With her motorboat at full speed Dawn gets to her fishing hole, which is 21 miles upstream, in 2 hours. The return trip takes 1.5 hours. How fast could her motorboat go in still water? What is the rate of the current?

Answer:

A. 40 mph

Step-by-step explanation:

A bird flies 2/3 miles per minute. You are trying to solve miles per hour.

Note that there are 60 minutes in an hour. Multiply 2/3 with 60:

2/3 x 60 = (2 * 60)/3 = (120)/3 = 40

A. 40 mph is your answer.

~

Answer:

0.3.

Step-by-step explanation:

The residual of a data point is equal to the observed value minus the predicted value. (Stat Trek)

What's the predicted y-value of a point with [tex]x = 5[/tex] based on this best-fit regression line?

[tex]y = -0.2\times 5 + 1.7 = 0.7[/tex].

The observed value here is [tex]y = 1[/tex]. As a result, the residual for this point is [tex]1 - 0.7 = 0.3[/tex].

Answer: 0.2

Step-by-step explanation:

Step-by-step explanation:

Let's do the volume first. Volume of any prism is the area of the base times the height.

V = Ah

The base is a large square with a smaller rectangle cut from the corner, so its area is:

A = (14)(14) - (7)(10)

A = 126

So the volume is:

V = (126)(6)

V = 756 m^3

Now the surface area of a prism is the area of the bases plus the base perimeter times the height:

S = 2A + Ph

We already found the area of the base. Now we just have to add the perimeter times height.

S = 2(126) + (14 + 14 +7 + 10 + 7)(6)

S = 480 m^2

Answer:

k(x)=5x+2

k(4)=5(4) +2 =22

k(1)= 5(1) +2 =7

k(4) - k(1) = 22 - 7 = 15

The answer is:

A). 15

Answer:

145,146,147

Step-by-step explanation:

Let x be the first number

x+1 is the next number

x+1 +1 is the next number

The sum of these three number is

x + x+1 + (x+1+1) = 438

Combine like terms

3x +3 = 438

Subtract 3 from each side

3x+3-3 = 438-3

3x= 435

Divide by 3

3x/3=435/3

x = 145

x+1 =146

x+1+1 = 147

Solution:

A

Step-by-step explanation:

It's y =-2x³

Hope it helps you..☺

The graph of y = x³ is transformed as y = -6x³.

It's a unique type of connection with a predetermined domain and range, and every value in the domain exists associated with precisely one value in the range, according to the function.

The given equation exists, y = x³

The graph of y = x³ describes the transformed function.

Therefore, the correct answer is option B. y = -6x³.

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Answer:

B

Step-by-step explanation:

edge 2021

The polynomial that is in standard form is 13x^5 + 11x - 6x^2 + 5.

The polynomial that is in standard form is 13x5 + 11x - 6x2 + 5. In standard form, the polynomial is arranged by descending order of exponents. The terms are written with the coefficient in front of each variable.

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Answer:

The product of  [tex](x^2+3x+1)(x^2+x+2)[/tex] is [tex]x^3+4x^3+6x^2+7x+2[/tex]

Step-by-step explanation:

We need to find the product of [tex](x^2+3x+1)(x^2+x+2)[/tex]

We need to multiply the first term with the second term.

Multiplying:

[tex](x^2+3x+1)(x^2+x+2)\\=x^2(x^2+x+2)+3x(x^2+x+2)+1(x^2+x+2)\\=x^4+x^3+2x^2+3x^3+3x^2+6x+x^2+x+2\\Adding\,\,like\,\,terms\,\,\\=x^4+x^3+3x^3+2x^2+3x^2+x^2+6x+x+2\\=x^3+4x^3+6x^2+7x+2\\[/tex]

So, the product of  [tex](x^2+3x+1)(x^2+x+2)[/tex] is [tex]x^3+4x^3+6x^2+7x+2[/tex]

Step one: 3x+4y=20; 10=40-3y

Step two: 3y=40-10, so y=(40-10)/3=10

Step three: 3x+4*10=20

Step four: 3x=20-40=-20, so x=-20/3=-6.66666...~ -6.67

Answer:

The ratio of their surface areas is 4:49

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

In this problem the scale factor is equal to the ratio 2:7

and

Remember that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore

In this problem the ratio of their surface areas is (2:7)^2 = 4:49

The ratio of their surface areas is,

⇒ 4 : 49

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

\

We know that;

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor.

