how to solve exponential equations​

Answer:

862.75 meters^3

Step-by-step explanation:

(17)(14.5)(3.5)=862.75

Answer:

862.75

Explanation:

17multiply by 14.5 multiply by 3.5

Answer:

4) 0, -1, 1, 1, 1

5) correct

6) [tex]x = -2 \pm 2\sqrt5[/tex]

Step-by-step explanation:

4) fill in the previous sequence element in the next. This sequence gets "stuck" at 1.

6) use the quadratic formula.

Answer:

The answer is A

Step-by-step explanation:

4.53 - 4.06 = .47

.47 is 10.4% of 4.53

Option A,-10.4% is the rate of change of stock XYZ for this particular week.

How to find percentage change?

Step 1: Calculate the change (subtract old value from the new value)

Step 2: Divide that change by the old value (you will get a decimal number)

Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

Note: when the new value is greater then the old value, it is a percentage increase, otherwise it is a decrease.

Finding percentage change

We have given,On Monday, stock XYZ opened at $4.53 which is the initial value or old value

On Friday, it closed at $4.06,which will be final value or new value.

First calculate, difference between the two value using,

Change=final value-initial value

Change=4.06-4.53

Change=-0.47

Now divide the change by initial value.

=-0.47/4.06

=-0.104

Now convert it to a percentage (by multiplying by 100 and adding a "%" sign)

=-0.104×100 %

=-10.4%

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Answer:

after one month = 100*.05=

$5 earned + $100 already there= $105

after 2 months = $105*.05=

$5.25 earned + $105 already there= $110.25

after 3 months = $110.25*.05=

$5.51 earned + $110.25 already there=

$115.76 is how much she'll have in the account after 3 mos.

Answer:

To ship a 2 pound package , the company will charge $10 and to ship a 3.5 pound package , the company will charge $20

Step-by-step explanation:

This question is on interpreting the information on the graph

In the first option, a 2 pound package lies on the second part of the charge line that charges $10. This value is similar to that charged for a package with 1.5 pounds too because it lies on same charge line.

In the second option, a package with 3.5 pounds will lie on the fourth part of the charge line that indicates $20. This value is similar to that charged a package with 4 pounds too because it lies on the same charge line.

From the graph, a parcel that weighs;

0 to 1 pound will be charged=$5

 1.5 to 2 pounds will be charged=$10

  2.5 to 3 pounds will be charged=$15

   3.5 to 4 pounds will be charged=$20

Answer:

Micah’s solution is wrong. The value of x=3 or -7/3

Step-by-step explanation:

First solve for the value of x

Given (1 – 3x) = 4(– + 2)

This can mean;  (1 – 3x) = 4(+ 2) or  (1 – 3x) = 4(-2)

In the first option (1 – 3x) = 4(+ 2) the value of x is ;

1 – 3x = 4(+ 2).....................open bracket

1-3x= 8...............................collect like terms

-3x=8-1

-3x=7....................................divide both sides by 3

x= -7/3  

In the second option

(1 – 3x) = 4(-2)

1-3x= -8

-3x= -8-1

-3x = -9

x= 3

Solutions  x= 3 0r -7/3

The values of x that make the statement true are 3 and -7/3

Answer:

Micah’s solution is wrong. There are no values of x that make the statement true.

Step-by-step explanation:

I just did this Instruction.

