Help please 11, 12, 13

Answer: Domain (-∞,∞) ; range: (0,∞)

Step-by-step explanation:

1. The exponential functions with the form [tex]f(x)=ab^{x}[/tex] has domain of all real numbers, becaure there is no values in the set of real number for which the value of [tex]x[/tex] is not define. When [tex]x[/tex] approches to ∞, the function approches to ∞.

2. When [tex]x[/tex] approches to -∞, the function approches to 0 but never touches it. This means  that [tex]y[/tex] is always greater than zero ([tex]y>0[/tex]). Therefore, the range of the function is (0,∞).

Answer:

Lesson 1 unit 5 exponential, logarithmic, pricewise functions

Step-by-step explanation:

1. A and D

2. C

3. B

4.c

The solution follows the sequence ...

The problem is in the first step, where parentheses are eliminated. One of the multiplications is done incorrectly, and the error is propagated through the rest of the solution.

0.15(y -0.2) = 0.15y - 0.03 . . . . not 0.15y - 0.3

If you carry forward the value 0.03 instead of 0.30, you find the answer is

... -153/35 = y

______

Some of the other steps should be ...

.15y -.03 = 2 - .5 + .5y

15y -3 = 150 +50y

-153 = 35y

Earl is incorrect

let x be the number of discount tickets sold

then the number of regular tickets sold is 6x

the total tickets sold is 1456, thus

x + 6x = 1456

7x = 1456 ( divide both sides by 7 )

x = 208

number of discount tickets sold = 208

[tex]\frac{1456}{6}[/tex] ≠ 208

but [tex]\frac{1456}{7}[/tex] = 208

Earl is incorrect , dividing by 7 gives the amount sold

B

the range of the function are the values that the domain map to

here range { - 4, 1, 7 , 15 }

The range is the output values (also known as the y values)

-4, 1, 7 ,15 or letter B

Answer:

Unit rate is 2.69 cups of water for 1 cup of lime juice.

Step-by-step explanation:

Rate of water (cups) per lime juice (cups) means how much water (cups) is added to 1 cup of lime juice to make limeade.

This can be calculated as,

Unit rate = Number of water (cups) / Number of lime juice (cups)

Unit rate = [tex]\frac{35}{13}[/tex]

Unit rate = 2.69 cups of water for 1 cup of lime juice.

Multiplication was invented to reduce the work involved in repeated addition.

... 88 + 88 + 88 + 88 = 4×88 = 352

352 passengers are carried to the island each day.

_____

Some questions must be answered before we can give a definite answer.

1. If the same person rides twice, are they counted twice?

2. Are passengers on the return trips (from the island) counted?

3. If return trip passengers are counted, is the ferry full on those trips?

4. Does every passenger to the island return the same day?

5. Does any passenger go to the island more than once per day?

Answer:

(3x-2)(5x+2)

Step-by-step explanation:

we have to multiply 15 and 4.

then find the factors of this product.

we get,

15 x 4=60

Now, factors of 60 which make 4 are 6 and 10

because   6-10=-4

So,

[tex]15 x^{2}-4x-4\\ =15x^{2} -10x+6x-4\\[/tex]

Now, we have to take common factor pairwise.

Taking 5x as common factor from first pair and 2 from second pair,

we get

[tex]15x^{2} -10x+6x-4\\=5x(3x-2)+2(3x-2)\\=(3x-2)(5x+2)[/tex]

(3x - 2 )(5x + 2 )

consider the factors of the product 15 × - 4 = - 60

which sum to give the coefficient of the middle term ( - 4 )

the factors required are - 10 and + 6

split the x- term using these factors

15x² - 10x + 6x - 4 ( factor by grouping )

= 5x(3x - 2) + 2(3x - 2)

Take out the common factor (3x - 2)

= (3x - 2)(5x + 2)

Let's make the mysterious, original price not-so-mysterious by calling it x. 245.97 is 3/5 of x.

We can equation this.

245.97 = 3/5x

x = 245.97 / (3/5)

x = 409.95

The answer, I believe, is $409.95. Hope this helps!

The original price of the laptop that Tom bought is calculated using the formula for the value of a part. This leads us to an equation, $245.97 / 0.6, resulting in the original price of the laptop being $409.95.

