cdot \: b = 16 - 20[/tex]

[tex]a \cdot \: b = - 4[/tex]

Answer: 658

Step-by-step explanation:

If Winslow wants to plant 12 vegetables and has 34 seeds of each kind of vegetable, then she has 12*34 seeds.

12*34=408

If a neighbor giver her 10 more packets, each with 25 seeds, she has 10*25 more seeds.

10*25=250

Then we add 408+250 to get 658 seeds

Notice that both sides of the equation have a similar form. If we ignore angle functions we end up with,

[tex]A+A\cdot B=B+B\cdot A[/tex]

That is true if condition [tex]A=B[/tex] is met.

Otherwise it is false.

Hope this helps.

r3t40

Answer:

It would be 5 liters because you gave 5 liter to C

Step-by-step explanation:

Hope this helped! :3

Tank C now has 5 more liters of water than tank A.

Assume the initial amount of water in tank C is "x" liters.

Given that:

Tank A originally had 10 more liters of water than tank C,

The initial amount of water in tank A is "x + 10" liters.

When five liters of water were poured from tank A into tank B,

The amount of water in tank A is reduced to "(x + 10) - 5" liters,

The amount of water in tank A  =  "(x + 5)" liters.

When ten liters of water are poured into tank C

So, the amount of water in tank C=  "x + 10" liters.

The amount of  extra water in tank C is calculated as;

Difference = (Amount of water in tank C) - (Amount of water in tank A)

Difference = (x + 10) - (x + 5)

Difference = x + 10 - x - 5

Difference = 10 - 5

Difference = 5

Tank C now has 5 more liters of water than tank A by 5 liters.

Learn more about liters here:

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For this case we have that by definition, the sum of the internal angles of a triangle is 180 degrees.

Then, according to the figure we have:

[tex][180- (6x + 1)] + 79+ (2x + 10) = 180[/tex]

We operate parentheses:

[tex]180-6x-1 + 79 + 2x + 10 = 180[/tex]

We add similar terms:

[tex]-4x + 268 = 180\\-4x = 180-268\\-4x = -88\\x = \frac {-88} {- 4}\\x = 22[/tex]

Thus, x has a value of 22 degrees.

Answer:

Option D

Answer:

(D) x= 22

Step-by-step explanation:

Answer:

Explanation contains answer.

Step-by-step explanation:

Question 1:

I would perfer to solve the first equation for y because there is only one operation to perform on both sides and it is subtraction of 2x on both sides.

The other equation requires two steps to isolate y; subtracting 3x on both sides then multiplying both sides by -1.

So basically solving the first one for y because it has coefficient 1.

Question 2:

They solved the 2nd equation for y and plugged into itself instead of plugging it into 1st equation.

Answer: (5x-2)(3^2-5)

Step-by-step explanation:

So using the commutative property, we can change the equation 15x^3-6x^2-25x+10 into 15x^3-25x -6x^2+10

Let’s split that into two sections so it’s easier to see:

(15x^3-25x) - (6x^2+10)

Next let’s look at what 15x^3 and -25x have in common. They have 5x in common.

Factoring out 5x, we get this: 5x(3^2-5)

Next let’s look at what -6x^2and 10 have in common. They only have 2 in common, so we factor out 2.

2(-3^2+5) we can write this as -2(3^2-5)

So the end result will be : 5x(3^2-5)-2(3^2-5)

And the complete factorization will be (5x-2)(3^2-5)

There are 16 different ways Sarah can top her sundae, considering no toppings, 1 topping or 2 toppings out of 5 available at the restaurant.

The subject of this question is in the field of combinatorics, a branch of mathematics. We are asked to find the number of ways Sarah can top her sundae with at most 2 toppings out of 5 available. The answer will be the number of ways she can pick no topping, or 1 topping, or 2 toppings.

The number of ways to pick no toppings is 1 (just the ice cream), to pick 1 topping out of 5 is 5 (assuming all toppings are different), and to pick 2 toppings out of 5 is represented by a combination formula '5 choose 2', which means: 5! / ((5 - 2)! * 2!) = 10, where '!' denotes factorial.

So by summing these possibilities (1+5+10), we come to the conclusion that Sarah can top her sundae in 16 different ways if she is restricted to at most 2 toppings.

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Sarah can top her sundae in 6 different ways if she is restricted to at most 2 toppings.

To calculate the number of ways or combinations, Sarah can top her sundae with at most 2 toppings, we can consider two cases. In the first case, she chooses 0 toppings. In the second case, she chooses 1 topping.

The total number of ways would be the sum of these two cases.

In the first case, she has only one choice, which is not to choose any topping.

In the second case, she can choose any one of the 5 toppings. So, the total number of ways would be 1 + 5 = 6.

Therefore, Sarah can top her sundae in 6 different ways if she is restricted to at most 2 toppings.

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Answer:

4

Step-by-step explanation:

The standard form of a circle is:

(x-h)^2+(y-k)^2=r^2

where (h,k) is the center and

r is the radius.

You compare your equation to mine you should see that:

-h=7 implies h=-7

-k=7 implies k=-7

r^2=16 implies r=4 since 4^2=16

The center is (-7,-7).

The radius is 4.

For this case we have that by definition, the equation of a circle in standard or canonical form is given by:

[tex](x-h) ^ 2 + (y-k) ^ 2 = r ^ 2[/tex]

Where:

(h, k) is the center

r: It's the radio

We have the following equation:

[tex](x + 7) ^ 2 + (y + 7) ^ 2 = 16\\(x + 7) ^ 2 + (y + 7) ^ 2 = 4 ^ 2[/tex]

Thus, the radius is 4.

Answer:

4

Answer:

The graphical is radical function sqrt(x) shifted 3 units left

Step-by-step explanation:

The argument of the radical function is x+3, this means, that if x=-3, then y=0 since sqrt(0)=0

The parent function y=sqrt(x), something simmilar ocurrs, y=0 when x=0

This is the key difference between the two given functions.

Answer:

(3/8) ^2

Step-by-step explanation:

P ( male history teacher) = Number males/ total

                                         = 3/8

Assuming nothing changes in year two

P ( male history teacher year two) = Number males/ total

                                         = 3/8

P( male, male) = 3/8 * 3/8 = (3/8) ^2

(3/8)^2 would be your answer.

Since there are 3 male and 5 female, that means there are 3/8 male and 5/8 female. We are talking about male and how many times it would happen in 2 years, so (3/8)^2 would be your answer.

Answer:

50

Step-by-step explanation:

20 / (2/5)

To divide by a fraction, multiply by the reciprocal.

20 × (5/2)

50

He can feed 50 cats.

50 cats

20 pounds is 100/5 pounds when written with a denominator of 5. Then you divide 100 by 2 and get 50.