Plz press the Thanks button :)

Answer:

4

Step-by-step explanation:

8x + 4 = 27 + 6x - 15

Combine Like Terms:

8x + 4 = 12 + 6x

Combine Like Terms:

2x = 8

Combine Like Terms:

X = 4

Answer:

Yes, B is correct

Step-by-step explanation:

substitute values of x

B is correct,

y-4=4/3(x-2)

= y-4 = 4/3x-8/3

= y=4/3x-8/3+4

= y= 4/3x-3/3

y= 4/3

0=4/3+4/3x

-4/3= 4/3x

= x = -1

Answer:

y-7=-(4/3)(x-5)  (point slope form)

y=-(4/3)x+(41/3) (slope intercept form)

4x+3y-41=0 (general form)

Step-by-step explanation:

step 1

Find the slope of the perpendicular line to 4y-3x+9=0

If two lines are perpendicular, then the product of their slopes is equal to -1

4y-3x+9=0

4y=3x-9

y=(3/4)x-9/4 -----> the slope is m=3/4

The perpendicular slope is

m*(3/4)=-1

m=-4/3

step 2

Find the equation of the line into slope point form

y-y1=m(x-x1)

we have

(x1,y1)=(5,7)

m=-4/3

substitute

y-7=-(4/3)(x-5) ----> equation of the line into point slope form

Convert to slope intercept form ----> y=mx+b

y-7=-(4/3)(x-5)

y-7=-(4/3)x+(20/3)

y=-(4/3)x+(20/3)+7

y=-(4/3)x+(41/3) -----> equation of the line into slope intercept form

Convert to general form ----> Ax+By+C=0

y=-(4/3)x+(41/3)

Multiply by 3 both sides

3y=-4x+41

4x+3y-41=0 -----> equation of the line in general form

Answer:

Whenever two supposedly independent variables are highly correlated, it will be difficult to assess their relative importance in determining some dependent variable. The higher the correlation between independent variables the greater the sampling error of the partials.

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

(12 + 6) x ( 11 - 7) = 72

18 x 4 = 72

72 = 72

Answer:

The answer is D.

Step-by-step explanation:

The only equation that equals 72 is letter D. if you add 12 + 6 you get 18 so now the equation is 18 * (11 - 7) = 72 then you do 11 - 7 and get 4 so now the equation is 18 * 4 = 72 and 18 * 4 equals 72 so your answer is correct.

Answer:

|x-99|<3

Step-by-step explanation:

|x-99|<3

The correct mathematical inequality representation for the problem given would be |x - 99| ≤ 3, accounting for people three places ahead or behind the 99th person in line who are eligible to win.

The inequality to find all the winners of the movie tickets, based on the information given, would be |x - 99| ≤ 3. This way of expressing the relationship tells us that as we move three places forward or backwards from the 99th person in line, they are still within the range to win a free movie ticket. The 'x' in the inequality stands for the position in line. In this case, the solution to the inequality |x - 99| ≤ 3 is the set of all numbers in line that are within three places of the 99th person, which are positions 96 to 102 inclusively.

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Step-by-step explanation:

If a ≤ b ≤ c is the length of the sides, then a + b > c.

(a)

We have a = 3cm, b = 4cm, c = 6cm.

Check:

a + b = 3cm + 4cm = 7cm

c = 6cm

7cm > 6cm → a + b > c   CORRECT :)

YES. It's possible.

(b)

We have a = 1cm, b = 3cm, c = 4cm

Check:

a + b = 1cm + 3cm = 4cm

c = 4cm

4cm = 4cm → a + b = c

NO. It's impossible.

Answer:

1. 15in^2

2. 3421.19in^3

3. 11494.04cm^3

4. Radius is 3.1

Hope this helps!

Step-by-step explanation:

The area of the base of first cylinder is 47.05 in², volume of a cone is 3421.2 in³, the  volume of a sphere is 11494.04 cm³ and the radius of last sphere is 3.102 cm.

Volume of cylinder is the amount of quantity, which is obtained by it in the 3 dimensional space.

Volume of cylinder can be given as,

V=πr²h

Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.