In this problem the scale factor is equal to the ratio 2/7,

Hence, If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore,

In this problem the ratio of their surface areas is ,

⇒ (2 / 7)²

⇒ 4 / 49

⇒ 4 : 49

Thus, The ratio of their surface areas is,

⇒ 4 : 49

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Answer:

y = 1/4 x - 1.

Step-by-step explanation:

The slope (from the 2 given points) =  (0 - -1) / (4 - 0) = 1/4.

The y-intercept is at y = -1, so the equation is:

y = 1/4 x - 1.

Answer:

B

Step-by-step explanation:

x is the number of years of experience.

In the graph, the point (y) is not shown for 5 years of experience but we can easly figure this out by plugging in 5 into x of the equation of best fit given.

Hence

[tex]y= 1.3x +5.5\\y= 1.3(5) +5.5\\y=12[/tex]

So, the best estimate is $12 per hour, the correct answer is B

Answer:

its b

hope its right

Explicit formula [tex]a_{n} =8n+15[/tex]

Recursive formula [tex]\left \{ {{a_{1} =23} \atop {a_{n}=a_{n-1}+8 }} \right.[/tex]

To solve this problem we have to use an arithmetic sequence. The cost of renting a kayak for 1 hour is $23, each additional hour is $8 more. So, the first element of the secuence will be 23 for one hour, then each addittional hour will be 23 + 8, making the secuence:

{23, 31, 39, 47, 55,.....,n}

Writing a recursive formula of the form [tex]a_{n} =a_{n-1} +d[/tex] where [tex]a_{n}[/tex] is the nth term, n the number of terms, and d the common difference in the secuence.

The common difference of the secuence {23, 31, 39, 47, 55,.....,n}. So, the first term is [tex]a_{1} =23[/tex], and the common diffenece is d = 8 which is the difference between each term.

[tex]\left \{ {{a_{1} =23} \atop {a_{n} =a_{n-1}+8 }} \right.[/tex]

Writing a explicit formula of the form [tex]a_{n} =a_{1} +d(n-1)[/tex] where where [tex]a_{n}[/tex] is the nth term, n the number of terms, [tex]a_{1}[/tex] the first term of the secuence, and d the common difference in the secuence.

With [tex]a_{1}=23[/tex], and d = 8:

[tex]a_{n} =23+8(n-1)[/tex]

[tex]a_{n} =23+8n-8[/tex]

[tex]a_{n} =8n+15[/tex]

Juan needs to sell 18 fruit baskets and 2 pencils to achieve his goal.

The number of items = (total price for the items)/(each price of the required item)

Given that,

Price of a fruit basket = $16.50

Price of a pencil = $1.50

His goal is to achieve $300

So,

The number of fruit baskets required to sell by the Juan = 300.00/16.50

⇒ 18.18 (rounding off)

⇒ 18 fruit baskets

And

Then 2 more pencils are to be sold to achieve his goal.

Therefore, 18 fruit baskets need to be sold by Juan.

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SA = (l x w x 2) + (l x h x 2) + (w x h x 2)

SA = (6 x 4 x 2) + (6 x 2 x 2) + (4 x 2 x 2)

SA = 48 + 24 + 16

SA = 88

The answer is 88 square units.

Answer:

A. 88 square units.

Step-by-step explanation:

Volume formula:

 ↓

[tex]V=L*W*H[/tex]

[tex]6*4*2=48[/tex]

[tex]L*H*2[/tex]

[tex]6*2*2=24[/tex]

[tex]W*H*2[/tex]

[tex]4*2*2=16[/tex]

Add the numbers from left to right.

48+24=72

72+16=88

88 is the correct answer.