The subject of this question is basic mathematics, predominantly fraction and ratio. The problem states that Tom paid $245.97, which was 3/5 of the original price of the laptop. To find the original price, we can apply the formula for the value of a part, which states that the whole is equal to the part divided by the ratio representing the part. In this case, this gives us the equation $245.97 / (3/5) = Original Price.

To make this easier, we can convert the fraction 3/5 to its decimal form, which is 0.6. So, we will then have $245.97 / 0.6 = Original Price, which should give us the original price of the laptop. Completing the math, we find that the original price of the laptop is $409.95.

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Steps:

subtract 3 from both sides:

2x²-5x+1 - 3 = 3 - 3

Simplify:  

2x² - 5x  - 2 = 0

Solve with the quadratic formula :

for a =  2 , b = - 5 ,  c =  - 2

x₁ =  -  ( - 5 ) +√ ( -5 )² - 4 * 2 ( - 2 )  / 2 * 2 =

x₁ =  5 + √ 41 / 4

x₂ = -  ( - 5 ) - √ ( -5 )² - 4 * 2 ( - 2 )  / 2 * 2

x₂ = 5 - √ 41 / 4

Answer:

      -4 - 2

m= --------- (over)

      -1 - 2

Step-by-step explanation:

2x - y = 2

obtain the equation of the line in slope-intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 2 ) and (x₂, y₂ ) = (- 1, - 4) ← 2 points on the line

m = [tex]\frac{-4-2}{-1-2}[/tex] = [tex]\frac{-6}{-3}[/tex] = 2

the line crosses the y-axis at (0, - 2 ) ⇒ c = - 2

y = 2x - 2 ← in point-slope form

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

rearrange y = 2x - 2 into this form

subtract y from both sides

0 = 2x - y - 2 ( add 2 to both sides )

2x - y = 2 ← in standard form

Direct variation is a relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).

Given the equation [tex]2x-4y=0,[/tex] you can see that

[tex]4y=2x,\\\\y=\dfrac{2}{4}x=\dfrac{1}{2}x.[/tex]

Then the constant [tex]k=\dfrac{1}{2}.[/tex]

Answer: correct choice is C.

Ask google if you still can't get the answer.

The figures in a plane can be reflected, rotated, translated or dilated to produce new figures or images.

A transformation that moves all points to the same distance and in the same direction. The final figure looks the same, just moved over. It does not flip or gets rotated. It also does not change size.This type of translation is called glide reflection. Its the summation of translation and reflection.

Answer:

Glide Reflection

Step-by-step explanation:

Given expression is [tex]7 \sqrt{50x^{15}y^{21}}[/tex] where x and y are non negative.

Now we have to simplify this to find the correct matching choice.

[tex]7 \sqrt{50x^{15}y^{21}}[/tex]

[tex]=7 \sqrt{25*2x^{15}y^{21}}[/tex]

[tex]=7 \sqrt{25*2x^{14}*xy^{20}*y}[/tex]

[tex]=7*5x^{7}y^{10} \sqrt{2*x*y}[/tex]

[tex]=35x^{7}y^{10} \sqrt{2xy}[/tex]

Which best matches with choice D.

Hence final answer is [tex]35x^{7}y^{10} \sqrt{2xy}[/tex] .

Answer:

B

Step-by-step explanation:

I also got 35x^7y^10√2xy

:)

[tex] \: \: \: \: \: \: \: \: \: \: \: \bold{ - 2x = - 9 - 5}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ - 2x = - 14}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = \cfrac{ - 14}{ - 2}} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = \cfrac{14}{2} }[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = 7}[/tex]

Note: For a problem like this, we must first subtract the number that is 5, then we must know that two negatives make a positive and that we must add 9 and 5 to give us 14, then we must put it as a fraction since it makes it easier for us to finish the problem, next it is known that two negative signs make a positive thus eliminating the less Parentheses and finally we divide so that we get a result of[tex]\bold{ x = 7}[/tex]

answer:

128

step-by-step explanation:

1. recognize how we get to each number in the pattern

to get from 2 to 8 we can either add 6 or multiply by 4

2. lets see if either of those match up with the rest of the numbers in the pattern

0.125 + 6 = 6.125

our next value is .5 not 6.125

0.125 × 4 = .5

that works! so lets see if it works with the rest of our pattern -

0.5 × 4 = 2

it works! so our pattern is multiplying each value by 4

3. use our pattern on the value of 8

8 × 4 = 32

32 is our 5th value but we are looking for our 6th value

4. use on pattern on the 5th value (32)

32 × 4 = 128

The 6th number in the pattern is calculated by identifying the rule that each number is being multiplied by 4 to get the next one. By continuously applying this rule, we find that the 6th number is 128.