The area of the base of a cylinder with a volume of 240π in³ and a height of 16 inches has to be find out. The radius of this cylinder is,

V=πr²h

240π=πr²(16)

r=√(240/16)

r=3.87 in

Thus, the surface area of the base is

A=πr²

A=π(3.87)²

A=47.05 in²

The volume of a cone with a height of 27 inches and a radius of 11 inches is,

V=(πr²h)/3

V=(π(11)²(27))/3

V=3421.2 in³

The volume of a sphere with a radius of 14 cm is;

V=(4πr³)/3

V=(4π(14)³)/3

V=11494.04 cm³

The volume of a sphere is 125 π cm³. The radius of it is,

V=(4πr³)/3

125=(4πr³)/3

r=∛(93.75/π)

r=3.102 cm.

Thus, the area of the base of first cylinder is 47.05 in², volume of a cone is 3421.2 in³, the  volume of a sphere is 11494.04 cm³ and the radius of last sphere is 3.102 cm.

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Answer:

x = 5

Step-by-step explanation:

To solve this, we just have to the multiplication and do the simplification (adding up the similar terms) afterwards:

3(x+1)=7(x-2)-3 becomes...

3x + 3 = 7x - 14 - 3

3x + 3 = 7x -17

Then we move all x's on one side and all plain numbers on the other side, we'll move the x's to the right since there's a bigger value there, and will move the plain numbers on the left side, by subtracting 3x and by adding 17 on both sides

3x + 3 - 3x + 17 = 7x -17 + 17 - 3x

20 = 4x

If we isolate x alone we have:

20/4 = x or x = 5

Answer:

Step-by-step explanation:

[tex]3(x+1)=7(x-2)-3\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(3)(x)+(3)(1)=(7)(x)+(7)(-2)-3\\\\3x+3=7x-14-3\qquad\text{combine like terms}\\\\3x+3=7x+(-14-3)\\\\3x+3=7x-17\qquad\text{subtract 3 from both sides}\\\\3x+3-3=7x-17-3\\\\3x=7x-20\qquad\text{subtract 7x from both sides}\\\\3x-7x=7x-7x-20\\\\-4x=-20\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{-20}{-4}\\\\x=5[/tex]

Answer:

[tex]\large\boxed{-8\sqrt9=-24}[/tex]

Step-by-step explanation:

[tex]\sqrt{a}=b\iff b^2=a\\\\\sqrt9=3\ \text{because}\ 3^2=9\\\\-8\sqrt9=-8(3)=-24[/tex]

Answer:

j = -9/14

Step-by-step explanation:

-4(7j + 2) = 10

-28j - 8 = 10

-28j = 18

j = -18/28

j = -9/14

Answer:

its an obtuse

Step-by-step explanation:

The triangle is:

               A.   Scalene.

               E.  Acute

Scalene triangle--

A triangle is said to be scalene if the length of all the three sides of a triangle are different.

Right triangle--

A triangle is said to be a right triangle if one of the angle is right angle i.e. measure of one of the angle is: 90 degrees.

Equilateral triangle--

A triangle is said to be equilateral if all of the sides of a triangle are equal.

Obtuse triangle--

A triangle is said to be obtuse if measure of one of the angle is more than 90 degrees but less than 180 degrees.

Acute triangle--

A triangle is said to be acute triangle if the measure of all the three angles of a triangle are less than 90 degrees.

Based on the diagram we observe that all the sides of a triangle are different and all the three angles of a triangle are less than 90 degrees.

Hence, the triangle is scalene and it is a acute triangle.

Answer:

After how many seconds does it explode? 4 sec

At what height does it explode? 256ft

Step-by-step explanation:

The question simply asks us to find the vertex of the parabola mentioned.

Given equation : h = -16t² + 128t

Lets break this down. The equation is in its standard form : ax² + bx + c

Hence,

a = -16

b = 128

c = 0

Find the vertex when a standard form is given:

( -b/2a , f(-b/2a) )

(-128/-32, f( -128/-32 ))

(4,f( 4 ))

f(4) = -16(4)² + 128(4)

f(4) = -256 + 512

f(4) = 256

Vertex = (4,256)

After how many seconds does it explode? 4 sec

At what height does it explode? 256ft

Answer:

60 degrees

Step-by-step explanation:

Since all sides of the triangle are congruent and the angles of a triangle add to 180 degrees, divide 180 by 3 sides and you get 60 degrees.