Answer:$0.08 per pen

Step-by-step explanation:

$1.60/20=0.08

Hope this helps :)

Answer:

Step-by-step explanation:

The standard form of an equation of a circle:

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

where

[tex](h, k)[/tex] - center

[tex]r[/tex] - radius

We have:

[tex](x-7)^2+(y-10)^2=4[/tex]

Therefore

[tex]h=7,\ k=10,\ r^2=4\to r=\sqrt4\to r=2[/tex]

The standard form of the equation of a circle is

(x - h)2 + (y - k)2 = r2

Where (h, k) is the center,

r is the radius

(x - 7)2 + (y - 10)2 = 4 [Given]

This is rewritten as (x - 7)2 + (y - 10)2 = 22

Comparing it with the standard form

(h, k) = (7, 10)

The radius of the circle r = 2 units

The radius of a circle is  Option A. 2 units

The diameter is a straight line that passes through the center of the circle. The radius is half of the diameter. It starts from a point on the circle, and ends at the center of the circle.

A straight line extending from the center of a circle or sphere to the circumference or surface: The radius of a circle is half the diameter. the length of such a line.

The radius of a circle is the distance from the center of the circle to any point on its circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

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Answer:

8,000,000

Step-by-step explanation:

all you have to do is multiply the 4*2 then add the missing 0's for example so its 8 then add the six zeros behind the 8

The value of the multiplication is 8, 000 , 000

First, we need to know that multiplication is an arithmetic operation.

Also, PEDMAS is the mathematical acronym used to represent the different arithmetic operations.

They are given as;

From the information given, we have that;

2,000 times 4,000

This is represented as;

2000 ×4000

Multiply the values

8, 000 , 000

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Answer:

So, the inverse of function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]

Step-by-step explanation:

We need to find the inverse of the given function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex]

To find the inverse we replace f(x) with y

[tex]y = \frac{-1}{2} \sqrt{x+3}[/tex]

Now, replacing x with y and y with x

[tex]x = \frac{-1}{2} \sqrt{y+3}[/tex]

Now, we will find the value of y in the above equation

Multiplying both sides by -2

[tex]-2x = \sqrt{y+3}[/tex]

Taking square on both sides

[tex](-2x)^2 = (\sqrt{y+3})^2[/tex]

[tex]4x^2 = y+3[/tex]  

Finding value of y

[tex]y = 4x^2-3[/tex]

Replacing y with f⁻¹(x)

[tex]f⁻¹(x)= 4x^2-3[/tex]

So, the inverse of function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]

ANSWER

[tex]f^{ - 1} (x) =4 {x}^{2}- 3[/tex]

EXPLANATION

A function will have an inverse if and only if it is a one-to-one function.

The given function is

[tex]f(x) = - \frac{1}{2} \sqrt{x + 3} \: \: where \: \: x \geqslant - 3 [/tex]

To find the inverse of this function, we let

[tex]y=- \frac{1}{2} \sqrt{x + 3}[/tex]

Next, we interchange x and y to get,

[tex]x=- \frac{1}{2} \sqrt{y+ 3}[/tex]

We now solve for y.

We must clear the fraction by multiplying through with -2 to get;

[tex] - 2x = \sqrt{y + 3} [/tex]

Square both sides of the equation to get:

[tex](- 2x)^{2} = (\sqrt{y+ 3}) ^{2} [/tex]

[tex]4x^{2} = y + 3[/tex]

Add -3 to both sides

[tex]4 {x}^{2} - 3 = y[/tex]

Or

[tex]y = 4 {x}^{2}- 3[/tex]

This implies that,

[tex]f^{ - 1} (x) =4 {x}^{2}- 3[/tex]

This is valid if and only if

[tex]x \geqslant - 3[/tex]

Answer:

f(2) = -4

Step-by-step explanation:

Plug in 2 for x:

f(x) = 4x - 12

f(2) = 4(2) - 12

Remember to follow PEMDAS. (PEMDAS = Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction) PEMDAS is what you follow to solve these questions.

First, Multiply:

f(2) = 4(2) - 12

f(2) = (4 * 2) - 12

f(2) = 8 - 12

Next, subtract:

f(2) = 8 - 12

f(2) = -4

f(2) = -4 is your answer.

~

Answer:

-4

Step-by-step explanation:

put 2 into all the x values in the equation.

4(2) - 12 = -4

Range is all the y values in this case that would be...

{-1, 4, 11, 13}

Keep in mind that there are different ways to show range. The one I showed it just one of them

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Mykel you should have 2 rows of -5

Step-by-step explanation:

so the first row should have 5 red blocks and the second row should also have 5 red blocks. The reason it should be red is because red stands for negative.