The subject of this question involves the identification and continuation of a numerical pattern. The given pattern is 0.125, 0.5, 2, 8. To recognize this pattern, observe the relationship between consecutive numbers. It seems like each number is being multiplied by 4 to obtain the next one. We can apply the same rule to find the 6th number in the sequence:

Therefore, the 6th number in the given pattern should be 128.

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A cell phone company sold 450 cell phones in three hour

450 is 30% of the number of phones sold that day

30% of number of phones = 450

We need to find the number of phones for 100%

Let x be the number of cell phones sold that day

30% of x is 450

[tex]\frac{30}{100} * x= 450[/tex]

multiply by 100 on both sides

30 * x = 45000

Divide by 30

x = 1500

So 1500 cell phones are sold that day

To find the total number of cell phones sold by the company in a day, set up a proportion using the given information and solve for the total number of cell phones sold. In this case, the company sold 15,000 cell phones that day.

A cell phone company sold 450 cell phones in three hours, which was 30% of the phones sold that day. To find the total number of cell phones sold that day, we can set up a proportion:

Let x be the total number of cell phones sold that day.

450/3 = x/100

450 × 100 = 3x

45000 = 3x

x = 15000

Therefore, the cell phone company sold 15,000 cell phones that day.

Answer:

$996

Step-by-step explanation:

The rectangular plot has an area that is the product of its length and width. We are given the width as 12 feet, and the area as 240 ft², so we can find the length from ...

... A = L×W

... 240 ft² = L×(12 ft)

... 240 ft²/(12 ft) = L = 20 ft

Opposite sides of the rectangle are the same length, so the cost of fence for a side of a given length will be the sum of the costs of the opposites sides.

The 12 ft side has one segment that is $18 per foot, and one that is $15 per foot. For the 20 ft sides, both are $15 per foot. Then the total cost can be figured from ...

... (12 ft)·($18/ft + $15/ft) + (20 ft)·($15/ft +$15/ft) = 12·$33 +20·$30 = $996

x³ - 3x² + 4x - 2

complex roots occur in conjugate pairs

1 + i is a root then so is 1 - i

the factors of the polynomial are therefore

f(x) = (x - 1 )(x - (1 + i))(x - (1 - i))

     = (x - 1 )(x² - 2x + 2 ) ( expand factors and simplify )

     = x³ - 3x² + 4x - 2

Answer:

f(x) = x3 – 3x2 + 4x – 2

Step-by-step explanation:

If they're making 75 pies an hour, and working 8 hours a day, you would multiply 8 by 75. 8x75=600. Hope this helps!

we are given

[tex]\frac{(1.6\times 10^{8})(5.8\times 10^{6})}{(4\times 10^{6})}[/tex]

Since, we have to write this in scientific form

so, we will make all 10^x terms together

and all other terms together

so, we get

[tex]=\frac{(1.6\times 5.8) (10^{8}\times 10^{6})}{(4\times 10^{6})}[/tex]

we can multiply terms

[tex]=\frac{(9.28) (10^{8+6})}{(4\times 10^{6})}[/tex]

[tex]=\frac{(9.28) }{4} \times 10^{8+6-6}[/tex]

[tex]=2.32 \times 10^{8}[/tex]

so, option-B...........Answer

Answer:

2.32 x 10^8

Step-by-step explanation:

2.32 x 108

108 + 6 - 6 = 108

and

(1.6)(5.8)

(4)

=  

9.28

4

= 2.32

thus,

2.32 x 108

the first number line

given | x + 4 | = 2

removing the bars from the absolute value gives

x + 4 = 2 or x + 4 = - 2

x = 2 - 4 or x = - 2 - 4

x = - 2 and x = - 6 ← solutions

these are indicated on the number line by a solid circle at - 2, - 6

Answer:

The solution is represented by  the first number line, wich has the solutions x=-6 and x=-2.