Answer:

60°

Step-by-step explanation:

Since the sides have all got the "equal" sign, all the angles must be the same.

Angles in a triangle add up to 180°.

From this, we can set up an equation ⇔ y + y + y = 180°

⇒ y + y + y = 180°

( Simplify )

⇒ 3 y = 180°

( Divide both sides by 3 to isolate y )

y = 60°

Answer:

Rosie now has c+3 charms

Explanation:

We are given that the original number of charms that Rosie has is c

We know that Ray gave Rosie 3 new charms

This means that the number of charms that Rosie originally had increased by 3

To express this increase, we use addition where we add 3 to the original number of charms that she had

New number of charms = original number of charms + 3

New number of charms = c + 3

Hope this helps :)

Answer:

c+3

Step-by-step explanation: she already had c charms, since we do not know what c is equal to, we can only simplify the question down to c(what she had) +3(what ray gave her)

Answer:  [tex]y=-7[/tex]

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Find the slope with this formula:

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

Given the points (-10,-7) (3,-7), substitute values into the formula. Then:

[tex]m=\frac{-7-(-7)}{-10-3}\\\\m=\frac{0}{-13}\\\\m=0[/tex]

Substitute the slope and any point into  [tex]y=mx+b[/tex] and solve for "b":

[tex]-7=0x+b\\b=-7[/tex]

Then, substituting "m" and "b" into the equation  [tex]y=mx+b[/tex], you get that the equation of this line is:

 [tex]y=0x-7[/tex]

 [tex]y=-7[/tex]

Answer:

Step-by-step explanation:

the answer is y=-7

Answer:

26 feet

Step-by-step explanation:

Perimeter of the Square = 4 x 6.5 = 26

addition since inverse means opposite

To isolate p in this equation you have to add 20 to both sides, since addition is the inverse operation of subtraction and vise versa. Adding 20 to both sides will cancel it out of the left side since -20 + 20 = 0.

Hope this helped!

The probability of drawing the coin labeled '1' from a bag containing coins labeled '1', '2', and '3' is 1/3, or roughly 0.333. This represents a 33.3% chance.

The question is asking you to calculate the probability of drawing the coin labeled '1' in one draw from a bag of three coins, each labeled '1', '2', or '3'. In probability, we define an event's likelihood as the number of ways that event can occur divided by the total number of possible outcomes.

Here, the event we're interested in is picking the coin labeled '1'. Since there is only one coin labeled '1', there is just one way this event can occur. The total number of possible outcomes is defined by the number of coins in the bag, which is 3 – the coins labeled '1', '2', and '3'.

Therefore, the probability of drawing the coin labeled '1' is calculated as 1/3, or roughly 0.333 when rounded to three decimal places. That means there is approximately a 33.3% chance that the coin labeled '1' will be the next drawn from the bag.

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the correct answer is (4.8)

Answer:

-2/3

Step-by-step explanation:

3x=sqrt4-4

3 times a number is 4 less than the square of that number. The negative solution is  -1

What are quadratic equations?

Quadratic equations are of the form ax² + bx + c where a ≠ 0.

Factorization, often known as factoring, is the process of expressing a number or another mathematical object or mathematical equations as a product of several factors.

Now, In the given question let's first assume that the unknown number is a variable x.

So, 3 times that number is (3 × x)

And then, 4 less than the square of that number is (x² - 4)

Now, as the question states that 3 times a number is 4 less than the square of that number,

So we can write,

3x = x² - 4

Now, we have to solve this quadratic equation with the help of factorization.

To solve the quadratic equation we first bring all the terms to any of the sides and after rearranging a little the equation is as follows:

x² - 3x - 4 = 0

Now, if we want to find the factors in the form ax² + bx + c we need to multiply a and c and then we have to identify what two numbers sum up to b and multiply to ac.