Answer:

B

Step-by-step explanation:

24 times 4 is 96 legs

196-96=100 divided by 2 is 50 humans

50 plus 24 is 74

Answer:

B 24 horses and 50 humans

Step-by-step explanation:

Let x = humans

y = horses

Each horse and human has 1 head, for a total of 74 heads

x+y = 74

Each human has 2 leags, 2x  and each horse has 4 legs, 4y for a total of 196 legs

2x+4y = 196

We have a system of equations

x+y = 74

2x+4y = 196

Multiply the first equation by -2

-2(x+y) = -2*74

-2x -2y - 154

Add the modified first equation to the second equation

-2x-2y = -154

2x+4y = 196

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

2y = 48

Divide by 2

2y/2 = 48/2

y = 24

There are 24 horses

x+y = 74

We know there are 24 horses

x+24 = 74

x+24-24 = 74-24

x=50

There are 50 humans

Final answer:

To solve the equation 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b, isolate x on one side of the equation, subtract 4 from both sides, then divide both sides by 9.

Explanation:

To solve the equation 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b, we need to isolate x on one side of the equation. Here's how to do it:

Therefore, the solution to the equation is x = 7/9.

Answer:

[tex]x=3\\y=-1\\\\(3,-1)[/tex]

Step-by-step explanation:

We have the following system of equations

[tex]4x-3y=15\\2x+2y=4[/tex]

To solve the system of equations multiply the second equation by -2 and add it to the first equation

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

[tex]-4x - 4y=-8\\4x-3y=15[/tex]

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

[tex]-7y = 7\\y=-1[/tex]

Now substitute the value of y in any of the two equations and solve for the variable x

[tex]4x-3(-1)=15[/tex]

[tex]4x+3=15[/tex]

[tex]4x=15-3[/tex]

[tex]4x=12[/tex]

[tex]x=\frac{12}{4}[/tex]

[tex]x=3[/tex]

Finally the solution is:

(3, -1)

Answer:

[tex]\large\boxed{\log_2\dfrac{x^3}{\left(\dfrac{3}{x+4}\right)}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\\log_ab^n=n\log_ab\\\\\log_a\left(\dfrac{c}{d}\right)=\log_ac-\log_ad\\\\==============================[/tex]

[tex]\text{We have:}\\\\3\log_2x-(\log_23-\log_2(x+4))\\\\=\log_2x^3-\log_2\dfrac{3}{x+4}\\\\=\log_2\dfrac{x^3}{\frac{3}{x+4}}[/tex]

The expression 3log(2)3 - log(2)(x+4) can be simplified by using the logarithmic laws, resulting in the final single logarithm of log2(39 / (x+4)).

The original expression, 3log(2)3 - log(2)(x+4), can be simplified using a few laws of logarithms. Firstly, using the rule that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, we can simplify. We find that the expression becomes log(2)33 - log(2)(x+4). Secondly, by applying the rule that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers, we can further simplify. The final expression is now log2(39 / (x+4)). This is the expression written as a single logarithm.

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Answer:

x=-1 or (-1,0)

Step-by-step explanation:

(-4 +- sqrt(4^2-4(5)(-1)))/2*5

(-4 +- sqrt(16+20))/10

(-4 +- sqrt(36))/10

(-4 +- 6)/10

x= (-4+6)/10 = 2/10 = 1/5 = 0.2

x= (-4-6)/10 = -10/10 = -1

x-intercepts: (0.2,0), (-1,0)

Answer:

7

Step-by-step explanation:

Replace a with 5 and b with 3.

5+3-1=7

Answer:

7.

Step-by-step explanation:

Substitute for a and b in the given identity:

5 * 3 = 5 + 3 - 1

= 8 - 1

= 7.

Answer:

y = -2x - 6

Step-by-step explanation:

4y = -8x - 24

y = -2x - 6

Answer:

y = -6 - 2x

Step-by-step explanation:

8x + 4y = -24

4y = -24 - 8x

y = (-24 - 8x) / 4

  = -[tex]\frac{24}{4}[/tex] - [tex]\frac{8}{4}[/tex]

  = -6 - 2x (ans)  or -(6 + 2x)