Step-by-step explanation:

We have an absolute value function for the equation. This means that we should have two differents solution in the real number line. As the equation is

[tex]|x+4|=2[/tex]

when we clear out the absolute value, we will have two possible solutions:

[tex]x+4=2[/tex]

and

[tex]-(x+4)=2[/tex]

now we clear x from both equations

[tex]x+4=2 \Leftrightarrow x=2-4 \Leftrightarrow x=-2[/tex]

[tex]-(x+4)=2 \Leftrightarrow -x-4=2 \Leftrightarrow -2-4=x \Leftrightarrow x=-6[/tex]

Then, we have that x=-2 and x=-4 are the solutions for the equation, and therefore the number line that represents the solution is the first one, where the points -6 and -2 are highlighted.

(11)

the equation of a line in point- slope form is

y = mx + c ( m is the slope and c the y-intercept

thus y = 4x + 3 ← in slope-intercept form

the equation of a line in point- slope form is

y - b = m(x - a ) ( m is slope and (a, b ) a point on the line )

thus y - 3 = 4 ( x - 0 ) or y - 3 = 4x ← in point- slope form

the equation of a line in standard form is

Ax + By = C ( a is a positive integer and B, C are integers

rearrange y - 3 = 4x into this form

4x - y = - 3 ← in standard form

(12)

y = - 2x - 1 ← in slope-intercept form

y + 1 = - 2x ← in point- slope form

2x + y = - 1 ← in standard form

Answer:

1/27

Step-by-step explanation:

Its 1/27 because you have to multiply (3)-3,

3 times 3 times 3

that will give you positive 27 so if your on usatestprep its positive  1/27

The number (3)⁻³ equals 1/27, which is the result of taking the reciprocal of 3 raised to the third power.

The question asks which number equals (3)⁻³. The notation (3)-3 indicates that we are dealing with an exponentiation operation, specifically raising the number 3 to the power of -3. To solve this, we'll use the rule that any number raised to a negative exponent is equal to 1 divided by that number raised to the positive exponent. Therefore, (3)⁻³ is equal to 1/(3³).

Now we'll calculate the exponent 3³, which is 3 multiplied by itself three times: 3 x 3 x 3 = 27. So, 1/(3³) is 1/27.

The final answer is therefore (3)⁻³ = 1/27.

remainder = - 1

6x² + 11x - 3 ÷ (x + 2 ) = 6x - 1 - [tex]\frac{1}{x+2}[/tex]

Answer:  The required remainder is 1.

Step-by-step explanation:  We are given to find the remainder when the following polynomial is divided by (x + 2) :

[tex]p(x)=6x^2+11x-3.[/tex]

Remainder Theorem :  If a polynomial f(x) is divided by (x - a), then the remainder is f(a).

So, for the given polynomial p(x), the remainder will be equal to p(-2).

We have

[tex]p(-2)\\\\=6(-2)^2+11(-2)-3\\\\=24-22-3\\\\=-1.[/tex]

Thus, the required remainder is -1.

We don't actually know what the problem originally was, so we don't know what the error was or what the correct answer should be.

If the numbers on the left are given, and the problem is to find the number on the right, then ...

Paolo added 0.2 instead of subtracting it.

-0.43 -0.2 = -0.63 . . . . . correct answer

_____

If the left and right numbers are given and the problem is to find the one in the middle, then ...

Paolo incorrectly calculated 0.43 -0.23, getting -0.2 instead of +0.2.

-0.43 +0.2 = -0.23 . . . . correct answer

_____

If the problem is to find the term on the left, then ...

Paolo incorrectly added 0.2 and -0.23, getting -0.43 instead of -0.03.

-0.03 -0.2 = -0.23 . . . . correct answer

13 .3333... = 13 [tex]\frac{1}{3}[/tex] %

percentage increase is calculated as [tex]\frac{increase}{original}[/tex] × 100%

increase = 255 - 225 = 30 and original = 225

[tex]\frac{30}{225}[/tex] × 100% = 13.33.... % = 13 [tex]\frac{1}{3}[/tex] %

C

given the 2 equations

8(a + b) + 3z = - 9 → (1)

(a + b) + z = 2 → (2)

multiply (2) by 3 so that the coefficients of z are equal

3(a + b) + 3z = 6 → (3)

subtract (1) - (3) to eliminate term in z

5(a + b) = - 15 ( divide both sides by 5 )

(a + b) = - 3 → C