Here, a = 1, b = -3 and c = -4

Now, ac = -4

So, we have to identify what two numbers sum up to b and multiply to ac. The numbers are -4 and 1 and we can check that they sum up to -3 and multiply to -4.

So first we have to split the equation: x² - 3x - 4 = 0

x² - 4x + 1x - 4 = 0

Now, we have to group the above equation,

(x² - 4x) + (1x - 4) = 0

Taking x common from the first group and taking 1 common from the second group we get,

(x)(x - 4) + (1)(x - 4) = 0

Now, again taking (x - 4) common from the equation we get,

(x - 4) × (x + 1) = 0

So, we set each factor to zero now,

(x - 4) = 0

Adding 4 to each side of the equation we get,

x - 4 + 4 = 4

Simplifying we get,

x = 4

(x + 1) = 0

Adding -1 to each side of the equation we get,

x + 1 - 1 = -1

Simplifying we get,

x = -1

So, we now have two solutions of x that is 4 and -1

But according to the question we only need the negative one.

Therefore, the negative solution is  -1

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Answer:

-288

Step-by-step explanation:

n=1/2 divided by -144. You then just plug that number which is .00347 into n in the equation and use a scientific calculator to find the answer.

The sum of the  infinite geometric series is:

                                 -288

We know that the sum of the infinite geometric series:

[tex]\sum_{n=1}^{\infty} ar^{n-1}[/tex]

is given by the formula:

[tex]Sum=\dfrac{a}{1-r}[/tex]

The series is given by:

     [tex]\sum_{n=1}^{\infty} (-144)\cdot (\dfrac{1}{2})^{n-1}[/tex]

By looking at the series we observe that the first term of the series is:

            [tex]a=-144[/tex]

and the common ratio of the series is:

[tex]r=\dfrac{1}{2}[/tex]

Hence, the sum of the series is:

[tex]Sum=\dfrac{-144}{1-\dfrac{1}{2}}\\\\Sum=\dfrac{-144}{\dfrac{1}{2}}\\\\Sum=-144\times 2\\\\Sum=-288[/tex]

The number with two digits wich sum of digits is 8 is 35.

To find the numbers that meet the condition of adding 8 and the unit of tens being two numbers greater than the other we must:

Identify numbers that add up to 8, for example:

Subsequently, we identify the sum in which one number has a value of two greater than the other.

Finally we organize the number with the required conditions:

According to the above, the number is 35.

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the ones digit is 5, and the tens digit is 5 - 2, which is 3. So the 2-digit number is 35.

The question requires us to find a 2-digit number where the tens digit is two less than the ones digit and the sum of the digits is 8. To figure this out, let's call the ones digit 'x'. Since the tens digit is two less than the ones digit, the tens digit would be 'x - 2'. The sum of these two digits equals 8, so we can write the equation:

x + (x - 2) = 8

Solving for x gives us:

2x - 2 = 8

2x = 8 + 2

2x = 10

x = 10 / 2

x = 5

Therefore, the ones digit is 5, and the tens digit is 5 - 2, which is 3. So the 2-digit number is 35.

Answer:

x=2 and y=5

Step-by-step explanation:

Given:

cost of Album= $10

cost of singles= $1

condition 1 :  She wants to purchase at least 5 singles

condition 2: she wants to spend no more than $25 total

Brandi purchases x albums and y singles, then combination of albums and singles that Brandi could purchase and stay within her guidelines=?

Cost of x albums= $10x

Cost of y singles= $1y

Applying condition 1, we get:

y≥5  ---------equation i

Applying condition 2, we get:

10x+y≤25   ---------equation ii

Solving the above two equation i and ii we get:

x=2 and y=5

So the possible combination of albums and singles that Brandi could purchase and stay within her guidelines is

10(2) + 5 =25 !